18 Cosmology

1. Universe at the Largest Scale

The largest scale

The Sloan Digital Sky Survey.
- 66,976 galaxies
- lying 12°
- a distance of almost 1000 Mpc
- The Sloan Great Wall (300 Mpc across) is marked at the center of the frame.
There is no evidence for any structure on larger scales.

The Hubble Ultra Deep Field

It is the result of a total exposure time of 1 million seconds.
It contains about 10,000 galaxies.

The cosmological principle

The Universe is homogenous (any 300-Mpc-square block appears much like any other) — the same everywhere.
The Universe also appears to be isotropic — the same in all directions.

Therefore, the cosmological principle includes the assumptions of isotropy and homogeneity.

2. The Expanding Universe

Olbers’s Paradox

If the universe were homogeneous, isotropic, infinite in extent, and unchanging

then any line of sight from Earth should eventually run into a star
and the entire night sky should be bright.

This obvious contradiction of the facts is known as Olbers’s paradox.

So, why is it dark at night?

The universe is homogeneous and isotropic—it must not be infinite or unchanging.

Birth of the universe

Hubble's Law: Galaxies are moving faster away from us, the farther away they are:

recession velocity = H0 × distance

How long did it take the galaxies to get there?

time = distance / velocity

= distance / (H0 × distance)

= 1 / H0

Since, H0 = 70 km/s/Mpc, the time is ...

» 14 billion years.

Hubble Expansion Hubble’s law is the same, regardless of who makes the measurements.
The top numbers are the distances and recessional velocities as seen by an observer on the middle of five galaxies, galaxy 3.
The bottom two sets of numbers are from the points of view of observers on galaxies 2 and 1, respectively.
In all cases, Hubble’s law holds:
- The ratio of the observed recession velocity to the distance is the same.

3. Big Bang

Let's go back in time this much (14 billion years):
- Everything in universe was confined to a single point: BIG BANG.
  - It marked the beginning of the universe.

Olber's Paradox - The Solution

Whether universe is finite or infinite in extent it is irrelevant:
- we see only a finite part of it ➨ 14 billion years.
- beyond this point is unknown.
  - its light has not yet had time to reach us ...

The BB event

Bib bang was not an explosion in an empty universe.
Bib bang involved the entire universe; not just the matter and radiation within it, but "the universe itselft"

The entire universe was a point
- That point was in no way different from the rest of the universe;
- That point was the the whole universe
  - Therefore, there was no point where Big Bang "happened";
  - Because, Big Bang involved the entire universe;
  - It happened everywhere at once.

Summary

No matter where in the Universe we are, we will measure the same relation between recessional velocity and distance with the same Hubble constant.

Receding Galaxies

Coins taped to the surface of a spherical balloon recede from one another as the balloon inflates (left to right).
Similarly, galaxies recede from one another as the universe expands.
As the coins recede, the distance between any two of them increases,
and the rate of increase of this distance is proportional to the distance between them.
Thus, the balloon expands according to Hubble’s law.

Cosmological Redshift

As the universe expands, photons of radiation are stretched in wavelength:
- In this case, as the baseline in the diagram stretches,
- the radiation shifts ...
  - from the short-wavelength blue region of the spectrum
  - to the longer wavelength red region.

4. The Fate of the Cosmos

There are two possibilities for the Universe in the far future:

It could keep expanding forever.
It could collapse.

Assuming that the only relevant force is gravity, which way the Universe goes depends on its density.

Model Universes

Distance between two galaxies as a function of time:

a low-density universe that expands forever and
a high-density cosmos that collapses.

The point where the two curves touch represents the present time.

Critical Density

There is a critical density between collapse and expansion. At this density the universe still expands forever, but the expansion speed goes asymptotically to zero as time goes on.

Given the present value of the Hubble constant, that critical density is:

9 × 10-27 kg/m3

five hydrogen atoms per cubic meter
-or- a household closet.
-or- 0.1 Milk Way

The Geometry of the Space

If space is homogenous, there are three possibilities for its overall structure. They can be described by comparing the actual density of the Universe ( Ω) to the critical density (Ω0).

Closed : Ω > Ω0 — Positive geometry — leads to ultimate collapse — surface of a sphere.
Flat : Ω = Ω0 — Flat geometry — this corresponds to the critical density — flat.
Open : Ω < Ω0 — Negative geometry — expands forever — surface of a saddle.

Einstein’s Curve Ball

In a closed universe, a beam of light launched in one direction might return someday from the opposite direction after circling the universe, just as motion in a “straight line” on Earth’s surface will eventually encircle the globe.

5. Will the Universe Expand Forever?

Let's check the actual density of the Universe

Measurements of luminous matter suggest that the actual density is only a few percent of the critical density.
But, we know there must be large amounts of dark matter.
However, the best estimates for the amount of dark matter bring the observed density up to about 0.3 times the critical density.
- Dark matter needs to bind galaxies in clusters, and explains gravitational lensing.
Therefore, dark matter is not enough to make the density critical.

Type-I Supernova

If the expansion of the Universe is decelerating the farthest galaxies had a more rapid recessional speed in the past,
and will appear as though they were receding faster than Hubble’s law would predict.

Accelerating Universe

Observations of distant supernovae:

In a decelerating universe (purple and red curves), redshifts of distant objects are greater than would be predicted from Hubble’s law (black curve).
The reverse is true for an accelerating universe. The points showing observations of some 50 supernovae strongly suggest that the cosmic expansion is accelerating.
The vertical scale shows redshift; for small velocities, redshift is just velocity divided by the speed of light.

Einsteind & Cosmological Constant

The cosmological constant (vacuum energy) was originally introduced by Einstein to prevent general relativity from predicting that a static universe (then thought to be the case) would collapse.
When the universe turned out to be expanding, Einstein removed the constant from his theory, calling it the biggest blunder of his career.
Now, it seems as though something like a cosmological constant may be necessary to explain the accelerating universe—theoretical work is still at a very early stage, though!

6. Dark Energy & Cosmology

In the very early life of the Universe, the geometry must be flat.
The assumption of a constant expansion rate predicts the Universe to be younger than we observe.
Therefore in the cosmic age the accelerating universe has to be included.
Given what we now know, the age of the universe works out to be 13.7 billion years.

Cosmic Age

The age of a universe without dark energy (represented by all three lower curves) is always less than 1/H0 and decreases for larger valus of the present-day density.

The existence of a repulsive cosmological constant (green curve) increases the age of the cosmos.
This is consistent with other observations, particularly of the age of globular clusters, and yields the following timeline:
- 14 billion years ago: Big Bang
- 13 billion years ago: Quasars form
- 10 billion years ago: First stars in our galaxy form

7. Cosmic Microwave Background

The cosmic microwave background was discovered by chance in 1964, as two researchers tried to get rid of the last bit of “noise” in their radio antenna.
Instead, they found that the “noise” came from all directions and at all times, and was always the same.
They were detecting photons left over from the Big Bang.
When these photons were created, it was only one second after the Big Bang, and they were very highly energetic.
The expansion of the universe has redshifted their wavelengths so that now they are in the radio spectrum, with a blackbody curve corresponding to about 3 K.

A map of the microwave sky shows a distinct pattern, due not to any property of the radiation itself, but to the Earth’s motion:

A COBE map of the microwave sky

It reveals that it is a little hotter in the direction of the Leo and
and a little cooler in the opposite direction.
The maximum temperature deviation from the average is about 3.4 mK, corresponding to a velocity of 400 km/s in the direction of Leo.

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