Physics 270 – The Universe: Astrophysics, Gravity and Cosmology

•Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270

Physics 270 – The Universe: Physics 270 – The Universe: Astrophysics, Gravity and CosmologyAstrophysics, Gravity and Cosmology


The History of CosmologyThe History of Cosmology

• Mythology vs the scientific methodMythology vs the scientific method

• Cosmos = Earth Cosmos = Earth solar system solar system Milky Milky Way Way Hubble sphere Hubble sphere

• Copernicus, Brahe, Kepler, GalileoCopernicus, Brahe, Kepler, Galileo


Newton: Cosmology Newton: Cosmology as a Scienceas a Science

• Galileo: The Scientific method & the Galileo: The Scientific method & the universality of scientific lawsuniversality of scientific laws

• Newton’s lawsNewton’s laws

• Newton’s gravity: The heavens and the Newton’s gravity: The heavens and the Earth follow the same scientific principlesEarth follow the same scientific principles

• Galileo: Relativity before EinsteinGalileo: Relativity before Einstein


Einstein’sEinstein’s Theories of Theories of Special and General Special and General Relativity Relativity

• Principle of RelativityPrinciple of Relativity

• Giving up absolute space and timeGiving up absolute space and time

• Space and time: where common sense Space and time: where common sense makes no sensemakes no sense

• what is here and there or now and then ?what is here and there or now and then ?


Special RelativitySpecial Relativity

• All inertial frames of reference are All inertial frames of reference are equivalentequivalent

• The speed of light is absolute (invariant)The speed of light is absolute (invariant)

• Maxwell’s equations are invariant under Maxwell’s equations are invariant under Lorentz transformationLorentz transformation

• Newton’s laws, which are based on Newton’s laws, which are based on absolute space and time, need to be absolute space and time, need to be modifiedmodified


Some open problemsSome open problems

• How to treat accelerations ?How to treat accelerations ?

• How to deal with gravity ?How to deal with gravity ?

• Newton’s gravity acts instantaneously, i.e. it Newton’s gravity acts instantaneously, i.e. it is inconsistent with special relativity’s is inconsistent with special relativity’s conclusion that information cannot be conclusion that information cannot be communicated faster than the speed of light.communicated faster than the speed of light.

• Distance is relative, so which distance to Distance is relative, so which distance to use in computing the gravitational force ?use in computing the gravitational force ?


Non-inertial reference frameNon-inertial reference frame

• Non-inertial frames Non-inertial frames fictitious forces fictitious forces– centrifugal forcecentrifugal force– Coriolis force Coriolis force


Why is the Space Shuttle orbiting?Why is the Space Shuttle orbiting?

The space Shuttle is continuously falling The space Shuttle is continuously falling towards the Earth towards the Earth


Is there no gravity in space ?Is there no gravity in space ?

No, there is No, there is gravity (actu- gravity (actually Earth’s ally Earth’s gravity at the gravity at the orbit of the orbit of the Shuttle is still Shuttle is still ~80-90% of ~80-90% of its strength on its strength on the groundthe ground

So why do astronauts appear So why do astronauts appear to be weightless ? to be weightless ?


What effect does mass have?What effect does mass have?

• Gravity: Gravity: tendency of massive bodies to tendency of massive bodies to attract each otherattract each other

• Inertia: Inertia: resistance of a body against changes resistance of a body against changes of its current state of motionof its current state of motion


Is gravity and inertia the same Is gravity and inertia the same thing ?thing ?• No. They are completely different physical No. They are completely different physical

concepts.concepts.• There is no a priori reason, why they should There is no a priori reason, why they should

be identical. In fact, for the electromagnetic be identical. In fact, for the electromagnetic force (Coulomb force), the source (the force (Coulomb force), the source (the charge charge QQ) and inertia () and inertia (mm) are indeed ) are indeed different.different.

• But for gravity they appear to be identicalBut for gravity they appear to be identical

Equivalence PrincipleEquivalence Principle


Eötvös experimentEötvös experiment

CoriolisGravity


Result of the Eötvös experimentResult of the Eötvös experiment

• Gravitational and inertial mass are identical Gravitational and inertial mass are identical to one part in a billion to one part in a billion

• modern experiments: identical to one part in modern experiments: identical to one part in a hundred billion a hundred billion


What effect does mass have?What effect does mass have?

• Source of gravitySource of gravity

• InertiaInertia

2r

mMGF gravity 2r

mMGF gravity

amF inertia amF inertia


Principle of Equivalence Principle of Equivalence

2r

mMGamF gravity

inertial 2r

mMGamF gravity

inertial

2r

MG

m

ma

inertial

gravity

2r

MG

m

ma

inertial

gravity

=1=1


Weak equivalence principleWeak equivalence principleThe The laws of mechanicslaws of mechanics are precisely are preciselythe same in all inertial and freely the same in all inertial and freely falling frames. In particular, gravity is falling frames. In particular, gravity is completely indistinguishable from completely indistinguishable from any other acceleration.any other acceleration.

Strong equivalence principleStrong equivalence principleThe The laws of physicslaws of physics are precisely the are precisely the same in all inertial and freely falling same in all inertial and freely falling frames, there is no experiment that frames, there is no experiment that can distinguish them. can distinguish them.


Consequences of the equivalenceConsequences of the equivalenceprinciple: mass bends lightprinciple: mass bends light

Observer in freely falling reference frame


Consequences of the equivalenceConsequences of the equivalenceprinciple: mass bends lightprinciple: mass bends light

Outside Observer


Examples for light bendingExamples for light bending


Some effects predicted by the Some effects predicted by the theory of general relativitytheory of general relativity

• gravity bends lightgravity bends light

• gravitational redshiftgravitational redshift

• gravitational time dilationgravitational time dilation

• gravitational length contractiongravitational length contraction


Least action principleLeast action principle

• light travels on a path that minimizes the light travels on a path that minimizes the distance between two pointsdistance between two points for flat space: straight line for flat space: straight line

• a path that minimizes the distance between a path that minimizes the distance between two points is called a two points is called a geodesicgeodesic

• Examples for geodesicsExamples for geodesics– plane: straight lineplane: straight line– sphere: great circlesphere: great circle


What is the shortest way to Europe?What is the shortest way to Europe?


SpacetimeSpacetime

• Fourth coordinate: Fourth coordinate: ctct

• time coordinate has different sign than time coordinate has different sign than spatial coordinatesspatial coordinates

• spacetime distance:spacetime distance:

, , , , :: metric coefficientsmetric coefficients

2222 xxtctcs 2222 xxtctcs


Weak equivalence principleWeak equivalence principleThe The laws of mechanicslaws of mechanics are precisely are preciselythe same in all inertial and freely the same in all inertial and freely falling frames. In particular, gravity is falling frames. In particular, gravity is completely indistinguishable from completely indistinguishable from any other acceleration.any other acceleration.

Strong equivalence principleStrong equivalence principleThe The laws of physicslaws of physics are precisely the are precisely the same in all inertial and freely falling same in all inertial and freely falling frames, there is no experiment that frames, there is no experiment that can distinguish them. can distinguish them.


General relativityGeneral relativity

• Mass tells space how to curveMass tells space how to curve

• Space tells mass how to moveSpace tells mass how to move


Why does space curvature result Why does space curvature result in attraction ?in attraction ?


Euclidean (flat) geometry:Euclidean (flat) geometry:

• Given a line and a point not on the line, Given a line and a point not on the line, only one line can be drawn through that only one line can be drawn through that point that will be parallel to the first linepoint that will be parallel to the first line

• The circumference of a circle of radius The circumference of a circle of radius rr is is 22 r r

• The three angles of a triangle sum up to The three angles of a triangle sum up to 180180


Spherical geometry:Spherical geometry:

• Given a line and a point not on the line, no Given a line and a point not on the line, no line can be drawn through that point that line can be drawn through that point that will be parallel to the first linewill be parallel to the first line

• The circumference of a circle of radius The circumference of a circle of radius rr is is smaller than smaller than 22 r r

• The three angles of a triangle sum up to The three angles of a triangle sum up to more than 180more than 180


Hyperbolic geometry:Hyperbolic geometry:

• Given a line and a point not on the line, an Given a line and a point not on the line, an infinite number of lines can be drawn infinite number of lines can be drawn through that point that will be parallel to the through that point that will be parallel to the first linefirst line

• The circumference of a circle of radius The circumference of a circle of radius rr is is larger than larger than 22 r r

• The three angles of a triangle sum up to less The three angles of a triangle sum up to less than 180than 180


Tidal forces (I)Tidal forces (I)


Tidal forces (II)Tidal forces (II)


Tidal forces (III)Tidal forces (III)


Tidal forces (IV)Tidal forces (IV)


So does the existence of tidal forces So does the existence of tidal forces violate the equivalence principle ?violate the equivalence principle ?• there is no freely falling frame of reference there is no freely falling frame of reference

in which gravity vanishes in which gravity vanishes globallyglobally

• there is a freely falling frame of reference in there is a freely falling frame of reference in which gravity vanishes which gravity vanishes locallylocally

• equivalence principle holds for equivalence principle holds for small labssmall labs, , “small” in comparison to distances over “small” in comparison to distances over which the gravitational field changes which the gravitational field changes significantly. significantly.

• spacetime is locally flatspacetime is locally flat


Towards a new theory for gravity ...Towards a new theory for gravity ...

Requirements:Requirements:

• it should locally fulfill the equivalence it should locally fulfill the equivalence principleprinciple

• it should relate geometry of space to the it should relate geometry of space to the distribution of mass and energydistribution of mass and energy

• it should be locally flatit should be locally flat

• it should reduce to Newtonian gravity for it should reduce to Newtonian gravity for small velocities (compared to small velocities (compared to cc) and for ) and for weak gravitational fieldsweak gravitational fields


The entire Universe in one lineThe entire Universe in one line

T

c

GG

4

8

Tc

GG

4

8

Geometry of Geometry of

spacetimespacetime

(Einstein tensor)(Einstein tensor)

Distribution ofDistribution of

mass and energymass and energy

in the universein the universe

(stress-energy tensor)(stress-energy tensor)


Why is general relativity (GR) Why is general relativity (GR) difficult ?difficult ?

• conceptually difficult (relativity of space conceptually difficult (relativity of space and time, curvature of spacetime)and time, curvature of spacetime)

• set of 10 coupled partial differential set of 10 coupled partial differential equations equations

• non linear (solutions do not superpose)non linear (solutions do not superpose)

• space and time are part of the solutionspace and time are part of the solution

exact solution known only for a very fewexact solution known only for a very few simple cases simple cases


ChecklistChecklist

• How to deal with accelerations ? How to deal with accelerations ?



• Distance is relative, so which distance to use Distance is relative, so which distance to use in computing the gravitational force ?in computing the gravitational force ?


So what is left to do ?So what is left to do ?

• Show that general relativity provides a Show that general relativity provides a consistent and accurate description of consistent and accurate description of naturenature test it by experiment/observation test it by experiment/observation


Some open problemsSome open problems

• How to deal with accelerations ?How to deal with accelerations ?



• Distance is relative, so which distance to Distance is relative, so which distance to use in computing the gravitational force ?use in computing the gravitational force ?


Boost factorBoost factor

• special relativity:special relativity:

2

2

1

1

cv

2

2

1

1

cv

• general relativity:general relativity:

2

2

2 1

1

1

12

c

vcR

GMesc

2

2

2 1

1

1

12

c

vcR

GMesc


First test: bending of lightFirst test: bending of light

• Star light should be bend as it passes Star light should be bend as it passes through the gravitational field of the Sun, through the gravitational field of the Sun, i.e., it should be possible to see a star i.e., it should be possible to see a star behind the Sunbehind the Sun


First test: bending of lightFirst test: bending of light

• Star light should be bend as it passes Star light should be bend as it passes through the gravitational field of the Sun, through the gravitational field of the Sun, i.e., it should be possible to see a star i.e., it should be possible to see a star behind the Sunbehind the Sun

• General relativity predicts an angle of General relativity predicts an angle of 1.75”, twice as big as that predicted by 1.75”, twice as big as that predicted by Newtonian gravityNewtonian gravity

• measured by Arthur Eddington in 1919. measured by Arthur Eddington in 1919. Key event for Einstein’s elevation to a Key event for Einstein’s elevation to a celebrity.celebrity.


Test 2: Perihelion shift of MercuryTest 2: Perihelion shift of Mercury• Planets do not move on perfect ellipses, but Planets do not move on perfect ellipses, but

ellipses are precessing. This effect is due to ellipses are precessing. This effect is due to the gravitational force exerted by the other the gravitational force exerted by the other planetsplanets


Test 2: Perihelion shift of MercuryTest 2: Perihelion shift of Mercury• Planets do not move on perfect ellipses, but Planets do not move on perfect ellipses, but

ellipses are precessing. This effects is ellipses are precessing. This effects is caused by the perturbing effect of the other caused by the perturbing effect of the other planets gravitational field.planets gravitational field.

• Mercury’s precession amounts to 5600” per Mercury’s precession amounts to 5600” per century, but only 5557” can be explained by century, but only 5557” can be explained by Newtonian gravity, leaves a discrepancy of Newtonian gravity, leaves a discrepancy of 43” per century.43” per century.

• General relativity predicts exactly this General relativity predicts exactly this additional precessionadditional precession


Test 3: gravitational time dilation Test 3: gravitational time dilation and redshiftand redshift• Can be measured by experiments on Earth Can be measured by experiments on Earth

(challenging, but feasible)(challenging, but feasible)• Better: Better: White DwarfsWhite Dwarfs (very compact objects; (very compact objects;

mass comparable to that of the Sun, radius mass comparable to that of the Sun, radius comparable to that of the Earth),comparable to that of the Earth), because because they have a stronger gravitational fieldthey have a stronger gravitational field

• Even better: Even better: Neutron StarsNeutron Stars and and PulsarsPulsars (very (very compact objects; mass comparable to that of compact objects; mass comparable to that of the Sun, radius only 10-100 km), the Sun, radius only 10-100 km), because because they have a very strong gravitational fieldthey have a very strong gravitational field


Test 4: Binary pulsar PSR 1913+16Test 4: Binary pulsar PSR 1913+16• Pulsar:Pulsar: a rapidly rotating highly magnetized a rapidly rotating highly magnetized

neutron star that emits radio pulses at neutron star that emits radio pulses at regular intervalsregular intervals

• Discovered by Bell and Hewish in 1967Discovered by Bell and Hewish in 1967

• Nobel Prize in physics (1974)Nobel Prize in physics (1974)


Test 4: Binary pulsar PSR 1913+16Test 4: Binary pulsar PSR 1913+16• Pulsar:Pulsar:


Test 4: Binary pulsar PSR 1913+16Test 4: Binary pulsar PSR 1913+16• Binary pulsar:Binary pulsar: two two

pulsars orbiting pulsars orbiting each othereach other

• Orbital time: 7.75hOrbital time: 7.75h

• Discovered by Discovered by Hulse and Taylor in Hulse and Taylor in 19741974

• Nobel Prize in Nobel Prize in physics (1993)physics (1993)


Test 4: Binary pulsar PSR 1913+16Test 4: Binary pulsar PSR 1913+16

• Precession: Precession: 4.2º 4.2º per yearper year



• Time delay: Time delay: Clocks tick slower in strong gravitational Clocks tick slower in strong gravitational fieldsfields



• Gravitational Waves: Gravitational Waves: Orbital decay due to emission of Orbital decay due to emission of gravitational radiationgravitational radiation

data points

Prediction of GR


Tests to come: Gravity Probe BTests to come: Gravity Probe B


Gravitational time dilation and Gravitational time dilation and redshiftredshift• Can be measured by experiments on Earth Can be measured by experiments on Earth

(challenging, but feasible)(challenging, but feasible)• Better: Better: White DwarfsWhite Dwarfs (very compact objects; (very compact objects;

mass comparable to that of the Sun, radius mass comparable to that of the Sun, radius comparable to that of the Earth),comparable to that of the Earth), because because they have a stronger gravitational fieldthey have a stronger gravitational field

• Even better: Even better: Neutron StarsNeutron Stars and and PulsarsPulsars (very (very compact objects; mass comparable to that of compact objects; mass comparable to that of the Sun, radius only 10-100 km), the Sun, radius only 10-100 km), because because they have a very strong gravitational fieldthey have a very strong gravitational field


Flash-back: Newtonian gravityFlash-back: Newtonian gravity

• What velocity is required to leave the What velocity is required to leave the gravitational field of a planet or star?gravitational field of a planet or star?

• Example: EarthExample: Earth– Radius: Radius: RR = 6470 km = 6.47 = 6470 km = 6.47101066 m m– Mass: Mass: MM = 5.97 = 5.97 10102424 kg kg escape velocity: escape velocity: vvescesc = 11.1 km/s = 11.1 km/s

R

MGvesc

2

R

MGvesc

2




• Example: SunExample: Sun– Radius: Radius: RR = 700 000 km = 7 = 700 000 km = 7101088 m m– Mass: Mass: MM = 2 = 210103030 kg kg escape velocity: escape velocity: vvescesc = 617 km/s = 617 km/s

R

MGvesc

2

R

MGvesc

2




• Example: a solar mass White DwarfExample: a solar mass White Dwarf– Radius: Radius: RR = 5000 km = 5 = 5000 km = 5101066 m m– Mass: Mass: MM = 2 = 210103030 kg kg escape velocity: escape velocity: vvescesc = 7300 km/s = 7300 km/s

R

MGvesc

2

R

MGvesc

2




• Example: a solar mass neutron starExample: a solar mass neutron star– Radius: Radius: RR = 10 km = 10 = 10 km = 1044 m m– Mass: Mass: MM = 2 = 210103030 kg kg escape velocity: escape velocity: vvescesc = 163 000 km/s = 163 000 km/s ½ c ½ c

R

MGvesc

2

R

MGvesc

2



• Can an object be so small that even light Can an object be so small that even light cannot escape ? cannot escape ? Black Hole Black Hole

R

MGvesc

2

R

MGvesc

2 2

2

c

MGRS 2

2

c

MGRS

RRSS:: “Schwarzschild Radius”“Schwarzschild Radius”

• Example: for a solar massExample: for a solar mass– Mass: Mass: MM = 2 = 210103030 kg kg Schwarzschild Radius: Schwarzschild Radius: RRSS = 3 km = 3 km


Some definitions ... and Black HolesSome definitions ... and Black Holes

• The The Schwarzschild radiusSchwarzschild radius RRSS of an object of of an object of

mass M is the radius, at which the escape mass M is the radius, at which the escape speed is equal to the speed of light.speed is equal to the speed of light.

• The The event horizonevent horizon is a sphere of radius is a sphere of radius RRSS. .

Nothing within the event horizon, not even Nothing within the event horizon, not even light, can escape to the world outside the light, can escape to the world outside the event horizon.event horizon.

• A A Black HoleBlack Hole is an object whose radius is is an object whose radius is smaller than its event horizon.smaller than its event horizon.


Sizes of objectsSizes of objects


Let’s do it within the context of Let’s do it within the context of general relativity — spacetimegeneral relativity — spacetime

• spacetime distance (flat space):spacetime distance (flat space):

2222 Rtcs 2222 Rtcs spacespacetimetime

• Fourth coordinate: Fourth coordinate: ctct

• time coordinate has different sign than time coordinate has different sign than spatial coordinatesspatial coordinates


Let’s do it within the context of Let’s do it within the context of general relativity — spacetimegeneral relativity — spacetime

• spacetime distance (curved space of a point spacetime distance (curved space of a point mass):mass):

2

2

222

2

21

121 RtcRc

GMsRc

GM

2

2

222

2

21

121 RtcRc

GMsRc

GM

2222

/1

11 R

RRtc

RR

sS

S

2222

/1

11 R

RRtc

RR

sS

S

timetime spacespace


2222

/1

11 R

RRtc

RR

sS

S

2222

/1

11 R

RRtc

RR

sS

S

What happens if What happens if RR R RSS

• RR > R> RSS:: everything o.k.: everything o.k.: time: +, space: time: +, space: but but gravitational time dilation and length contractiongravitational time dilation and length contraction

• RR R RSS:: time time 0 space 0 space • RR < R< RSS:: signs change!! signs change!! time: time: , space: +, space: +

“space passes”,“space passes”, everything falls to the center everything falls to the center infinite density at the center, infinite density at the center, singularitysingularity

timetime spacespace


Structure of a Black HoleStructure of a Black Hole


What happens to an astronaut What happens to an astronaut who falls into a black hole?who falls into a black hole?• Far outside: nothing specialFar outside: nothing special

• Falling in: long before the astronaut reaches Falling in: long before the astronaut reaches the event horizon, he/she is torn apart by the event horizon, he/she is torn apart by tidal forcestidal forces

• For an outside observer:For an outside observer: – astronaut becomes more and more redshifted astronaut becomes more and more redshifted – The astronaut’s clock goes slower and slower The astronaut’s clock goes slower and slower – An outside observer never sees the astronaut An outside observer never sees the astronaut

crossing the event horizon.crossing the event horizon.


What happens, if an astronaut What happens, if an astronaut falls into a black hole?falls into a black hole?

• For the astronaut:For the astronaut: – He/she reaches and crosses the event horizon in He/she reaches and crosses the event horizon in

a finite time. a finite time. – Nothing special happens while crossing the Nothing special happens while crossing the

event horizon (except some highly distorted event horizon (except some highly distorted pictures of the local environment)pictures of the local environment)

– After crossing the event horizon, the astronaut After crossing the event horizon, the astronaut has 10 microseconds to enjoy the view before has 10 microseconds to enjoy the view before he/she reaches the singularity at the center.he/she reaches the singularity at the center.


Cosmic censorshipCosmic censorship• Singularity:Singularity: a point at which spacetime a point at which spacetime

divergesdiverges– infinite forces are actinginfinite forces are acting– laws of physics break down laws of physics break down – quantum gravity may help ?quantum gravity may help ?– no problem as long as a singularity is shielded no problem as long as a singularity is shielded

from the outside world by an event horizonfrom the outside world by an event horizon

• Hypothesis:Hypothesis: Every singularity is surrounded Every singularity is surrounded by an event horizon. by an event horizon.

There are no naked singularitiesThere are no naked singularities


Near a black hole: bending of lightNear a black hole: bending of light


The Photon sphereThe Photon sphere

The photon sphere is a sphere of radius 1.5 RThe photon sphere is a sphere of radius 1.5 RSS. .

On the photon sphere, light orbits a black hole On the photon sphere, light orbits a black hole on a circular orbit. on a circular orbit.


Structure of a rotating black holeStructure of a rotating black hole

Within the ergosphere (or static sphere) Within the ergosphere (or static sphere) nothing can remain at rest. Spacetime is nothing can remain at rest. Spacetime is dragged around the holedragged around the hole


No-Hair theoremNo-Hair theorem

• Properties of a black hole:Properties of a black hole:– it has a massit has a mass– it has an electric chargeit has an electric charge– it has a spin (angular momentum)it has a spin (angular momentum)– that’s it. Like an elementary particle, but much that’s it. Like an elementary particle, but much

more massivemore massive

Black holes have no hairBlack holes have no hair


Hawking RadiationHawking Radiation

• Heisenberg uncertainty principle:Heisenberg uncertainty principle:EEt t h/2 h/2Energy need not be conserved over Energy need not be conserved over

short periods, only on averageshort periods, only on average

• Virtual particles: particle-Virtual particles: particle-antiparticle pairs created from antiparticle pairs created from vacuum energy fluctuations which vacuum energy fluctuations which quickly disappearquickly disappear

• Virtual particles that can "steal" Virtual particles that can "steal" energy from elsewhere become realenergy from elsewhere become real



• Virtual pairs near a black hole can steal Virtual pairs near a black hole can steal energy from the gravitational fieldenergy from the gravitational field– Tidal stresses accelerate one particle outward, Tidal stresses accelerate one particle outward,

one drops into event horizonone drops into event horizon– Energy of new particle comes from gravitational Energy of new particle comes from gravitational

energy of BH, so BH mass must decreaseenergy of BH, so BH mass must decrease– Black hole evaporates!Black hole evaporates!



• Energy for new particles comes from tidal Energy for new particles comes from tidal stressesstresses– Tidal effects must be large over short path Tidal effects must be large over short path

lengths of virtual pairslengths of virtual pairs– Smaller black holes have steeper gravitational Smaller black holes have steeper gravitational

gradientsgradients

=> Smaller black holes evaporate more quickly=> Smaller black holes evaporate more quickly

ttevapevap = 10 = 101010(M(MBHBH /10 /101212 kg) kg)33 yr yr

ttevapevap(1M(1Msolarsolar) ~ 10) ~ 106565 yr yr



• Black holes emit as black bodiesBlack holes emit as black bodies– Temperature of black hole proportional to rate of Temperature of black hole proportional to rate of

radiationradiation

– TTBHBH = 10 = 10-7-7 (M (Msolar solar / M/ M

BHBH))

– T(1 MT(1 Msolarsolar) ~ 10) ~ 10-7 -7 K K

– T(10T(1066 M Msolarsolar) ~ 10) ~ 10-13 -13 KK


ExoticaExotica

• White holes - a phenomenon analogous to a White holes - a phenomenon analogous to a black hole from which light can black hole from which light can onlyonly escape. escape. No obvious way to make or power oneNo obvious way to make or power one

• Wormholes - conduits between two points in Wormholes - conduits between two points in spacetime. Unstable, difficult to avoid spacetime. Unstable, difficult to avoid singularity without going faster than singularity without going faster than cc, , solutions with timelike paths only size of solutions with timelike paths only size of elementary particles. If they exist, probably elementary particles. If they exist, probably not useful for travel since stable solutions not useful for travel since stable solutions require "exotic matter"require "exotic matter"


A Practical PerspectiveA Practical Perspective

• Two main types of black hole in the universeTwo main types of black hole in the universe– Stellar mass black holes: created by the collapse Stellar mass black holes: created by the collapse

of a massive star at the end of its life, of a massive star at the end of its life,

~3-100? M~3-100? Msolarsolar

– Supermassive black holes (SMBH): found in the Supermassive black holes (SMBH): found in the centers of galaxies, power quasars and AGN,centers of galaxies, power quasars and AGN,

~a few times 10~a few times 1066 - 10 - 1099 M M


Stellar Black HolesStellar Black Holes

• Created from stars of more than ~30 MCreated from stars of more than ~30 Msolarsolar

• Detectable in binary systemsDetectable in binary systems– Normal or evolved star transfers mass to black Normal or evolved star transfers mass to black

hole via accretion diskhole via accretion disk– Measure orbital period and velocity of Measure orbital period and velocity of

companion and use Kepler's laws to derive lower companion and use Kepler's laws to derive lower limits on masslimits on mass

– Neutron stars < 3 MNeutron stars < 3 Msolarsolar so any larger invisible so any larger invisible

companion must be black hole or unknown companion must be black hole or unknown physicsphysics



• X-Ray BinariesX-Ray Binaries– Viscosity (friction) of gas in disk heats up diskViscosity (friction) of gas in disk heats up disk– A few to 40% of gravitational potential energy A few to 40% of gravitational potential energy

(= rest mass energy) liberated(= rest mass energy) liberated– Temperatures of ~10Temperatures of ~1055-10-106 6 K in inner disk K in inner disk – Spectrum peaks in soft x-raysSpectrum peaks in soft x-rays– Optically thin material in corona or inner disk at Optically thin material in corona or inner disk at

>10>1077 K gives hard x-ray emission K gives hard x-ray emission– Some with relativistic jetsSome with relativistic jets

– Luminosities of order 10Luminosities of order 1055 L Lsolarsolar


Supermassive Black HolesSupermassive Black Holes

• Active Galactic Nuclei (AGN)Active Galactic Nuclei (AGN)– Many types; most commonly discussed are radio Many types; most commonly discussed are radio

galaxies, Seyferts, quasars, and QSOsgalaxies, Seyferts, quasars, and QSOs– Large black holes at the centers of galaxies form Large black holes at the centers of galaxies form

at early epochs, possibly from collapse of dense at early epochs, possibly from collapse of dense stellar clusters, and grow by accretion over stellar clusters, and grow by accretion over lifetime of universelifetime of universe

– Luminosity from accretion disks as in X-ray Luminosity from accretion disks as in X-ray binaries, but larger BH = lower temperaturebinaries, but larger BH = lower temperature



• AGN structureAGN structure– Accretion disk at a few x 10Accretion disk at a few x 1044 K, peak emission in K, peak emission in

UV (R ~ 100AU ~100 RUV (R ~ 100AU ~100 RSS))

– Hot, rarefied gas in x-ray halo or corona (R ~ 1-Hot, rarefied gas in x-ray halo or corona (R ~ 1-10 AU ~ R10 AU ~ R

SS))

– Broad emission line region (BLR); clouds with Broad emission line region (BLR); clouds with velocities of 10velocities of 1044 kms kms-1-1, indicate strong , indicate strong gravitational field (R ~ 0.01pc)gravitational field (R ~ 0.01pc)

– Dusty molecular torus in plane of disk (R ~ 0.1-Dusty molecular torus in plane of disk (R ~ 0.1-1pc) IR emission1pc) IR emission



• AGN structure continuedAGN structure continued– Narrow emission line region (NLR); clouds of Narrow emission line region (NLR); clouds of

ionized gas with widths of a few hundred kmsionized gas with widths of a few hundred kms-1-1 Seen in cones extending from ~50pc to 15kpcSeen in cones extending from ~50pc to 15kpc

– Relativistic jets - accelerated by magnetic fields Relativistic jets - accelerated by magnetic fields in disk to significant fraction of in disk to significant fraction of cc. Looking head-. Looking head-on into quasar jets, see OVVs and BL Lacson into quasar jets, see OVVs and BL Lacs

– Jets in radio galaxies may extend ~1 MpcJets in radio galaxies may extend ~1 Mpc



• AGN characteristicsAGN characteristics– Emission over 21 orders of magnitude in Emission over 21 orders of magnitude in

frequency - from radio to frequency - from radio to -rays-rays– Range of luminosities, from barely discernable to Range of luminosities, from barely discernable to

> 10> 101515 L Lsolarsolar, 10,000 times the luminosity of a , 10,000 times the luminosity of a

bright galaxybright galaxy– Radio quiet and radio loudRadio quiet and radio loud– Often associated with starbursts, interacting Often associated with starbursts, interacting

galaxies, Luminous Infrared Galaxies (LIRGs, galaxies, Luminous Infrared Galaxies (LIRGs, ULIRGs, HLIRGs)ULIRGs, HLIRGs)



• EvidenceEvidence– Kinematic evidenceKinematic evidence

• Stellar motions in center of Milky WayStellar motions in center of Milky Way

• Stellar and gas motions in other galaxiesStellar and gas motions in other galaxies

• OH masers in NGC 4258OH masers in NGC 4258

• All imply tremendous mass in a tiny areaAll imply tremendous mass in a tiny area

– Images of dusty torii and accretion disksImages of dusty torii and accretion disks– Only way of producing enough energy to make a Only way of producing enough energy to make a

quasar in so little spacequasar in so little space


Supermassive Supermassive Black HolesBlack Holes


Questions:Questions:• Do they really exist ? (Observe gravitational Do they really exist ? (Observe gravitational

effects )effects )

• How do we observe something that does not How do we observe something that does not emit light? (Light bends around them)emit light? (Light bends around them)


The cosmic distance ladderThe cosmic distance ladder• ParallaxParallax

– solar neighborhood (< 1 kpc)solar neighborhood (< 1 kpc)

• Main sequence fittingMain sequence fitting – distances within the Galaxy (<100 kpc)distances within the Galaxy (<100 kpc)

• CepheidsCepheids – nearby galaxies (< 20 Mpc)nearby galaxies (< 20 Mpc)

• Tully-FisherTully-Fisher relationrelation– distant galaxies (< 500 Mpc)distant galaxies (< 500 Mpc)

• Type 1a supernovae Type 1a supernovae – cosmological distances (~ 1 Gpc)cosmological distances (~ 1 Gpc)


Nature of spiral nebulae and the Nature of spiral nebulae and the Milky Way (MW)Milky Way (MW)

CurtisCurtis• MW is 10 kpc acrossMW is 10 kpc across• Sun near centerSun near center• spiral nebulae were other spiral nebulae were other

galaxiesgalaxies– high recession speedhigh recession speed– apparent sizes of nebulaeapparent sizes of nebulae– did not believe van did not believe van

Maanen’s measurementMaanen’s measurement

Milky Way = one galaxy Milky Way = one galaxy among many othersamong many others

ShapleyShapley• MW is 100 kpc acrossMW is 100 kpc across• Sun off centerSun off center• spiral nebulae part of the spiral nebulae part of the

GalaxyGalaxy– apparent brightness of apparent brightness of

nova in the Andromeda nova in the Andromeda galaxygalaxy

– measured rotation of measured rotation of spirals (via proper motion) spirals (via proper motion) by van Maanenby van Maanen

Milky Way = UniverseMilky Way = Universe


SolutionSolution

• Role of dustRole of dust– obscuration:obscuration: Kapteyn/Curtis could only see a Kapteyn/Curtis could only see a

small fraction of the Milky Way disksmall fraction of the Milky Way disk– dimming:dimming: stars appear to be dimmer stars appear to be dimmer Shapley, Shapley,

ignoring dust, concluded that globular clusters ignoring dust, concluded that globular clusters are farther away than they actually are.are farther away than they actually are.

Milky Way is 30 kpc across, Sun is 8.5 kpc off Milky Way is 30 kpc across, Sun is 8.5 kpc off center.center.

Spiral nebulae are galaxies like the Milky Spiral nebulae are galaxies like the Milky Way. Distance: millions of parsec.Way. Distance: millions of parsec.


Edwin Hubble Edwin Hubble (1889-1953)(1889-1953)Four major accomplishments Four major accomplishments in extragalactic astronomyin extragalactic astronomy

• The establishment of the The establishment of the Hubble classification Hubble classification scheme of galaxiesscheme of galaxies

• The convincing proof that galaxies are island The convincing proof that galaxies are island “universes”“universes”

• The distribution of galaxies in spaceThe distribution of galaxies in space

• The discovery that the universe is expandingThe discovery that the universe is expanding


The Hubble classificationThe Hubble classification


The Hubble classificationThe Hubble classification

• Elliptical galaxiesElliptical galaxies (E0-E7) (E0-E7)– classified according to their flattening: 10classified according to their flattening: 10(1-b/a)(1-b/a)

• Spiral galaxiesSpiral galaxies (S0, Sa-Sd) (S0, Sa-Sd)– classified according to their bulge-to-disk ratioclassified according to their bulge-to-disk ratio– Sa: large bulge, Sd: small bulgeSa: large bulge, Sd: small bulge– S0: transition spiral to ellipticalS0: transition spiral to elliptical

• Barred spiral galaxiesBarred spiral galaxies (SB0, SBa-SBd) (SB0, SBa-SBd)– classified according to their bulge to disk ratioclassified according to their bulge to disk ratio

• Irregular galaxiesIrregular galaxies (Irr) (Irr)


THE EXPANDING UNIVERSE:Using the Doppler Effect to Measure Velocity

Blueshift Redshift

T1T2T3T4


Calcium

Magnesium

Sodium

Galaxy Spectrum

Stellar Spectrum

Spectra of a nearby star and a distant galaxyStar is nearby,

approximately at restGalaxy is distant,

traveling away from us at 12,000 km/s

Galaxy Spectroscopy

The larger the redshift: the greater the distance from us


Doppler effectDoppler effect

red shiftred shiftblue shiftblue shift

The light of an approaching source is shifted to the blue, The light of an approaching source is shifted to the blue,

the light of a receding source is shifted to the red.the light of a receding source is shifted to the red.


Doppler effectDoppler effect

redshift:redshift:

zz=0: not moving=0: not moving

zz=2: =2: vv=0.8=0.8cc

zz==: : vv==cc

cv

cvz

/1

/11

cv

cvz

/1

/11


The redshift-distance relationThe redshift-distance relation


Key resultsKey results• Most galaxies are moving away from usMost galaxies are moving away from us• The recession speed v is larger for more The recession speed v is larger for more

distant galaxies. The relation between distant galaxies. The relation between recess velocity recess velocity vv and distance and distance dd fulfills a fulfills a linear relation: linear relation: v = Hv = H0 0 d d

• Hubble’s measurement of the constant Hubble’s measurement of the constant HH00:: HH00 = 500 km/s/Mpc = 500 km/s/Mpc

• today’s best fit value of the constant:today’s best fit value of the constant: HH00 = 70 km/s/Mpc = 70 km/s/Mpc


Question:Question:If all galaxies are moving away from us,If all galaxies are moving away from us,

does this imply that we are at the center?does this imply that we are at the center?

Answer:Answer:Not necessarily, it also can indicate that the Not necessarily, it also can indicate that the universe is expanding and that we are at no universe is expanding and that we are at no special place. If the velocity of recession is special place. If the velocity of recession is proportional to distance, then any point is at the center proportional to distance, then any point is at the center of the expansionof the expansion


The great synthesis (1930)The great synthesis (1930)

• Meeting by Einstein, Hubble and LemaîtreMeeting by Einstein, Hubble and Lemaître– Einstein: theory of general relativityEinstein: theory of general relativity– Friedmann and Lemaître: expanding universe Friedmann and Lemaître: expanding universe

as a solution to Einstein’s equationas a solution to Einstein’s equation– Hubble: observational evidence that the Hubble: observational evidence that the

universe is indeed expandinguniverse is indeed expanding

• Consequence:Consequence:– Universe started from a pointUniverse started from a point

The Big Bang Model The Big Bang Model


History of the Universe (with History of the Universe (with Inflation)Inflation)


Let’s apply Einstein’s equation to Let’s apply Einstein’s equation to the Universethe Universe• What is the solution of Einstein’s equation What is the solution of Einstein’s equation

for a homogeneous, isotropic mass for a homogeneous, isotropic mass distribution?distribution?– As in Newtonian dynamics, gravity is always As in Newtonian dynamics, gravity is always

attractiveattractive– a homogeneous, isotropic and initially static a homogeneous, isotropic and initially static

universe is going to collapse under its own universe is going to collapse under its own gravitygravity

– Alternative: expanding universe (Friedmann) Alternative: expanding universe (Friedmann)


Einstein’s proposal: cosmological Einstein’s proposal: cosmological constant constant • There is a repulsive force in the universeThere is a repulsive force in the universe

vacuum exerts a pressurevacuum exerts a pressure empty space is curved rather than flatempty space is curved rather than flat

• The repulsive force compensates the attractive The repulsive force compensates the attractive gravity gravity static universe is possible static universe is possible

• but:but: such a universe turns out to be unstable: such a universe turns out to be unstable: one can set up a static universe, but it simply one can set up a static universe, but it simply does not remain staticdoes not remain static

• Einstein: “greatest blunder of his life”, Einstein: “greatest blunder of his life”, butbut is it is it really … ? really … ?


initial distance: initial distance: 1 length unit1 length unitfinal distance: final distance: 2 length units2 length unitsrecess velocity: recess velocity: 1 length unit per time unit1 length unit per time unit

initial distance: initial distance: 2 length units2 length unitsfinal distance: final distance: 4 length units4 length unitsrecess velocity: recess velocity: 2 length units per time unit2 length units per time unit


A metric of an expanding UniverseA metric of an expanding Universe

• Recall: flat spaceRecall: flat space

• better: using spherical coordinates (better: using spherical coordinates (r,r,,,))

22222 zyxtcs 22222 zyxtcs

22222222 sin rrrtcs 22222222 sin rrrtcs



• But, this was for a static space. How does But, this was for a static space. How does this expression change if we consider an this expression change if we consider an expanding space ?expanding space ?

• R(t)R(t) is the so-called is the so-called scale factorscale factor

222222222 sin)( rrrtRtcs 222222222 sin)( rrrtRtcs


Example: static universeExample: static universe

R(t)

t


Example: expanding at a constant Example: expanding at a constant raterate

R(t)

t


Example: expansion is Example: expansion is slowing downslowing down

R(t)

t


Example: expansion is Example: expansion is acceleratingaccelerating

R(t)

t


Example: collapsingExample: collapsing

R(t)

t


How old is the universe?How old is the universe?

• A galaxy at distance A galaxy at distance dd recedes at velocity recedes at velocity v=Hv=H0 0 d d..

• When was the position of this galaxy When was the position of this galaxy identical to that of our galaxy? Answer: identical to that of our galaxy? Answer:

0

1

Hv

dtHubble

0

1

Hv

dtHubble

• ttHubbleHubble: Hubble time. For : Hubble time. For HH00 = 65 km/s/Mpc: = 65 km/s/Mpc:

ttHubbleHubble = 15 Gyr= 15 Gyr


How big is the universe?How big is the universe?• We can’t tell. We can only see (and are affected We can’t tell. We can only see (and are affected

by) that part of the universe that is closer than by) that part of the universe that is closer than the distance that light can travel in a time the distance that light can travel in a time corresponding to the age of the Universecorresponding to the age of the Universe

• But we can estimate, how big the observable But we can estimate, how big the observable universe is:universe is:

0H

cctd HubbleHubble

0H

cctd HubbleHubble

• ddHubbleHubble: Hubble radius. For : Hubble radius. For HH00 = 65 km/s/Mpc: = 65 km/s/Mpc:

ddHubbleHubble = 4.6 Gpc= 4.6 Gpc



• But, so far, we only considered a flat space. But, so far, we only considered a flat space. What, if there is curvature ?What, if there is curvature ?

• k k is the curvature constantis the curvature constant– k=0k=0: flat space: flat space– k>0k>0: spherical geometry: spherical geometry– k<0k<0: hyperbolic geometry: hyperbolic geometry

222222

2222 sin

1)( rr

kr

rtRtcs

222222

2222 sin

1)( rr

kr

rtRtcs



• But, so far, we only considered a flat space. But, so far, we only considered a flat space. What, if there is curvature ?What, if there is curvature ?


k>0k>0 k<0k<0k=0k=0


Cosmological redshiftCosmological redshift

• While a photon travels from a distance While a photon travels from a distance source to an observer on Earth, the source to an observer on Earth, the Universe expands in size from Universe expands in size from RRthenthen to to RRnownow..

• Not only the Universe itself expands, but Not only the Universe itself expands, but also the wavelength of the photon also the wavelength of the photon changeschanges..

emittedthen

nowreceived R

R emittedthen

nowreceived R

R


Cosmological redshiftCosmological redshift

• General definition of redshift:General definition of redshift:

for cosmological redshift: for cosmological redshift:

emitted

emittedreceivedz

emitted

emittedreceivedz

then

now

emitted

received

R

Rz

1then

now

emitted

received

R

Rz

1


Cosmological redshiftCosmological redshift• Examples:Examples:

– z=1 z=1 RRthenthen//RRnownow = 0.5 = 0.5• at at z=1z=1, the universe had , the universe had 50% of its present day size50% of its present day size• emitted emitted blue lightblue light (400 nm) is shifted all the way (400 nm) is shifted all the way

through the optical spectrum and is received as through the optical spectrum and is received as red red lightlight (800 nm) (800 nm)

– z=4 z=4 RRthenthen//RRnownow = 0.2 = 0.2• at at z=4z=4, the universe had , the universe had 20% of its present day size20% of its present day size• emitted emitted blue lightblue light (400 nm) is shifted deep into the (400 nm) is shifted deep into the

infraredinfrared and is received at 2000 nm and is received at 2000 nm

– most distant astrophysical object discovered so most distant astrophysical object discovered so far: z=5.8far: z=5.8


• Friedmann equationFriedmann equation

• k k is the curvature constantis the curvature constant

222

3

8kcR

Gv 222

3

8kcR

Gv

Let’s switch to general relativityLet’s switch to general relativity


• Friedmann equationFriedmann equation

• k k is the curvature constantis the curvature constant– k=0k=0: flat space, forever expanding: flat space, forever expanding– k>0k>0: spherical geometry, eventually recollapsing: spherical geometry, eventually recollapsing– k<0k<0: hyperbolic geometry, forever expanding: hyperbolic geometry, forever expanding

222

3

8kcR

Gv 222

3

8kcR

Gv

Let’s switch to general relativityLet’s switch to general relativity


k>0k>0 k<0k<0k=0k=0


222

3

8kcR

Gv 222

3

8kcR

Gv

2

2

2

2

3

8

R

kcG

R

v

2

2

2

2

3

8

R

kcG

R

v

Can we predict the fate of the Can we predict the fate of the Universe ?Universe ?• Friedmann equation:Friedmann equation:

2

2

2

220 3

8

R

kcG

R

vH

2

2

2

220 3

8

R

kcG

R

vH

• k=0k=0::

G

Hcrit

8

3 20

G

Hcrit

8

3 20


• If the density If the density of the Universe of the Universe ==critcrit:: flat space, forever expandingflat space, forever expanding

>>critcrit:: spherical geometry, recollapsingspherical geometry, recollapsing

< < critcrit:: hyperbolic geometry, forever expandinghyperbolic geometry, forever expanding

• so what is the density of the universe?so what is the density of the universe?– We don’t know preciselyWe don’t know precisely >>critcrit very unlikelyvery unlikely

– currently favored modelcurrently favored model: : 0.30.3critcrit

Can we predict the fate of the Can we predict the fate of the Universe ?Universe ?


How big is How big is critcrit ? ?

critcrit == 881010-30-30 g/cmg/cm33 1 atom per 200 liter 1 atom per 200 liter

• density parameterdensity parameter 00

00 =1 =1:: flat space, forever expanding (open)flat space, forever expanding (open)

00 >1 >1:: spherical geometry, recollapsing (closed)spherical geometry, recollapsing (closed)

00 <1 <1:: hyperbolic geometry, forever expandinghyperbolic geometry, forever expanding

• currently favored model:currently favored model: 00 = 0.3 = 0.3

G

H

crit

8

3 20

0 G

H

crit

8

3 20

0


How can we measure How can we measure 00 ? ?

• Count all the mass we can “see”Count all the mass we can “see”– tricky, some of the mass may be hidden …tricky, some of the mass may be hidden …

• Measure the rate at which the expansion of Measure the rate at which the expansion of the universe is slowing downthe universe is slowing down– a more massive universe will slow down fastera more massive universe will slow down faster

• Measure the geometry of the universeMeasure the geometry of the universe– is it spherical, hyperbolic or flat ?is it spherical, hyperbolic or flat ?


Let’s try to measure the Let’s try to measure the decelerationdeceleration• Acceleration according to Newton:Acceleration according to Newton:

• deceleration parameterdeceleration parameter

RG

R

MGa

3

42

R

G

R

MGa

3

42

20

20

v

aRq

20

20

v

aRq


So what’s the meaning of So what’s the meaning of qq00 ? ?

• deceleration parameter deceleration parameter qq00 – qq00>0.5:>0.5: deceleration is so strong that deceleration is so strong that

eventually the universe eventually the universe stops stops expanding and starts expanding and starts collapsingcollapsing

– 0<0<qq00<0.5:<0.5: deceleration is too weak to stop deceleration is too weak to stop expansionexpansion

• What’s the difference between What’s the difference between qq00, , 00 and and kk ??– kk:: curvature of the universecurvature of the universe 00:: mass content of the universemass content of the universe– qq00:: kinematics of the universe kinematics of the universe


So let’s measure So let’s measure qq0 0 !!

• How do we do that?How do we do that?– Measure the rate of expansion at different Measure the rate of expansion at different

times, i.e. measure and compare the expansion times, i.e. measure and compare the expansion based on nearby galaxies and based on high based on nearby galaxies and based on high redshift galaxiesredshift galaxies

• Gravity is slowing down expansion Gravity is slowing down expansion expansion rate should be higher at high expansion rate should be higher at high redshift. redshift.


So let’s measure So let’s measure qq0 0 !!

qq00 = 0 = 0qq00 = 0.5 = 0.5

more distantmore distant

fain

ter

fain

ter

Data indicates:Data indicates:

qq00 < 0 < 0

Expansion Expansion

is acceleratingis accelerating


Science discovery of the year 1998Science discovery of the year 1998

• The expansion of the universe is The expansion of the universe is accelerating !!!accelerating !!!

• But gravity is always attractive, so it only But gravity is always attractive, so it only can deceleratecan decelerate

Revival of the cosmological constant Revival of the cosmological constant


• k k is the curvature constantis the curvature constant– k=0k=0: flat space, flat universe: flat space, flat universe– k>0k>0: spherical geometry, closed universe: spherical geometry, closed universe– k<0k<0: hyperbolic geometry, open universe: hyperbolic geometry, open universe

222

3

8kcR

Gv 222

3

8kcR

Gv

Friedmann’s equation for Friedmann’s equation for >0 >0

33

8 2222 R

kcRG

v

33

8 2222 R

kcRG

v


• but for sufficiently large but for sufficiently large a spherically curved a spherically curved universe may expand foreveruniverse may expand forever


Deceleration parameter Deceleration parameter qq for for >0 >0

• Acceleration according to Newton:Acceleration according to Newton:


RG

a3

4 R

Ga

3

4

20

20

v

aRq

20

20

v

aRq

• Acceleration according to Newton:Acceleration according to Newton:


with with

RRG

a33

4

RR

Ga

33

4

2

020 v

aRq

20

20 v

aRq

203H

2

03H


k=+1

=0

>0

The fate of the Universe for The fate of the Universe for >0 >0


Is the fate of the Universe well Is the fate of the Universe well determined ?determined ?• deceleration:deceleration:

– ½½00 – – > 0> 0: decelerating: decelerating

– ½½00 – – < 0< 0: accelerating: accelerating

• curvaturecurvature 00 + + = 1= 1: flat: flat

00 + + < 1< 1: hyperbolic: hyperbolic

00 + + > 1> 1: spherical: spherical

• two equations for two variables two equations for two variables well well posed problemposed problem


Cosmology: the quest for three Cosmology: the quest for three numbersnumbers• The Hubble constant The Hubble constant HH00

how fast is the universe expandinghow fast is the universe expanding

• The density parameter The density parameter 00

how much mass is in the universehow much mass is in the universe

• The cosmological constant The cosmological constant

the vacuum energy of the universethe vacuum energy of the universe

• current observational situation:current observational situation:• HH00 = 65 km/s/Mpc= 65 km/s/Mpc

00 = 0.3 = 0.3;; = 0.7 = 0.7 flat space flat space


How old is the Universe?How old is the Universe?

• A galaxy at distance A galaxy at distance dd recedes at velocity recedes at velocity v=Hv=H0 0 d d..

• When was the position of this galaxy When was the position of this galaxy identical to that of our galaxy? Answer: identical to that of our galaxy? Answer:

0

1

Hv

dtHubble

0

1

Hv

dtHubble

• ttHubbleHubble: Hubble time. For : Hubble time. For HH00 = 65 km/s/Mpc: = 65 km/s/Mpc:

ttHubbleHubble = 15 Gyr= 15 Gyr


The age of the Universe revisitedThe age of the Universe revisited• So far, we have assumed that the expansion So far, we have assumed that the expansion

velocity is not changing (velocity is not changing (qq00=0=0, empty , empty

universe)universe)• How does this How does this

estimate change, estimate change, if the expansion if the expansion decelerates, i.e. decelerates, i.e. qq00>0 >0 ??

• An An 00>0>0, , =0=0 universe is younger than 15 Gyr universe is younger than 15 Gyr

now


now

• So far, we only have considered So far, we only have considered decelerating universesdecelerating universes

• How does this How does this estimate change, estimate change, if the expansion if the expansion accelerates, i.e. accelerates, i.e. qq00<0 <0 ??

The age of the Universe revisitedThe age of the Universe revisited

• An An >0>0 universe can be older than 15 Gyr universe can be older than 15 Gyr


00=0=0, , =0=0: : ttHubbleHubble ==1/1/HH00 = 15 Gyr = 15 Gyr00=1=1, , =0=0: : ttHubbleHubble ==2/(32/(3HH00))= 10 Gyr= 10 Gyr• open universes with open universes with 0<0<00<1<1, , =0 =0 are are

between 10 and 15 Gyr oldbetween 10 and 15 Gyr old• closed universes with closed universes with 00>1>1, , =0 =0 are less are less

than 10 Gyr oldthan 10 Gyr old>0 >0 increases, increases, <0 <0 decreases the age of the decreases the age of the

universeuniverse00=0.3=0.3, , =0.7=0.7: : ttHubbleHubble ==0.96/0.96/HH00 = 14.5 Gyr = 14.5 Gyr

The age of the Universe revisitedThe age of the Universe revisited


• not directlynot directly

• but we can constrain the age of the but we can constrain the age of the Universe. It must not be younger than the Universe. It must not be younger than the oldest star in the Universe.oldest star in the Universe.

• How do we measure the age of stars?How do we measure the age of stars?– radioactive datingradioactive dating– stellar evolution modelsstellar evolution models

• Result: age of the oldest star ~12-14 GyrResult: age of the oldest star ~12-14 Gyr00>~1 strongly disfavored>~1 strongly disfavored

Can we measure the age of the Can we measure the age of the Universe ?Universe ?


The life of a universe – key factsThe life of a universe – key facts

• Unless Unless is sufficiently large (which is is sufficiently large (which is inconsistent with observations) all inconsistent with observations) all cosmological models start with a big bang.cosmological models start with a big bang.

• An universe doesn’t change its geometry. An universe doesn’t change its geometry. A flat universe has always been and will A flat universe has always been and will always be flat, a spherical universe is always be flat, a spherical universe is always spherical and so on. always spherical and so on.

• Two basic solutions:Two basic solutions:– eventual collapse for largeeventual collapse for large 00 or negativeor negative – eternal expansion otherwiseeternal expansion otherwise


Some common misconceptionsSome common misconceptions

• The picture that the Universe expands into a The picture that the Universe expands into a preexisting space like an explosionpreexisting space like an explosion

• The question “what was before the big The question “what was before the big bang?”bang?”

• Remember: spacetime is part of the solution Remember: spacetime is part of the solution to Einstein’s equationto Einstein’s equation

• Space and time are created in the big bangSpace and time are created in the big bang


So is the big crunch the same as So is the big crunch the same as the big bang run in reverse ?the big bang run in reverse ?• No. The Universe has meanwhile formed No. The Universe has meanwhile formed

stars, black holes, galaxies etc.stars, black holes, galaxies etc.

• Second law of thermodynamics:Second law of thermodynamics:The entropy (disorder) of a system at best The entropy (disorder) of a system at best stays the same but usually increases with stays the same but usually increases with time, in any process. There is no perpetual time, in any process. There is no perpetual motion machine.motion machine.

• Second law of thermodynamics defines an Second law of thermodynamics defines an arrow of time.arrow of time.


• At early epochs, the first term dominatesAt early epochs, the first term dominates the early universe appears to be almost flatthe early universe appears to be almost flat

• At late epochs, the second term dominatesAt late epochs, the second term dominates the late universe appears to be almost emptythe late universe appears to be almost empty

2

2

3

8

R

kcGH

2

2

3

8

R

kcGH

Friedmann’s equation for Friedmann’s equation for =0, =0, 00<1<1

Expansion rateExpansion rate

of the Universeof the UniverseFalls off like Falls off like

the cube of Rthe cube of R

Falls off like Falls off like

the square of Rthe square of R


• At early epochs, the first term dominatesAt early epochs, the first term dominates the early universe appears to be almost flatthe early universe appears to be almost flat

• At late epochs, the third term dominatesAt late epochs, the third term dominates the late universe appears to be exponentially expandingthe late universe appears to be exponentially expanding

33

82

2

R

kcGH

33

82

2

R

kcGH

Friedmann’s equation for Friedmann’s equation for >0, >0, 00<1<1

Expansion rateExpansion rate

of the Universeof the UniverseFalls off like Falls off like

the cube of Rthe cube of RFalls off like Falls off like

the square of Rthe square of R

constantconstant


A puzzling detailA puzzling detail

=0=0: for most of its age, the universe looks : for most of its age, the universe looks either to be flat or to be emptyeither to be flat or to be empty

>0>0: for most of its age, the universe looks : for most of its age, the universe looks either to be flat or to be exponentially either to be flat or to be exponentially expandingexpanding

• Isn’t it strange that we appear to live in that Isn’t it strange that we appear to live in that short period between those two extremes ?short period between those two extremes ?

Flatness problemFlatness problem


The life of a universe – key factsThe life of a universe – key facts

• Unless Unless is sufficiently large (which is is sufficiently large (which is inconsistent with observations) all inconsistent with observations) all cosmological models start with a big bang.cosmological models start with a big bang.

• An universe doesn’t change its geometry. An universe doesn’t change its geometry. A flat universe has always been and will A flat universe has always been and will always be flat, a spherical universe is always be flat, a spherical universe is always spherical and so on. always spherical and so on.

• Two basic solutions:Two basic solutions:– eventual collapse for largeeventual collapse for large 00 or negativeor negative – eternal expansion otherwiseeternal expansion otherwise


General acceptance of the big General acceptance of the big bang modelbang model• Until mid 60ies: big bang model very Until mid 60ies: big bang model very

controversial, many alternative modelscontroversial, many alternative models• After mid 60ies: little doubt on validity of After mid 60ies: little doubt on validity of

the big bang modelthe big bang model• Four pillars on which the big bang theory is Four pillars on which the big bang theory is

resting:resting:– Hubble’s law Hubble’s law – Cosmic microwave background radiationCosmic microwave background radiation– The origin of the elementsThe origin of the elements– Structure formation in the universeStructure formation in the universe


Georgy Gamov (1904-1968)Georgy Gamov (1904-1968)

• If the universe is expanding, then If the universe is expanding, then there has been a big bangthere has been a big bang

• Therefore, the early universe must Therefore, the early universe must have been very dense and hothave been very dense and hot

• Optimum environment to breed the elements by Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948)nuclear fusion (Alpher, Bethe & Gamow, 1948)– success: predicted that helium abundance is 25%success: predicted that helium abundance is 25%– failure: could not reproduce elements more massive failure: could not reproduce elements more massive

than lithium and beryllium (than lithium and beryllium ( formed in stars) formed in stars)


Hoyle’s ”Big Bang”Hoyle’s ”Big Bang”


What are the consequences (Gamow)?What are the consequences (Gamow)?

• In order to form hydrogen and helium at the right In order to form hydrogen and helium at the right proportions, the following conditions are required:proportions, the following conditions are required:– density:density: 10 10-5-5 g/cm g/cm-3-3

– temperature:temperature: T T 10 109 9 KK

• Radiation from this epoch should be observable as an Radiation from this epoch should be observable as an isotropic background radiation isotropic background radiation

• Due to the expansion of the universe to Due to the expansion of the universe to 331010-30-30 g/cmg/cm33, the temperature should have , the temperature should have dropped to dropped to T T 5 5 K (-450 F)K (-450 F)

• Can we observe this radiation ?Can we observe this radiation ?


The discovery of the relic The discovery of the relic radiationradiation• Gamov’s result on the background radiation Gamov’s result on the background radiation

was not well recognized by the scientific was not well recognized by the scientific communitycommunity

• Result was rediscovered by Dicke and Result was rediscovered by Dicke and Peebles in the early sixties. They started Peebles in the early sixties. They started developing an antenna to search for the developing an antenna to search for the background radiationbackground radiation

• T T 5 5 K K microwaves microwaves

• but …but …


Penzias and Wilson 1965Penzias and Wilson 1965

• Working at Bell labsWorking at Bell labs

• Used a satellite dish to measure radio Used a satellite dish to measure radio emission of the Milky Wayemission of the Milky Way

• They found some extra noise in the They found some extra noise in the receiver, but couldn’t explain itreceiver, but couldn’t explain it discovery of the background radiation discovery of the background radiation

• Most significant cosmological observation Most significant cosmological observation since Hubblesince Hubble

• Nobel prize for physics 1978Nobel prize for physics 1978


A quote ...A quote ...

• John Bahcall: "The discovery of the cosmic John Bahcall: "The discovery of the cosmic microwave background radiation changed microwave background radiation changed forever the nature of cosmology, from a forever the nature of cosmology, from a subject that had many elements in common subject that had many elements in common with theology to a fantastically exciting with theology to a fantastically exciting empirical study of the origins and evolution empirical study of the origins and evolution of the things that populate the physical of the things that populate the physical universe."universe."


The Big Bang and the Creation of The Big Bang and the Creation of the elements (Hoyle + Saltpeter)the elements (Hoyle + Saltpeter)• Atoms are mostly empty spaceAtoms are mostly empty space

• Atoms consist of protons (+), neutrons (o) and Atoms consist of protons (+), neutrons (o) and electrons (-)electrons (-)

• protons and neutrons protons and neutrons form the atomic form the atomic nucleusnucleus

• # of protons deter-# of protons deter-mines the elementmines the element

• electrons in the outskirts determine chemistryelectrons in the outskirts determine chemistry


The structure of matterThe structure of matter

• Neutrons and protons are very similar, butNeutrons and protons are very similar, but– Protons are electrically charged, neutrons are notProtons are electrically charged, neutrons are not– Neutrons have a slightly higher massNeutrons have a slightly higher mass

• Electrons are much less massive than Electrons are much less massive than nucleons nucleons most of the mass of an atom is in most of the mass of an atom is in its nucleusits nucleus

• If charges of the same sign repel, and the If charges of the same sign repel, and the nucleus is made of protons, why don’t the nucleus is made of protons, why don’t the protons fly apart ?protons fly apart ?


n n p p++n n p p++ + e + e-- + n + n p p++ + e + e--

The four forces of natureThe four forces of nature

• gravity gravity

• electromagnetismelectromagnetism

• strong nuclear forcestrong nuclear force– keeps atomic nuclei togetherkeeps atomic nuclei together

• weak nuclear forceweak nuclear force– decay of free neutrons into protonsdecay of free neutrons into protons


The structure of matterThe structure of matter


Abundance of elementsAbundance of elements

• Hydrogen and helium Hydrogen and helium most abundantmost abundant

• gap around Li, Be, Bgap around Li, Be, B


Thermal history of the universeThermal history of the universe

• When the universe was younger than When the universe was younger than 300 000 yrs, it was so hot that neutral atoms 300 000 yrs, it was so hot that neutral atoms separated into nuclei and electrons. It was separated into nuclei and electrons. It was too hot to bind atomic nuclei and electrons too hot to bind atomic nuclei and electrons to atoms by the electromagnetic force to atoms by the electromagnetic force

• When the universe was younger than When the universe was younger than ~1 sec, it was so hot that atom nuclei ~1 sec, it was so hot that atom nuclei separated into neutrons and protons. It was separated into neutrons and protons. It was too hot to bind protons and neutrons to too hot to bind protons and neutrons to atomic nuclei by the strong nuclear force atomic nuclei by the strong nuclear force


Formation of helium in the big bangFormation of helium in the big bang

• HydrogenHydrogen: 1 nucleon (proton): 1 nucleon (proton)• HeliumHelium:: 4 nucleons (2 protons, 2 4 nucleons (2 protons, 2

neutrons)neutrons)• In order to from helium from hydrogen one In order to from helium from hydrogen one

has tohas to– bring 2 protons and 2 neutrons close together, so bring 2 protons and 2 neutrons close together, so

the strong nuclear force can act and hold them the strong nuclear force can act and hold them togethertogether

– close together: Coulomb repulsion has to be close together: Coulomb repulsion has to be overcome overcome high velocities high velocities high temperatures high temperatures

• but: but: 4 body collisions are highly unlikely4 body collisions are highly unlikely


Transforming hydrogen into heliumTransforming hydrogen into helium

• Hot big bang: Hot big bang: neutronsneutrons and and protonsprotons

• Use a multi step procedure:Use a multi step procedure:– p + n p + n 22H H – p + p + 22H H 33HeHe– n + n + 22H H 33HH– 33He + He + 33He He 44He + 2 pHe + 2 p

• some side reactions:some side reactions:– 33He + He + 33H H 77Li Li – 33He + He + 33He He 77Be Be


Mass gap/stability gap at A=5 and 8Mass gap/stability gap at A=5 and 8

• There is no stable atomic nucleus with 5 or There is no stable atomic nucleus with 5 or with 8 nucleonswith 8 nucleons

• Reaction chain stops at Reaction chain stops at 77LiLi

• So how to form the more massive elements?So how to form the more massive elements?

• There exist a meta-stable nucleus (There exist a meta-stable nucleus (88B*B*). If ). If this nucleus is hit by another this nucleus is hit by another 44HeHe during its during its lifetime, lifetime, 1212CC and other elements can be and other elements can be formedformed


Mass gap/stability gap at A=5 and 8Mass gap/stability gap at A=5 and 8• Reaction chain:Reaction chain:

– 44He + He + 44He He 88B* B* – 88B* + B* + 44He He 1212CC

• so-called 3-body reaction (Saltpeter)so-called 3-body reaction (Saltpeter)• in order to have 3-body reactions, high in order to have 3-body reactions, high

particle densities are requiredparticle densities are required– densities are not high enough in the big-bangdensities are not high enough in the big-bang– but they are in the center of evolved starsbut they are in the center of evolved stars

• Conclusion: big bang synthesizes elements up Conclusion: big bang synthesizes elements up to to 77Li. Higher elements are formed in starsLi. Higher elements are formed in stars


Primordial nucleosynthesisPrimordial nucleosynthesis

Result:Result:• abundance of abundance of

H,He and Li is H,He and Li is consistentconsistent

• but:but: bb ~0.04 ~0.04

Consistent with Consistent with

abundanceabundance

of H, He and Liof H, He and Li


How far can we see ?How far can we see ?

• Naked eye: 2 million Light years Naked eye: 2 million Light years (Andromeda galaxy)(Andromeda galaxy)

• Large telescopes: 14 billion Lyr (z=5.8)Large telescopes: 14 billion Lyr (z=5.8)

• What are the limiting factors ?What are the limiting factors ?– there are no bright sources at high zthere are no bright sources at high z– light is redshifted into the infraredlight is redshifted into the infrared– absorptionabsorption

• The universe appears to be fairly The universe appears to be fairly transparent out to z=5.8transparent out to z=5.8


When does a gas become opaque?When does a gas become opaque?• A gas appears opaque (e.g. fog) if light is A gas appears opaque (e.g. fog) if light is

efficiently scattered by the atoms/molecules efficiently scattered by the atoms/molecules of the gasof the gas

The three important factors are thusThe three important factors are thus– the density of the gas the density of the gas

(denser (denser more particles more particles more scattering) more scattering)– the efficiency with which each individual the efficiency with which each individual

particle can scatter lightparticle can scatter light– wavelength of the lightwavelength of the light


The transition from a transparent The transition from a transparent to an opaque universeto an opaque universe

• At At zz=0=0 the universe is fairly transparent the universe is fairly transparent

• At higher At higher zz, the universe becomes denser , the universe becomes denser (( = = 00(1+z)(1+z)33) and hotter () and hotter (T=TT=T00(1+z)(1+z)))

• At At zz=1100=1100, the universe is so dense that its , the universe is so dense that its temperature exceeds 3000K. In a fairly temperature exceeds 3000K. In a fairly sharp transition, the universe becomes sharp transition, the universe becomes completely ionized and opaque to visible completely ionized and opaque to visible light. (last scattering surface)light. (last scattering surface)

• At At zz=1100=1100, the universe is ~300 000 yrs old, the universe is ~300 000 yrs old


Black body radiationBlack body radiation

• A hot a body is brighter than a cool one A hot a body is brighter than a cool one ((LLTT44, , Stefan-Boltzmann’s lawStefan-Boltzmann’s law))

• A hot body’s spectrum is bluer than that of a A hot body’s spectrum is bluer than that of a cool one (cool one (maxmax1/1/TT, , Wien’s lawWien’s law))


The cosmic microwave The cosmic microwave background radiation (CMB)background radiation (CMB)

• Temperature of Temperature of 2.728±0.004 K2.728±0.004 K

• isotropic to isotropic to 1 part in 100 0001 part in 100 000

• perfect black bodyperfect black body

• 1990ies: CMB is 1990ies: CMB is one of the major tools to study cosmologyone of the major tools to study cosmology

• Note: ~1% of the noise in your TV is from Note: ~1% of the noise in your TV is from the big bangthe big bang


Should the CMB be perfectly Should the CMB be perfectly smooth ?smooth ?

• No. Today’s Universe No. Today’s Universe is homogeneous and is homogeneous and isotropic on the largest isotropic on the largest scales, but there is a fair scales, but there is a fair amount of structure on amount of structure on small scales, such as small scales, such as galaxies, clusters of galaxies, clusters of galaxies etc.galaxies etc.


Should the CMB be perfectly Should the CMB be perfectly smooth ?smooth ?

• We expect some We expect some wriggles in the CMB wriggles in the CMB radiation, corresponding radiation, corresponding to the seeds from which to the seeds from which later on galaxies growlater on galaxies grow


The Cosmic Background Explorer The Cosmic Background Explorer (COBE)(COBE)

Main objectives:Main objectives:

• To accurately To accurately measure the measure the temperature of the temperature of the CMBCMB

• To find the expected To find the expected fluctuations in the fluctuations in the CMBCMB


Main results from COBEMain results from COBE


More results from the CMBMore results from the CMB

• The Earth is moving The Earth is moving with respect to the with respect to the CMB CMB Doppler shift Doppler shift– Earth’s motion around Earth’s motion around

the Sunthe Sun– Sun’s motion around Sun’s motion around

the Galaxythe Galaxy– Motion of the Galaxy Motion of the Galaxy

with respect to other with respect to other galaxies (large scale galaxies (large scale flows)flows)



• The Earth is moving The Earth is moving with respect to the with respect to the CMB CMB Doppler shift Doppler shift

• The emission of the The emission of the GalaxyGalaxy



• The Earth is moving The Earth is moving with respect to the with respect to the CMB CMB Doppler shift Doppler shift

• The emission of the The emission of the GalaxyGalaxy

• Fluctuations in the Fluctuations in the CMBCMB


The BOOMERANG missionThe BOOMERANG mission• COBE was a satellite mission, why ?COBE was a satellite mission, why ?

– Measure at mm and sub-mm wavelengthsMeasure at mm and sub-mm wavelengths– Earth atmosphere almost opaque at those wave-Earth atmosphere almost opaque at those wave-

lengths due to water vaporlengths due to water vapor– satellite missions take a satellite missions take a

long time and are expensivelong time and are expensive

• What can be done from the What can be done from the ground ?ground ?– Balloon experimentBalloon experiment– desert desert South Pole South Pole


The BOOMERANG missionThe BOOMERANG mission


How can we measure How can we measure the the geometry of the universegeometry of the universe• We need a yard stick on the CMBWe need a yard stick on the CMB

• For different curvatures, a yard stick of For different curvatures, a yard stick of given length appears under different anglesgiven length appears under different angles


Measuring the Curvature of the Measuring the Curvature of the Universe Using the CMBUniverse Using the CMB


Measuring the Curvature of the Measuring the Curvature of the Universe Using the CMBUniverse Using the CMB• Recall: with Recall: with

supernovae, one supernovae, one measures measures qq00 =½ =½00 – –

• CMB fluctuations CMB fluctuations measure curvaturemeasure curvature 00 + +

• two equations for two equations for two variablestwo variables problem solved problem solved


What comes next ?What comes next ?

WMAPWMAP PlanckPlanck


Can we see the sound of the Can we see the sound of the universe ?universe ?• Compressed gas heats upCompressed gas heats up

temperature fluctuations temperature fluctuations


Acoustic Oscillations in the CMBAcoustic Oscillations in the CMB

• Although there are fluctuations on all scales, there is Although there are fluctuations on all scales, there is a characteristic angular scale.a characteristic angular scale.


Acoustic Oscillations in the CMBAcoustic Oscillations in the CMB

WMAP team (Bennett et al. 2003)WMAP team (Bennett et al. 2003)


Last scattering surfaceLast scattering surface

transparenttransparent

opaqueopaque


Sound Waves in the Early UniverseSound Waves in the Early Universe

Before recombination:Before recombination:– Universe is ionized. Universe is ionized.

– Photons provide enormous Photons provide enormous pressure and restoring force. pressure and restoring force.

– Perturbations oscillate as Perturbations oscillate as acoustic waves.acoustic waves.

After recombination:After recombination:– Universe is neutral.Universe is neutral.

– Photons can travel freely Photons can travel freely past the baryons.past the baryons.

– Phase of oscillation at tPhase of oscillation at trecrec

affects late-time amplitude.affects late-time amplitude.

Big

Ban

g Tod

ay

Recombinationz ~ 1000

~400,000 yearsIonized Neutral

Time


Sound WavesSound Waves

• Each initial overdensity (in DM & gas) Each initial overdensity (in DM & gas) is an overpressure that launches a is an overpressure that launches a spherical sound wave.spherical sound wave.

• This wave travels outwards at This wave travels outwards at 57% of the speed of light.57% of the speed of light.

• Pressure-providing photons decouple at Pressure-providing photons decouple at recombination. CMB travels to us from recombination. CMB travels to us from these spheres.these spheres.

• Sound speed plummets. Wave stalls at a Sound speed plummets. Wave stalls at a radius of 150 Mpc.radius of 150 Mpc.

• Overdensity in shell (gas) and in the Overdensity in shell (gas) and in the original center (DM) both seed the original center (DM) both seed the formation of galaxies. Preferred formation of galaxies. Preferred separation of 150 Mpc.separation of 150 Mpc.

QuickTime™ and aGIF decompressor

are needed to see this picture.


A Statistical SignalA Statistical Signal

• The Universe is a super-The Universe is a super-position of these shells.position of these shells.

• The shell is weaker than The shell is weaker than displayed.displayed.

• Hence, you do not Hence, you do not expect to see bullseyes expect to see bullseyes in the galaxy in the galaxy distribution.distribution.

• Instead, we get a 1% Instead, we get a 1% bump in the correlation bump in the correlation function.function.


Cosmological ConstraintsCosmological Constraints

12

WMAP 1 range

Pure CDM degeneracy

Acoustic scale alone


The History of the UniverseThe History of the UniverseThe The “Concordance” Model“Concordance” Model (not yet the “Standard Model”) of (not yet the “Standard Model”) of

Cosmology:Cosmology:

The Universe is homogeneous and flat (horizon problem The Universe is homogeneous and flat (horizon problem and flatness problem)and flatness problem)

The Universe evolved from a quantum fluctuation no bigger The Universe evolved from a quantum fluctuation no bigger

thanthan 1010-35-35 mm in diameter.in diameter.

Since gravitational energy is negative and the energy of a Since gravitational energy is negative and the energy of a massive object is positive, the total energy of the quantummassive object is positive, the total energy of the quantumfluctuation can be zerofluctuation can be zeroIf the fluctuation now expands it may become the entire universeIf the fluctuation now expands it may become the entire universeThe “Concordance” Model postulates that the initial expansion wasThe “Concordance” Model postulates that the initial expansion wasvery rapid indeed (cosmic inflation) very rapid indeed (cosmic inflation)


History of the Universe (with History of the Universe (with Inflation)Inflation)


Inflation (potential)Inflation (potential)


Matter eraMatter era

• The energy of matter is nowadays ~10000 The energy of matter is nowadays ~10000 times higher than that of radiationtimes higher than that of radiation

• but temperature rises like but temperature rises like (1+z)(1+z)

• 2.7K < T < 10000K2.7K < T < 10000K: matter era: matter era

• dominate particles (in order of decreasing dominate particles (in order of decreasing contribution:contribution:– baryonsbaryons, photons, neutrinos, photons, neutrinos

• dominant forces:dominant forces:– gravitygravity


Radiation eraRadiation era

• As the temperature exceeds ~ 10000K, As the temperature exceeds ~ 10000K, radiation starts dominatingradiation starts dominating

• 10000K < T < 1010000K < T < 101010KK: radiation era: radiation era

• dominate particles (in order of decreasing dominate particles (in order of decreasing contribution:contribution:– photons, neutrinosphotons, neutrinos, baryons, baryons

• dominant forces:dominant forces:– electromagnetismelectromagnetism, gravity, gravity


Electron-positron annihilationElectron-positron annihilation

• As the temperature exceeds ~ 10As the temperature exceeds ~ 101010K, K, creation of electron-positron pairscreation of electron-positron pairs– T > 10T > 101010K: equilibrium between electron-K: equilibrium between electron-

positron pair creation and annihilationpositron pair creation and annihilation– T < 10T < 101010K: freeze-out. Remaining pairs K: freeze-out. Remaining pairs

annihilateannihilate


Lepton eraLepton era

• 10101010KK < T << T < 10101212KK

• dominate particles (in order of decreasing dominate particles (in order of decreasing contribution:contribution:– electrons, positrons, photons, neutrinos, electrons, positrons, photons, neutrinos,

antineutrinosantineutrinos, baryons, baryons

• dominant forces:dominant forces:– electromagnetism, weak nuclearelectromagnetism, weak nuclear, gravity, gravity


Hadron annihilationHadron annihilation

• As the temperature exceeds ~ 10As the temperature exceeds ~ 101212K, K, creation of hadron-antihadron pairs (e.g. creation of hadron-antihadron pairs (e.g. proton-antiproton)proton-antiproton)– T > 10T > 101212K: equilibrium between hadron pair K: equilibrium between hadron pair

creation and annihilationcreation and annihilation– T < 10T < 101212K: freeze-out. Remaining pairs K: freeze-out. Remaining pairs

annihilateannihilate


Hadron eraHadron era

• 10101212KK < T << T < 10101313KK

• dominate particles (in order of decreasing dominate particles (in order of decreasing contribution:contribution:– baryons+antiparticles, mesons+antiparticles, baryons+antiparticles, mesons+antiparticles,

electrons, positrons, photons, neutrinos, electrons, positrons, photons, neutrinos, antineutrinosantineutrinos

• dominant forces:dominant forces:– electromagnetism, strong nuclear, weak electromagnetism, strong nuclear, weak

nuclearnuclear, gravity, gravity


Still quark eraStill quark era

• 10101313KK < T << T < 10101515KK• hadrons (baryons, mesons) break into hadrons (baryons, mesons) break into

quarksquarks• dominate particles (in order of decreasing dominate particles (in order of decreasing

contribution:contribution:– quarks, antiquarks, electrons, positrons, quarks, antiquarks, electrons, positrons,

photons, neutrinos, antineutrinosphotons, neutrinos, antineutrinos

• dominant forces:dominant forces:– electromagnetism, strong nuclear, weak electromagnetism, strong nuclear, weak

nuclearnuclear, gravity, gravity


Electroweak phase transitionElectroweak phase transition

• As the temperature exceeds ~ 10As the temperature exceeds ~ 101515K, K, electromagnetism and weak nuclear force electromagnetism and weak nuclear force join to form the electroweak forcejoin to form the electroweak force– T > 10T > 101515K: electroweak forceK: electroweak force– T < 10T < 101515K: electromagnetism, weak nuclear K: electromagnetism, weak nuclear

forceforce

• Limit of what we can test in particle Limit of what we can test in particle accelerators.accelerators.

• Nobel prizes 1979 (theory) and 1984 Nobel prizes 1979 (theory) and 1984 (experiment)(experiment)


Quark eraQuark era

• 10101515KK < T << T < 10102929KK

• dominate particles (in order of decreasing dominate particles (in order of decreasing contribution:contribution:– quarks, antiquarks, electrons, positrons, quarks, antiquarks, electrons, positrons,

photons, neutrinos, antineutrinosphotons, neutrinos, antineutrinos

• dominant forces:dominant forces:– electroweak, strong nuclearelectroweak, strong nuclear, gravity, gravity


GUT phase transitionGUT phase transition

• As the temperature exceeds ~ 10As the temperature exceeds ~ 102929K, K, electroweak force and strong nuclear force electroweak force and strong nuclear force join to form the GUT (grand unified join to form the GUT (grand unified theories)theories)– T > 10T > 102929K: GUTK: GUT– T < 10T < 102929K: electroweak force, strong nuclear K: electroweak force, strong nuclear

forceforce

• relatively solid theoretical framework (but relatively solid theoretical framework (but may be wrong), but pretty much no may be wrong), but pretty much no constraint by experimentsconstraint by experiments


GUT eraGUT era

• 10102929KK < T << T < 10103232KK

• dominate particles (in order of decreasing dominate particles (in order of decreasing contribution:contribution:– Zillions of particles, most of them not detected Zillions of particles, most of them not detected

yet yet

• dominant forces:dominant forces:– GUTGUT, gravity, gravity


Planck epochPlanck epoch

• T > 10T > 103232K unification of GUT and gravityK unification of GUT and gravity

• Particles:Particles:– ??????

• Forces:Forces:– TOE (theory of everything)TOE (theory of everything)

• The last frontier ...The last frontier ...


Structure formation in the Big-Bang Structure formation in the Big-Bang modelmodel


The Hubble sequence of galaxiesThe Hubble sequence of galaxies


A galaxy census: spiral galaxies A galaxy census: spiral galaxies • Most common type among the luminous Most common type among the luminous

galaxies (~75%)galaxies (~75%)• two major classes, two major classes, SS and and SBSB

– regular spirals (regular spirals (SS))– barred spirals (barred spirals (SBSB))

• further classified from further classified from aa to to dd according to according to the bulge-to-disk ratiothe bulge-to-disk ratio– aa: very large, prominent bulge: very large, prominent bulge– dd: essentially no bulge at all: essentially no bulge at all

• The Milky Way is a Sbc or a SBbc galaxyThe Milky Way is a Sbc or a SBbc galaxy


A galaxy census: spiral galaxies A galaxy census: spiral galaxies • Spiral galaxies are disk like and in Spiral galaxies are disk like and in

centrifugal equilibriumcentrifugal equilibrium• The are “cold”, i.e. the velocity dispersion The are “cold”, i.e. the velocity dispersion

(random motion of individual stars) (random motion of individual stars) is is much smaller than the rotation velocity much smaller than the rotation velocity vvrot rot

(Milky Way: (Milky Way: =20 km/s=20 km/s; ; vvrotrot=220 km/s=220 km/s))• They mainly consist of stars, but ~10% of They mainly consist of stars, but ~10% of

the mass is gas and dustthe mass is gas and dust• They actively form stars (Milky Way: ~ 1 They actively form stars (Milky Way: ~ 1

star per year)star per year)


A galaxy census: elliptical galaxies A galaxy census: elliptical galaxies • ~20% of the luminous galaxies are ellipticals~20% of the luminous galaxies are ellipticals• classified according to the flattening E0-E7: classified according to the flattening E0-E7:

n=10n=10(1-b/a)(1-b/a)– E0: circularE0: circular

– E7: minor axis only 30% of major axisE7: minor axis only 30% of major axis

• They are “hot”, i.e. the velocity dispersion They are “hot”, i.e. the velocity dispersion is much is much larger than the rotation velocity larger than the rotation velocity vvrot rot

• flattened by an anisotropic velocity dispersionflattened by an anisotropic velocity dispersion• little gas, no recent star formationlittle gas, no recent star formation• predominantly in clusters of galaxiespredominantly in clusters of galaxies


A galaxy census: other galaxies A galaxy census: other galaxies

• Irregular galaxies (~ 5% of the luminous Irregular galaxies (~ 5% of the luminous galaxies)galaxies)

• dwarf galaxiesdwarf galaxies– dwarf irregularsdwarf irregulars– dwarf spheroidalsdwarf spheroidals– dwarf ellipticalsdwarf ellipticals– blue compact dwarfsblue compact dwarfs– ......


Toomre & Toomre Toomre & Toomre (mid 70s)(mid 70s)• 11 out of the 4000 galaxies 11 out of the 4000 galaxies

in the in the New General CatalogNew General Catalog (NGC) show indications of(NGC) show indications ofrecent interactions (e.g. tails)recent interactions (e.g. tails)

• Those tidal features last a few 10Those tidal features last a few 1088 years years• Over the age of the universe, several Over the age of the universe, several

hundred of those interactions must have hundred of those interactions must have taken placetaken place

• There are several hundred elliptical galaxies There are several hundred elliptical galaxies in the NGCin the NGC


Do ellipticals form by merging Do ellipticals form by merging spirals ?spirals ?


Younger galaxies should be smaller ...Younger galaxies should be smaller ...


How good is the assumption of How good is the assumption of isotropy?isotropy?• CMB: almost perfectCMB: almost perfect

• but what about the closer neighborhood ?but what about the closer neighborhood ?


How good is the assumption of How good is the assumption of isotropy?isotropy?• CMB: almost perfectCMB: almost perfect

• but what about the closer neighborhood ?but what about the closer neighborhood ?

The great The great

wallwall


• Galaxies are not randomly Galaxies are not randomly distributed but correlateddistributed but correlated

• Network of structures Network of structures (filaments, sheets, walls) (filaments, sheets, walls) “cosmic web” “cosmic web”

The spatial distribution of galaxiesThe spatial distribution of galaxies

Courtesy: Huan LinCourtesy: Huan Lin


z=9.00z=9.00

65 M

pc65

Mpc

50 million 50 million particle particle N-body N-body simulationsimulation


z=4.00z=4.00

65 M

pc65

Mpc



z=2.33z=2.33

65 M

pc65

Mpc



z=1.00z=1.00

65 M

pc65

Mpc



z=0.00z=0.00

65 M

pc65

Mpc



Does a picture like this look Does a picture like this look familiar ?familiar ?


Counting all the mass ...Counting all the mass ...

• Obstacle: Obstacle: we want mass, but we see lightwe want mass, but we see light• Procedure:Procedure:

– count all the stars you see and multiply them count all the stars you see and multiply them with there luminosity with there luminosity total visible luminosity total visible luminosity

– correct for dust absorption correct for dust absorption total luminosity total luminosity– convert luminosity into mass using a mass-to-convert luminosity into mass using a mass-to-

light ratiolight ratio

– The sun has The sun has =1=1 by definition. by definition.

sun

sun

LL

MM

/

/

sun

sun

LL

MM

/

/


Overall result:Overall result:

Implications:Implications:• less than the nucleosynthesis constraint of less than the nucleosynthesis constraint of =0.04 =0.04

in baryons in baryons consistent consistent• Most of the baryons in the universe (~75%) do not Most of the baryons in the universe (~75%) do not

shine [are too dim to be detected] shine [are too dim to be detected] – gas and dustgas and dust– stellar remnants (white dwarfs, neutron stars, black stellar remnants (white dwarfs, neutron stars, black

holes)holes)– brown dwarfs [failed stars]brown dwarfs [failed stars]

01.0 01.0


Evidence of dark matter: Evidence of dark matter: rotation curves of spiral galaxiesrotation curves of spiral galaxies


Fritz Zwicky Fritz Zwicky

He measured the He measured the velocities of galaxies velocities of galaxies in galaxy clusters in galaxy clusters and concluded that and concluded that most of the cluster’s most of the cluster’s mass must be darkmass must be dark


Evidence of dark matter: Evidence of dark matter: X-ray clusters X-ray clusters


Evidence of dark matter: Evidence of dark matter: clusters of galaxies clusters of galaxies


Evidence of dark matter: Evidence of dark matter: large scale flowslarge scale flowsEvidence of dark matter: Evidence of dark matter: large scale flowslarge scale flows


Overall result:Overall result:

Implications:Implications:• most of the mass in the Universe is darkmost of the mass in the Universe is dark• most of it is even of non-baryonic originmost of it is even of non-baryonic origin• the perfect Copernican principlethe perfect Copernican principle

– The Earth is not at the center of the solar systemThe Earth is not at the center of the solar system– The Sun is not at the center of the Milky WayThe Sun is not at the center of the Milky Way– The Milky Way is not at the center of the UniverseThe Milky Way is not at the center of the Universe– We may not even be made from the most abundant type of We may not even be made from the most abundant type of

matter in the Universe matter in the Universe

3.0 3.0


Is the claim that dark matter exist Is the claim that dark matter exist really so embarrassing ?really so embarrassing ?• When Leverrier was proposing in When Leverrier was proposing in

the 1840s that there maybe anthe 1840s that there maybe an8th planet in the solar system,8th planet in the solar system,NeptuneNeptune, a planet that can explain , a planet that can explain the irregularities of Uranus’ orbit,the irregularities of Uranus’ orbit,this planet was also this planet was also “dark matter”“dark matter”

• But it was a clear prediction that eventually But it was a clear prediction that eventually could be tested observationallycould be tested observationally

• The discovery of The discovery of NeptuneNeptune by Galle was one by Galle was one of the finest moments of science of the finest moments of science


MACHOs ?MACHOs ?• MAMAssive ssive CCompact ompact HHalo alo OObjectsbjects• Brown dwarfs (stars not massive enough to Brown dwarfs (stars not massive enough to

shine)shine)• Dim white dwarfs (relics of stars like the Dim white dwarfs (relics of stars like the

Sun)Sun)• Massive black holes (stars that massive that Massive black holes (stars that massive that

even light cannot escape)even light cannot escape)• but: but: if the DM is really in MACHOs, if the DM is really in MACHOs,

something with the nucleosynthesis something with the nucleosynthesis constraint must be wrongconstraint must be wrong


How can we see MACHOs ?How can we see MACHOs ?

• Gravitational lensing:Gravitational lensing:

• If foreground object has only little mass, the If foreground object has only little mass, the image split is too small to be observedimage split is too small to be observed

• But the amplification (brightening) is But the amplification (brightening) is observableobservable



• How likely is it for a star in the Milky Way How likely is it for a star in the Milky Way to get amplified ?to get amplified ?

• Once every 10 million yearsOnce every 10 million years



• Solution: monitor 10 million stars Solution: monitor 10 million stars simultaneouslysimultaneously



Alcock et al. 1993Alcock et al. 1993

Magnification due Magnification due to gravitational to gravitational lensinglensing

There are not There are not enough brown enough brown dwarfs to account dwarfs to account for the dark matter for the dark matter in the Milky Way.in the Milky Way.


WIMPs ?WIMPs ?• WWeakly eakly IInteracting nteracting MMassive assive PParticlesarticles• Massive neutrino Massive neutrino

– at least we know that it existsat least we know that it exists– we don’t know whether it has mass or notwe don’t know whether it has mass or not– hot dark matter (hot: moving at speeds near the hot dark matter (hot: moving at speeds near the

speed of light) speed of light)

• Another (yet undiscovered) particle Another (yet undiscovered) particle predicted by some particle physicistspredicted by some particle physicists– cold dark matter (cold: moving much slower cold dark matter (cold: moving much slower

than the speed of light)than the speed of light)


SummarySummary

• The Universe is stranger than Alice’s The Universe is stranger than Alice’s WonderlandWonderland

• We have only scratched the surface of what We have only scratched the surface of what is know is know

• Many insights and observations still to Many insights and observations still to come come

Physics 270 – The Universe: Astrophysics, Gravity and Cosmology

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Transcript of Physics 270 – The Universe: Astrophysics, Gravity and Cosmology