1010574
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.
- a''/a = -4piG/3 (ro + 3P/c^2)
- A) Matter
Dominated
Unierse
- k = 0 flat universe
- Pressure of NR matter = 0
- ro = ro0 (a0/a)^3
- a'^2 = 8piG(a0^3)ro0 / 3a
- a'(t=0) >0
- a ~ t^2/3
- Ro ~ 1/t^2
- H ~1/t
- a'(t=0) >0
- k = 0 flat universe
- B) Radiation
Dominated
Flat Universe
- eq. Of state for a photon gas
- ro ~ P = ro c^2 /3
- Fluid eq. Ro' + 3H(ro + 1/3
ro) -> duro/ro = -4da/a
- Ro ~ 1/ a^4
- 1/a^3 dilution
- 1/a redshift
- 1/a^3 dilution
- H ~ 1/2t
- A radiation
universe
expands
slower than
a matter
one
- A radiation
universe
expands
slower than
a matter
one
- Ro ~ 1/ a^4
- ro ~ P = ro c^2 /3
- eq. Of state for a photon gas
- A) Matter
Dominated
Unierse
- a''/a = -4piG/3 (ro + 3P/c^2)
- Cosmological Constant L
- F. Equations can be derived from Einstein eq.
using R.W.metric and the Energy Momentum
tensor of an homogeneous fluid.
- Modified F.eq.
- To recover originals
- Fluid eq. Not modified
- F. Equations can be derived from Einstein eq.
using R.W.metric and the Energy Momentum
tensor of an homogeneous fluid.
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