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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 Homogeneity does not imply isotropy 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 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