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Fundamental Cosmology 3.Newtonian Cosmology
If I have seen further than others, it is by
standing upon the shoulders of giants. Sir
Isaac Newton (1642-1727) b. Woolsthorpe, England
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3.1 Newtonian Cosmology

• Newton Laws of Motion

• Bodies move with constant velocity unless acted
  on by outside force i.e. move in straight
  lines
• The rate of change of momentum of a body is
  proportional to its acceleration
• For every action there is an equal and opposite
  reaction

Equivalence Principle
Galileo acceleration independent of mass
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3.1 Newtonian Cosmology

• Gravity Dominates

Range (m) Coupling (J.m) mass
Strong Nuclear 10-15 10-27 1.4MeV
Electromagnetic ? 10-28 0
Weak Nuclear 10-18 10-31 1Gev
Gravity ? 10-64 0

• mediator is massless
• infinite range
• only one charge

On large scales - Gravity dominates
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3.1 Newtonian Cosmology

• Can we derive the cosmological equations from
  purely Newtonian dynamics ??

All distances scaled by factor R(t) with
increasing time with simple isotropic expansion
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3.2 Newtonian (Dynamic) Derivation of Friedmann
Equations

• Simple derivation from dynamical arguments

• Newton For a given observer at position , r,
  within a sphere.
• Only mass interior to sphere affects the
  observer.
• The mass exterior to sphere does not exert a
  force on the interior.

• c.f.GR BIRKHOFFs THEOREM
• The gravitational field within a spherical
  cavity embedded within an infinite medium is zero.

Consider a particle P, on the edge of an
isotropically expanding sphere
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3.2 Newtonian (Dynamic) Derivation of Friedmann
Equations

• The Friedmann Equations

ACCELERATION EQUATION
Let 2cf kc2
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3.3 Newtonian (Energetic) Derivation of
Friedmann Equations

• Derivation from Energetic arguments Friedmann
  Equation

Analogous assumption Ignore matter outside
sphere of radius r(t) in expanding homogeneous
universe
Friedmann Equation
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3.3 Newtonian (Energetic) Derivation of
Friedmann Equations

• Dynamics in the Newtonian Universe

• Ugt0 RHS gt0 for all time

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3.3 Newtonian (Energetic) Derivation of
Friedmann Equations

• The Fluid Equation

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3.3 Newtonian (Energetic) Derivation of
Friedmann Equations

• The Acceleration Equation

Fluid Equation
Friedmann Equation

• For any positive Energy Density the Universe is
  deccelerating
• Pressure is always positive for baryons,
  photons, neutrinos, even WIMPS
• but if Plt-e/3 ???

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3.4 Summary

• Newtonian Cosmology

• Can derive cosmological equations from a purely
  Newtonian Perspective

• However its a bit ???, e.g.,
• Finite sphere embedded in Universe - violates
  HOMOGENEITY - special place !
• Preferred direction towards centre of sphere -
  violates ISOTROPY
• Euclidean flat Universe is assumed

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3.4 Summary
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Fundamental Cosmology 3. Newtonian Cosmology
Fundamental Cosmology 4. General Relativistic
Cosmology
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