Astr 328 Mar3, 2003: Physical cosmology: adding dynamics  

Volume of curved space (continued) -- evaluating integrals

Intuitive ideas of volume in curved space

How to add dynamics to the RW metric: field equation

Friedmann and local energy conservation equations

How does pressure come in to energy conservation?

Calculate pressure from galaxy motions

Equation of state

Pressure from cosmological constant term

Rewriting Friedmann equation in terms of rho_lambda

Universe with Lambda only

Critical density

"Dust" universe : pressure is negligible

Ignore cosmological constant too, for a while

Evolution of Hubble parameter H with time

Evolution of Omega with time

Now get redshift vs time in terms of observable parameters........

Einstein-de Sitter model (Omega=1)

Redshift vs time for different Omega

Age of the universe from the Hubble constant, with Omega=1 and Lambda=0

Parametric form for solution when k=+/-1

Universe with Lambda only

Lookback time to z=6.8 QSO

Let's look at Lambda again