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First Friedmann Equation forms

  • #1

Homework Statement


the first friedmann equation is:
([itex]\frac{\dot{a}}{a})^2[/itex]=[itex]\frac{8\pi G\rho}{3}[/itex]-[itex]\frac{kc^2}{a^2}[/itex]+[itex]\frac{\Lambda}{3}[/itex]
In the case of a closed Universe (k > 0) containing only non-relativistic matter and no cosmological constant, write the Friedmann equation in terms of, H(a), H0, a and Ω0 (where Ω0 is the current matter density parameter). Assume that the current scale factor, a0 = 1

Homework Equations





The Attempt at a Solution


so far what I have is:
H(a)2=H02Ω0-[itex]\frac{kc^2}{a^2}[/itex]+[itex]\frac{\Lambda}{3}[/itex]
I've seen things like
H(a)2=H02[[itex]\Omega_0\frac{a}{a_0}[/itex]+1-[itex]\Omega_0[/itex]]

but I have no explanation for this and so can't tell if it's right.
 

Answers and Replies

  • #2
4
0
usyd student? if so try lecture 7 slide 12 ;)
I'm not sure about solving the fluid equation for p=0 - apparently its a seperable integral or something, but i think you can use what's provided on slides without proof. From there I think you are just trying to draw a relationship between the flat universe when k=0 and this closed universe for some k>0. For me, it is very time consuming to understand and show working.

I don't fully understand how we can create a single form of Friedmann for a closed universe by using flat universe equations for density, etc. Very confusing.
 

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