Dynamics of the Universe

Second Friedmann equation, Cosmological constant, Density Parameter, Solution of the Friedmann equations for some extreme cases, Cosmological redshift, Determintion of ΩV.
2nd Friedman Eq.
1. a''/a = -4piG/3 (ro + 3P/c^2)
  1. A) Matter Dominated Unierse
    1. k = 0 flat universe
    2. Pressure of NR matter = 0
    3. ro = ro0 (a0/a)^3
    4. a'^2 = 8piG(a0^3)ro0 / 3a
      1. a'(t=0) >0
      2. a ~ t^2/3
      3. Ro ~ 1/t^2
      4. H ~1/t
  2. B) Radiation Dominated Flat Universe
    1. eq. Of state for a photon gas
      1. ro ~ P = ro c^2 /3
      2. Fluid eq. Ro' + 3H(ro + 1/3 ro) -> duro/ro = -4da/a
        Ro ~ 1/ a^4
        1/a^3 dilution
        1/a redshift
        H ~ 1/2t
        A radiation universe expands slower than a matter one
Cosmological Constant L
1. F. Equations can be derived from Einstein eq. using R.W.metric and the Energy Momentum tensor of an homogeneous fluid.
2. Modified F.eq.
  3. To recover originals
3. Fluid eq. Not modified

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	Created by eilisdaes almost 11 years ago