Cosmology

Observational evidence?

“Cosmologists are often in error but never in doubt.”

L.D. Landau

Cosmology

Observation #1: universe is homogeneous and isotropic at large scales

It cannot be stationary! It should expand or contract

Observation #2: universe is expanding (Hubble)

It should have a beginning! Hot or cold??

Observation #3: Cosmic microwave background radiation

Hot Big Bang!

Fate of the universe: depends on mass distribution (or curvature)

Observation #4: Abundance of light elements

Confirms Hot Big Bang

Observation #5: density measurements

Observation #6: Fluctuations of background radiation

Universe is nearly flat; it contains dark matter and “dark energy”

Problems with standard Big Bang model

Theory of inflation

Formation of structure;Planck scale, Theory of Everything

WHY our universe has the parameters that we observe?

Anthropic Principle and beyond

"The Universe must have those properties which allow carbon-based life to develop within it at some stage in its history."

Observation #1: universe is very inhomogeneous and anisotropic at smaller scales …

Groups clusters superclusters

The universe is homogeneous. This means there is no preferred observing position in the universe. The universe is also isotropic. This means you see no difference in the structure of the universe as you look in different directions.

… but homogeneous and isotropic at large scale(The Cosmological Principle)

The Cosmological PrincipleConsidering the largest scales in the universe, we make the following fundamental assumptions:

1) Homogeneity: On the largest scales, the local universe has the same physical properties throughout the universe.

Every region has the same physical properties (mass density, expansion rate, visible vs. dark matter, etc.)

2) Isotropy: On the largest scales, the local universe looks the same in any direction that one observes.

You should see the same large-scale structure in any direction.

3) Universality: The laws of physics are the same everywhere in the universe.

The universe cannot be stationary!

Force per unit mass:

2

)(

r

rGMF

Energy per unit mass:

const)(

2

2

r

rGMvE

Conclusion: the universe should either contract or expand with decreasing speed, because the gravity slows down the expansion

What is in reality?

Hubble and Humason 1931: Vrecession = H0 R

The universe expands!

Edwin Hubble

Hubble’s Law

Distant galaxies are receding from us with a speed proportional to distance

The Necessity of a Big Bang

If galaxies are moving away from each other with a speed proportional to distance, there must have been a beginning, when everything was concentrated in one single point:

The Big Bang!

?

The Age of the Universe

Knowing the current rate of expansion of the universe, we can estimate the time it took for galaxies to move as far apart as they are today:

T ≈ d/v = 1/H ~ 15 billion years

Time = distance / velocity

velocity = (Hubble constant) * distance

Necessity of the Big Bang

RHv 0

The time of expansion is T ~ 1/H0 ~ 15 billion years

15 billion years ago all distances R were equal to 0

Velocity = distance / time

Current value of the Hubble constant H0 70 km/s/Mpc

Olbers’s ParadoxWhy is the sky dark at night?

If the universe is infinite, then every line of sight should end on

the surface of a star at some point. The night sky should be as

bright as the surface of stars!

Solution to Olbers’s Paradox:

If the universe had a beginning, then we can only see light from galaxies that has

had time to travel to us since the beginning of the universe.

The visible universe is finite!

Mass within radius r(t):

const3

4)( 3 RtM

Energy per unit mass:

const)(

2

2

R

RGMvE

Hubble law:

dt

dRtRtHv )()(

Newtonian model of the universe

dt

dRtRtHv )()(

)(

)()(

)(

1)(

tR

tv

dt

tdR

tRtH

Hubble “constant” changes with time!

Solution for k = 0:

2

2

8

3

R

k

G

H

Main equation:

ttH

ttttR

3

2)(;

1)(;)( 2

3/2

Critical density:G

Hc

8

3 2

:0, kc Indefinite expansion

:0, kc Expansion will be replaced by contraction

:0, kc Indefinite expansion but with speed approaching zero

32910~cm

gc

T = 2/3H0 = 9.5 billion years

But the age of globular clusters is 13 billion years!

Cosmology and General Relativity

According to the theory of general relativity, gravity is caused by

the curvature of space-time.

The effects of gravity on the largest cosmological scales should be related to the curvature of space-time!

The curvature of space-time, in turn, is determined by the distribution of mass and energy in the universe.

Space-time tells matter how to move;

matter tells space-time how to curve.

General relativistic models

Matter (mass, energy, pressure)

Geometry of space-time

Einstein’s equations

The Expanding UniverseOn large scales, galaxies are moving apart,

with velocity proportional to distance.

It’s not galaxies moving through space.

Space is expanding, carrying the galaxies along!

The galaxies themselves are not expanding!

2D analogy with houses on the balloon

Now add another dimension and you have our situation. Just like there is not new balloon material being created in the 2D analogy, new three-dimensional space is not being created in the expansion. Like any analogy, though, the balloon analogy has its limits. In the analogy, the balloon expands into the region around it---there is space beyond the balloon. However, with the expanding universe, space itself is expanding in three dimensions---the whole coordinate system is expanding. Our universe is NOT expanding ``into'' anything ``beyond''.

No center and no edge

The Expanding Universe (2)

You have the same impression from any other galaxy as well.

Hubble law does not mean that we are at the center of the universe!

Expanding Space

Analogy:

A loaf of raisin bread where the dough is rising and expanding, taking the raisins with it.

Raisin Bread

(SLIDESHOW MODE ONLY)

1)(

)(

1

0 tR

tRz

Cosmological redshift

t1 t0

General relativity picture

Galaxies are at rest in the comoving (expanding) frame

Due to the presence of matter, the universe is non-stationary: all distances change; scale factor R(t) is a function of time

222222222

22 )sin)((1

)(dtdrdrtRdr

kr

tRds

Metric of the homogeneous and isotropic Universe

Robertson, Walker, Friedman, Lemaitre

Curvature = )(2 tR

k

Scale factor R(t) describes expansion or contraction

2222222222 )sin( dtdrdrRdrRds

Compare with metric for empty flat space:

Finite, But Without Edge?

2-dimensional analogy: Surface of a sphere:

Surface is finite, but has no edge.

For a creature living on the sphere, having no sense of the

third dimension, there’s no center (on the sphere!): All points are

equal.

Alternative: Any point on the surface can be defined as the center of a coordinate system.

k = +1: positive curvature (sphere)

k = -1: negative curvature (saddle)

k = 0: zero curvature (flat)

finite volume )(2 32 tRV

Curvature = )(2 tR

k

Shape and Geometry of the Universe

Back to our 2-dimensional analogy:

Measure curvature of its space!

Closed surface

Flat surface

Open surface

(positive curvature)

(zero curvature)

(negative curvature)

How can a 2-D creature investigate the geometry of the sphere?

p.309

p.309

p.309

Equation of state: relation between pressure P and energy density c2

= 0 for dust (no pressure) = 1/3 for radiation (very hard pressure)

Or: acceleration = )31(3

42

2

R

G

dt

Rd

Einstein’s equations:

const)1(3 R

2

22

8

3

8

3

GR

kc

G

H

2cP

c

Critical parameter

G

Hc

8

3 2

0:1

1:1

1:1

k

k

k

dt

tdR

tRtH

)(

)(

1)(

George Gamow (lived 1904--1968) predicted in 1948 that there should be a faint glow left over from when the universe was much hotter and denser. The entire universe would have glowed first in the gamma ray band, then the X-ray band, then to less energetic bands as the universe expanded. By now, about 14 billion years after the start of the expansion, the cold universe should glow in the radio band.

Hot or cold universe??Any signatures of the past around us?

Microwave background radiation!

Stopped here 12/1/05

The cosmogenesis paper with Alpher (“The origin of chemical elements”) was published as the Alpher-Bethe-Gamow theory, Gamow had added the name of Hans Bethe to make a pun on the first three letters of the Greek alphabet, alpha beta gamma.

George Gamow

Proposed the concept of the Hot Big Bang

Explained the origin of chemical elements in the universe

Built the theory of radioactivity and explained the nucleosynthesis in stars

Proposed a concept of genetic code and explained how the code is implemented in DNA by the order of nucleotides

Born 1904 in Russia Studied and worked at St.-Petersburg UniversityFled Russia in 1934Worked at GW University and University of Colorado

Looking Back Towards the Early Universe

The more distant the objects we observe, the further back into the past of the universe we are looking.

Fig. 15-9, p.304

The Cosmic Background Radiation

R. Wilson & A. Penzias

The radiation from the very early phase of the universe should still be detectable today

Was, in fact, discovered in mid-1960s as the Cosmic Microwave Background:

Blackbody radiation with a temperature of T = 2.73 K

Arno Penzias and Robert Wilson observed in 1965 a radio background source that was spread all over the universe---the cosmic microwave background radiation. The radiation has the same intensity and spectral character as a thermal continuous source at 3 K (more precisely, 2.728 ± 0.004 K) as measured by the COBE satellite in every direction observed. To a high degree of precision the sky is uniformly bright in radio. The uniformity of the background radiation is evidence for the cosmological principle.

From 3000 K to 2.7 K:The redshift of 1000!

Fig. 15-6c, p.301

The History of the Universe

Universe expands as time passes

Un

ive

rse

coo

ls d

own

as

time

pa

sse

s

The Early History of the UniverseElectron

Positron

Gamma-ray photon

Electrons, positrons, and gamma-rays in equilibrium between pair

production and annihilation

For reasons not completely understood, there was a very slight excess of ordinary matter over antimatter (by about 1 part in 109). This is why there was still some ordinary matter left over when all the antimatter had been annihilated. (This must be the case, otherwise you wouldn't be here!) All of the protons, neutrons, and electrons in matter today were created in the first few seconds after the Big Bang.

The Early History of the Universe (2)

Protons and neutrons form a few helium nuclei; the rest of protons

remain as hydrogen nuclei

Almost no elements heavier

than helium are produced.

25% of mass in helium 75% in hydrogen

No stable nuclei with 5 and 8 protons

Cosmic Abundance of Helium and HydrogenThe Big Bang theory provides a natural way to explain the present abundance of the elements. At about 2 to 3 minutes after the Big Bang, the expanding universe had cooled to below about 109 K so that protons and neutrons could fuse to make stable deuterium nuclei (a hydrogen isotope with one proton and one neutron) that would not be torn apart by energetic photons. Protons react to produce deuterium, deuterium nuclei react to make Helium-3 nuclei, and Helium-3 nuclei react to make the stable Helium-4 nucleus.

The deuterium nucleus is the weak link of the chain process, so the fusion chain reactions could not take place until the universe had cooled enough. The exact temperature depends sensitively on the density of the protons and neutrons at that time. Extremely small amounts of Lithium-7 were also produced during the early universe nucleosynthesis process. After about 15 minutes from the Big Bang, the universe had expanded and cooled so much that fusion was no longer possible. The composition of the universe was 10% helium and 90% hydrogen (or if you use the proportions by mass, then the proportions are 25% helium and 75% hydrogen). Except for the extremely small amounts of the Lithium-7 produced in the early universe, the elements heavier than helium were produced in the cores of stars.

Fig. 15-8, p.303

Fig. 15-14, p.311

The Nature of Dark MatterCan dark matter be composed of normal matter?

• If so, then its mass would mostly come from protons and neutrons = baryons

• The density of baryons right after the big bang leaves a unique imprint in the abundances of deuterium and lithium.

• Density of baryonic matter is only ~ 4 % of critical density.

• Most dark matter must be non-baryonic!

The Early History of the Universe (3)

Photons are incessantly scattered by free electrons; photons are in

equilibrium with matter

Radiation dominated era

Photons have a blackbody spectrum at the same temperature

as matter.

RecombinationProtons and electrons recombine

to form atoms => universe becomes transparent for photons

Transition to matter dominated era

z ≈1000

The Cosmic Background Radiation (2)After recombination, photons can travel freely through space.

Their wavelength is only stretched (red shifted) by cosmic expansion.

Recombination:

z = 1000; T = 3000 K

This is what we can observe today as the cosmic background radiation!

The cosmic microwave background radiation can be explained only by the Big Bang theory. The background radiation is the relic of an early hot universe. The Big Bang theory's major competitor, called the Steady State theory, could not explain the background radiation, and so fell into disfavor.

The amount of activity (active galaxies, quasars, collisions) was greater in the past than now. This shows that the universe does evolve (change) with time. The Steady State theory says that the universe should remain the same with time, so once again, it does not work.

The number of quasars drops off for very large redshifts (redshifts greater than about 50% of the speed of light). The Hubble Law says that these are for large look-back times. This observation is taken to mean that the universe was not old enough to produce quasars at those large redshifts. The universe did have a beginning.

The abundance of hydrogen, helium, deuterium, lithium agrees with that predicted by the Big Bang theory. The abundances are checked from the spectra of the the oldest stars and gas clouds which are made from unprocessed, primitive material. They have the predicted relative abundances.

Observations are consistent with Hot Big Bang Model

Fate of the Universe Depends on mass-energy density (Curvature of Space)

The more mass there is, the more gravity there is to slow down the expansion. Is there enough gravity to halt the expansion and recollapse the universe or not? If there is enough matter (gravity) to recollapse the universe, the universe is ``closed''. In the examples of curved space above, a closed universe would be shaped like a four-dimensional sphere (finite, but unbounded). Space curves back on itself and time has a beginning and an end. If there is not enough matter, the universe will keep expanding forever. Such a universe is ``open''. In the examples of curved space, an open universe would be shaped like a four-dimensional saddle (infinite and unbounded). Space curves away from itself and time has no end.

Deceleration of the Universe

• Fate of the universe depends on the matter density in the universe.

• Expansion of the universe should be slowed down by mutual gravitational attraction of the galaxies.

• Define “critical density”, c, which is just enough to slow the cosmic expansion to a halt at infinity.

Solution for k = 0:

2

2

8

3

R

k

G

H

Main equation:

ttH

ttttR

3

2)(;

1)(;)( 2

3/2

Critical density:G

Hc

8

3 2

:0, kc Indefinite expansion

:0, kc Expansion will be replaced by contraction

:0, kc Indefinite expansion but with speed approaching zero

32910~cm

gc

Model Universes

Siz

e s

cale

of t

he

Un

iver

se

Time

< c => universe will expand forever

> c => Universe will collapse back

If the density of matter equaled the critical density, then the curvature of space-time by the matter would be just sufficient to make the geometry of the universe flat!

= c => Flat UniverseMaximum age of the universe:

~ 1/H0

Deriving geometry of the universe from density measurements

Orbital speeds of stars in galaxies

Faint gas shells around ellipticalsEllipticals have faint gas shells that need massive ``dark'' haloes to contain them. The gas particles are moving too quickly (they are too hot) for the gravity of the visible matter to hang onto it.

Motion of galaxies in a clusterGalaxy cluster members are moving too fast to be gravitationally bound unless there is unseen mass.

Hot gas in clustersThe existence of HOT (i.e., fast moving) gas in galaxy clusters. To keep the gas bound to the cluster, there needs to be extra unseen mass.

Quasar spectraAbsorption lines from hydrogen in quasar spectra tells us that there is a lot of material between us and the quasars. Gravitational LensingGravitational lensing of the light from distant galaxies and quasars by closer galaxies or galaxy clusters enables us to calculate the amount of mass in the closer galaxy or galaxy cluster from the amount of bending of the light. The derived mass is greater than the amount of mass in the visible matter.

Current tallies of the total mass of the universe (visible and dark matter) indicate that all matter constitutes only 27% of the critical density.

Deriving geometry of the universe from microwave background radiation

Cosmology with the Cosmic Microwave Background

If the universe were perfectly homogeneous on all scales at the time of recombination (z = 1000), then the CMB should be perfectly isotropic over the sky.

Instead, it shows small-scale fluctuations:

The universe could not have been perfectly uniform, though. The universe must have been slightly lumpy to form galaxies later on from the internal gravity of the lumps. Initial density variations had to exist in order to provide some direction to where surrounding matter could be attracted. The COBE satellite found slight variations in the brightness of the background radiation of about 1 part in 100,000. The slight variations exist because some parts of the universe were slightly denser than other parts. The slightly denser regions had more gravity and attracted more material to them while the expansion occurred. Over time, the denser regions got even denser and eventually formed galaxies about 1 billion years after the Big Bang.

Fluctuations of the CMB temperature

Evidence for the formation of galaxies and large-scale structure

CMB fluctuations are the direct probe of the Large Scale Structure

A large survey of distant galaxies

shows the largest structures in the

universe:

Filaments and walls of galaxy

superclusters, and

voids, basically empty space.

Deriving geometry of the universe from microwave background radiation

The case of a missing Universe

Dark matter accounts for only 27% of the total mass-energy density: DM = 0.27

Observations suggest that the universe is flat: = 1

The rest 70% is something else!!

Visible matter accounts for ~ 4% of the total mass-energy density: v = 0.04

This something else is termed “dark energy”

It apparently causes the universe to accelerate in its expansion!!

The accelerating Universe

dt

tdR

tRtH

)(

)(

1)(

redshift z

dist

ance

or recession velocity

Supernovae are too faint

Equation of state: relation between pressure P and energy density c2

= 0 for dust (no pressure) = 1/3 for radiation (very hard pressure)

Or: acceleration = )31(3

42

2

R

G

dt

Rd

Einstein’s equations:

const)1(3 R

2

2

8

3

GR

kcc

2cP

= -1 ??

To have acceleration, 02

2

dt

Rdwe must have negative pressure!

Accelerating now, but decelerating in the past?!

Fig. 15-18, p.316

Problems with standard model. Inflation

• Flatness problem

• Horizon problem

• Initial fluctuations

• Absence of magnetic monopoles

• “Fine tuning”

Solution of the Problems of the Big Bang by InflationIf this inflationary epoch really took place, it could cure all the problems of the big bang:

The tremendous expansion means that regions that we see widely separated in the sky now at the horizon were much closer together before inflation and thus could have been in contact by light signals.

The tremendous expansion greatly dilutes any initial curvature. In fact, the inflationary theory predicts unequivocally that the Universe should globally be exactly flat, and therefore that the average density of the Universe should be exactly equal to the closure density.

The rapid expansion of the Universe tremendously dilutes the concentration of any magnetic monopoles that are produced. Simple calculations indicate that they become so rare in any given volume of space that we would be very unlikely to ever encounter one in an experiment designed to search for them.

Density Fluctuations as Seeds for Galaxy Formation

Detailed considerations indicate that inflation is capable of producing small density fluctuations that can later in the history of the Universe provide the seeds to cause matter to begin to clump together to form the galaxies and other observed structure.

Fig. 15-16, p.313

What could be the reason for inflation?

Do we live in a special universe??

• Change of physical constants by a very small amount would render impossible the life in the universe as we know it

• Adding or subtracting just one spatial dimension would make the formation of planets and atoms impossible

• Life as we know it needs a universe which is large enough, flat, homogeneous, and isotropic

Anthropic Principle

We observe the universe to be as it is because only in such a universe could observers like ourselves exist.

That is, selection effects would say that it is only in universes where the conditions are right for life (thus pre-selecting certain universe) is it possible for the questions of specialness to be posed.

This is a solution, but can we do better?

History of science teaches us that there is nothing special in the place we live

• Our local country is nothing special (ancient travelers)• Planet Earth is nothing special (Copernicus)• Milky Way galaxy is nothing special (Hubble)• Our part of the Universe is nothing special

– Self-reproducing Universe– Eternal Big Bang and ensemble of universes

Linde, Vilenkin

Landscape of the multiverse

Planck scale:

Planck Length

Planck Mass

Planck density 1094 g/cm3

Eternal multiverse;

Individual universes are being continuously “inflated” from a space-time “foam”.

Some of these universities can harbor life as we know it; others don’t.

A large fraction of universes CAN harbor life