Seb Oliver

1
Distant Universe

• Seb Oliver
• Lecture 2 Homogeneity Isotropy

2
Main Topics

• Standard Hot Big Bang Model
• Classical Observational Cosmology
• Galaxy Evolution
• The Hunt for the First Galaxies
• Background Light
• Structure Formation

3
Standard Hot Big Bang Model

• Assumptions of Homogeneity and Isotropy
• Nearly-Newton Cosmology
• Equations of State
• Geometry and fate of the Universe
• The Early Universe

4
Copernican Principle

• The earth does not occupy a special position in
  the universe
• This principal was possibly first formulated by
  Giordano Bruno and not Copernicus, but in any
  case it was a rather radical proposition with
  profound implications for the thinking of the
  universe at the time

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Definitions

• A fundamental observer is someone who is at rest
  with respect to the rest of the Universe in their
  locality
• Homogeneous at any given time the Universe
  appears the same to fundamental observers, e.g.
  the observers will measure the same mean density
  or any other scalar quantity
• Isotropic the Universe appears the same in all
  directions

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Homogeneity

• Homogeneous

• Not homogeneous

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Isotropy

• Isotropic at

• Not isotropic

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Homogeneous ? Isotropic
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Isotropy Copernican Principle ? Homogeneity
Isotropy about A
Isotropy about B
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Cosmological Principle

• The cosmological principle is that the universe
  is isotropic and homogeneous
• Equivalently is isotropic for every fundamental
  observer
• The cosmological principle alone can tell us some
  very useful things

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Cosmological Principle implies a cosmological time

• The Cosmological Principal implies a cosmological
  time.
• Since the Universe appears the same to all
  fundamental observers at any given time, they can
  all synchronise their watches to some event which
  occurs in the history of the Universe, thereafter
  all the watches measure the same cosmological time

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Cosmological Principle Hubbles Law
2,3,4
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Cosmological Principle Hubbles Law
including a t dependence
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Cosmological Principle Hubbles Law

• Simply assuming that the universe is homogeneous
  isotropic has lead us to the conclusion that
• i.e. the universe is either
• Static h(t) v 0
• Uniformly expanding h(t) gt 0
• Uniformly contracting h(t) lt 0

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H(t) is Hubble parameter
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Cosmological Principle Hubbles Law
trial solution
comoving position
proper position
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scale factor
9
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We have gone a long way with very little
but how do we know how H (or a) varies with time?
to go any further we need some physics ....
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Standard Hot Big Bang Model

• Assumptions of Homogeneity and Isotropy
• Nearly-Newton Cosmology
• Equations of State
• Geometry and fate of the Universe
• The Early Universe