Cosmology

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

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

Necessity of the Big Bang

RHv 0

The time of expansion is T ~ 1/H0 ~ 14 billion years

14 billion years ago all distances R were equal to 0

Velocity = distance / time

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

Fig. 15-12, p.307

Olbers' Paradox and the Dark Night SkyIF the universe is infinite, eternal, and static, then the sky should be as bright as the surface of the Sun all of the time! Heinrich Olbers (lived 1758--1840) popularized this paradox in 1826, but he was not the first to come up with this conclusion. Thomas Digges wrote about it in 1576, Kepler stated it in 1610, and Edmund Halley and Jean Philippe de Cheseaux talked about it in the 1720's.If the universe is uniformly filled with stars, then no matter which direction you look, your line of sight will eventually intersect a star (or other bright thing).

Solved by finite size of the expanding universe

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

Fig. 15-12, p.307

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

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

Curvature = )(2 tR

k

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

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 ~ 14 billion years

Time = distance / velocity

velocity = (Hubble constant) * distance

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!

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