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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
Homogeneity does not imply
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
• 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
• 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
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!'_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.
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