Dynamics of the Universe: Hubble law, Friedmann equation, fluid equation

Hubble Law v = H r
1. Universe expanding
  1. Chocolate chip analogy
    1. Objects that are held together by their own gravity, are contained together within a path of non-expanding space
  2. -> Redshift
    1. L / L0 = 1 + z
      1. Ratio of streching
      2. Compare with relativistic Doppler effect z = v/c
2. H cnt. Is normalized
  1. h = H/100 = 0.67
3. Violated @ small scales
4. BUT it's needed GR
  1. Universe dominated by matter
    1. Constant density
    2. slope determined by the total energy of the universe => ro
      1. ro < roc , U > 0 , k < 0 , H > 0
      2. ro > roc , U < 0 , k > 0 , H < 0
      3. ro = roc , U = 0 , k = 0
        ro ~ t^-2
  2. By energy conservation + Cosmo. Principle
    1. Uniform expansion
      1. r = a(t) x
        H = (a' / a) = 8piGro/3 - kc^2/a^2
        H = H(t)
        (k=0) Roc = 3H^2/8piG
  3. Friedman Eq.
thermodynamics
1. adiabatic
  1. dE + pdV = 0
    1. Fluid Eq.
      1. ro' + 3H (ro + p/c^2) = 0
O = ro/roc
1. kc^2/a^2H^2= O - 1
  1. O - 1 = -0.1 · 10^-2
    1. Universo is very flat
      1. Ov = 0.6
        L > 0, Pv < 0
Vacuum Dominated Universe
1. Inflation, exponentially expanding
  1. Negative pressure
2. Expanding universe with L>0 be omens vacuum dominated

Resource summary

	Created by eilisdaes almost 11 years ago