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

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

1. Hubble Law v = H r

   • Universe expanding
     • Chocolate chip analogy
       • Objects that are held together by their own gravity, are contained together within a path of non-expanding space
     • -> Redshift
       • L / L0 = 1 + z
         • Ratio of streching
         • Compare with relativistic Doppler effect z = v/c
   • H cnt. Is normalized
     • h = H/100 = 0.67
   • Violated @ small scales
   • BUT it's needed GR
     • Universe dominated by matter
       • Constant density
       • slope determined by the total energy of the universe => ro
         • ro < roc , U > 0 , k < 0 , H > 0
         • ro > roc , U < 0 , k > 0 , H < 0
         • ro = roc , U = 0 , k = 0
           • ro ~ t^-2
     • By energy conservation + Cosmo. Principle
       • Uniform expansion
         • r = a(t) x
           • H = (a' / a) = 8piGro/3 - kc^2/a^2
             • H = H(t)
             • (k=0) Roc = 3H^2/8piG
     • Friedman Eq.

2. thermodynamics

   • adiabatic
     • dE + pdV = 0
       • Fluid Eq.
         • ro' + 3H (ro + p/c^2) = 0

3. O = ro/roc

   • kc^2/a^2H^2= O - 1
     • O - 1 = -0.1 · 10^-2
       • Universo is very flat
         • Ov = 0.6
           • L > 0, Pv < 0

4. Vacuum Dominated Universe

   • Inflation, exponentially expanding
     • Negative pressure
   • Expanding universe with L>0 be omens vacuum dominated