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

Homogeneity does not imply isotropy

Cosmological Principle (cont)

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

Cosmological Principle Tested

The Perfect Cosmological Principle

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 r 3. So the night sky should be bright if the Universe is sufficiently large!

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.

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