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Cosmology

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... isotropy. Homogeneity does not imply isotropy ... Isotropy and Homogeneity ... The cosmological principle of isotropy and homogeneity, like other scientific ... – PowerPoint PPT presentation

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Title: Cosmology


1
Cosmology
  • Physics466

Olbers Paradox Cosmological principle Expansion
of the Universe Big Bang Theory Steady State
Model Dark Matter Dark Energy Structure Formation
2
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

3
Homogeneity does not imply isotropy
4
Homogeneity does not imply isotropy
5
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6
Cosmological Principle (cont)
7
Isotropy and Homogeneity
  • Homogeneous -gt we see no difference when we
    change position there is no preferred position
    in the universe (translational invariance)
  • Isotropic -gt 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)-gt universe is
    homogeneous and isotropic (at a given
    cosmological time)

8
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

9
Tests
Galaxies arranged in superclusters that appear
as long sheets surrounded by voids
10
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11
Cosmological Principle Tested
12
The Perfect Cosmological Principle
13
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14
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.

15
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
16
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17
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18
Olbers Paradox in another way
There will be a tree at every line of direction
if the forest is sufficiently large
19
Olbers Paradox
  • A star filled spherical shell, of radius r, and
    thickness dr, centered on the Earth.

20
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/G
R/olbers.html
21
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.

22
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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