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### Cosmology

Physics466

Olbers Paradox

Cosmological principle

Expansion of the Universe

Big Bang Theory

Steady State Model

Dark Matter

Dark Energy

Structure Formation

Cosmological Principle

- On large scales (greater than 100 Mpc) the Universe is homogenious and isotropic
- The Earth is not at a preferred place (Copernican Principle)
- Homogenious: Every point is equivalent
- Isotropic: Every direction is equivalent

Isotropy and Homogeneity

- Homogeneous -> we see no difference when we change position; there is no preferred position in the universe (translational invariance)
- Isotropic -> no difference when we look at a different direction
- Examples: Surface of uniform cylinder is homogeneous but not isotropic- what about the surface of a sphere – or chessboard ?
- Cosmological Principle (CP)-> universe is homogeneous and isotropic (at a given cosmological time)

CP

- Cosmological principle means that physical laws are assumed to be the same everywhere, too
- The cosmological principle of isotropy and homogeneity, like other scientific hypotheses, is testable by confrontation with data.
- So far, observations support this hypothesis

Tests

Galaxies arranged in superclusters that appear as long sheets surrounded by voids

Perfect Cosmological Principle

- What about time? Every “time” equivalent?
- The Universe is homogenious and isotropic in space and time.
- The universe looks the same everywhere (on the large scale) as it always has and always will.
- The evolution of Galaxies does not confirm this principle. The universe seems to evolve.

Olbers’ Paradox (1826)

- Consider a static, infinite universe of stars
- Every line of sight would end in a star
- Then why isn't the night sky bright?
- Mathematically, radiative flux drops by r-2 but the number of stars in a volume increases with r3.
- So the night sky should be bright if the Universe is sufficiently large!

http://en.wikipedia.org/wiki/Olbers'_paradox

Olbers’ Paradox in another way

There will be a tree at every line of direction

if the forest is sufficiently large

Olbers’ Paradox

- A star filled spherical shell, of radius r, and thickness dr, centered on the Earth.

Possible Explanations

- There's too much dust to see the distant stars.
- The Universe has only a finite number of stars.
- The distribution of stars is not uniform. So, for example, there could be an infinity of stars,but they hide behind one another so that only a finite angular area is subtended by them.
- The Universe is expanding, so distant stars are red-shifted into obscurity.
- The Universe is young. Distant light hasn't even reached us yet.

http://math.ucr.edu/home/baez/physics/Relativity/GR/olbers.html

Correct Answer(s)

- The Universe is expanding
- The Universe is young
- In fact the sky is ablaze, but the temperature of the radiation is only 2.7 K (CMBR)
- All starlight ever emitted amounts only to a few percent of the CMBR energy density.

The Universe is young

- We live inside a spherical shell of "Observable Universe" which has radius equal to the lifetime of the Universe.
- Objects more than about 13.7 thousand million years old (the latest figure) are too far away for their light ever to reach us.
- Redshift effect certainly contributes. But the finite age of the Universe is the most important effect.

References: Wesson, 1991, ApJ. 367, 399

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