Expanding Universe |

But then we go on to find values of ##w## for a

- matter dominated universe (now) which gives ##\rho_M\propto a^{-3}##
- radiation dominated universe (early) which gives ##\rho_R\propto a^{-4}##
- vacuum dominated (late / de Sitter and anti-de Sitter) ##\rho_\Lambda\propto a^0##

The first has an energy-momentum tensor for dust, the second for electromagnetism and the third from another sort of perfect fluid where ##p=-\rho## is the equation of state.

We then apply Einstein's equation and using the metric, the energy-momentum tensor and Ricci tensor for this metric that we found in the previous section we get the Friedmann equations which define Friedmann-Robertson-Walker (FRW) universes and can determine the evolution of the scale factor ##a##.

Finally I tried evolving the ##a## in the matter dominated universe and rewrote the Friedmann equations using the conventional metric

Find out what the equations are and how to get them Commentary 8.3 Friedmann equation.pdf (7 pages)

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