Reading Assignment: Arny: Chapter 16 & 17, Cosmos: Chapter 10.

- infinite in extent
- homogenously filled with matter
- inifinitely old

Assuming there is obscuring dust doesn't help. It would just heat up and re-emit all of the radiation. In such a Universe it must reach *thermodynamic equillibrium*: the same temperature everywhere.

So, why is the sky dark at night? We think that it is because the Universe is not infinitely old (c). The Universe has an age somewhere between 10-20 billion years.

There is **no center** of the expansion (infinite raisin bread) and

The **density** of the Universe *decreases* as the Universe expands.

We define a scale factor, R, which can be thought of as the distance between any two clusters of galaxies. This scale factor is getting larger with time (the Universe is expanding).

Run the expansion backward in time. Density and Temperature increase as R decreases. When R = 0, density = infinity, temperature = infinity (a singularity!!!).

We call this the **Hot Big Bang**. Which is a misnomer. It was actually a name given the theory by a Fred Hoyle who was trying to discredit the theory. Unfortunately the name has stuck.

The Big Bang was not an explosion. An explosion implies the sudden release of energy and expansion into space. The expansion of the Universe is not an expansion of matter into space, but rather an expansion of *space itself*. Therefore the Big Bang did not happen at some point in space, but rather *everywhere in space at the same time*.

We know that d = vt. And v = H_{o}d. Therefore, the age of the Universe is t_{o} = 1/H_{o}.

If H_{o} = 50 km/s/Mpc then,

= 6.17x10^{17} s ·(1 yr/3.16x10^{7}) = 1.96x10^{10} yrs = ** 19.6 billion years**.

If H_{o} = 80 km/s/Mpc then,

= 3.86x10^{17} s ·(1 yr/3.16x10^{7}) = 1.22x10^{10} yrs = ** 12.2 billion years**.

(if we ignore the effects of a possible Cosmological Constant). Then we must conclude that the expansion was **faster in the past**: **gravity** is slowing it down. So the Universe must be in fact *younger* than the Hubble Time.

Globular stars clusters are thought to be between 11-15 billion years old: Possibly inconsistent with the expansion age. The discrepancy was worse in the past, but new data is causing us to date the globular clusters a bit younger and find the Universe a bit older. So things are starting to work out. STAY TUNED!!

The Cosmological Principle states that *on the largest scales* the Universe must look the same for any observer in space. The Universe must therefore be **Homogeneous** (same average density) and **Isotropic** (looks the same in all directions).

**Evidence** to support these assumptions: (1) Largest structures are superclusters. Beyond that things seem to smooth out. (2) Cosmic "Black body radiation" the same everywhere.

NOTE: density can change with *time*. These assumptions of for all *space* at any given time.

The results are that there are 3 types of possible homogeneous and isotropic Universes and the global geometry of the Universe can be 1 of 3 possible geometries:

- Flat (Euclidean Geometry)

2-D example: plane - Positive Curvature

2-D example: sphere - Negative Curvature

2-D example: infinite saddle or Pringles potato chip

There is a critical average density (matter + energy) that makes the Universe globally flat. It is calculated from Einstein's equations:

If we choose H_{o} = 65 km/s/Mpc, then the current critical density is

> _{crit} Positive Curvature: **Closed**. Volume is finite but unbounded.

= _{crit} Zero Curvature: **Flat**. Volume is infinite.

< _{crit} Negative Curvature: **Open**. Volume is infinite.

If < _{crit} Universe Expands Forever.

If = _{crit} Universe Expands Forever, but stops at time equal to infinity.

If > _{crit} Universe Eventually Stops Expanding and Collapses Back to a Hot, Dense State. (Big Crunch).

If the Universe **Expands Forever**, eventually all galaxies will redshift away from our cosmic horizon. Eventually, star formation comes to an end as all matter is locked up in white dwarfs, brown dwarfs, planets, and other such debris. After 10^{45} years the protons and neutrons that make up atomic nuclei decay into neutrinos, electrons, and photons. All that remains with any significant gravity are black holes. After 10^{100} years black holes will have evaporated via Hawking radiation. The Universe is **very** cold and empty, containing only photons and leptons (electrons, neutrinos, etc.).

If the Universe **Stops Expanding and Collapses**, eventually we will see all of the galaxies go from all being redshifted to blueshifted. The Universe will get hotter and denser as space gets smaller and smaller. Eventually all life will be extinguished in the overwhelming temperatures (matter becomes completely ionized and then broken up into its fundamental particles) and the Universe will collapse to some incredibly small size of unknown proportions. Some speculate that from this dense and hot state a new Universe will born from the ashes of the former. Some call this the **Phoenix** Universe.

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