- #1
unscientific
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Homework Statement
(a) Show that the equations satisfy FRW equations.
(b) Show the metric when ##\eta## is taken as time
Homework Equations
The Attempt at a Solution
[/B]
The FRW equation is:
[tex] 3 \left( \frac{\dot a}{a} \right)^2 = 8\pi G \rho [/tex]
Using ##\frac{da}{dt} = \frac{da}{d\eta} \frac{d\eta}{dt}##:
[tex] \dot a = \frac{\frac{1}{\eta_*} sin \left( \frac{\eta}{\eta_*}\right)}{1 - cos \left( \frac{\eta}{\eta_*} \right)} [/tex]
[tex]\dot a = \frac{C sin \left( \frac{\eta}{\eta_*} \right)}{\eta_* a} [/tex]
The LHS is then
[tex] 3 \left( \frac{\dot a}{a} \right)^2 = 3 \left[ \frac{C^2 sin^2 (\frac{\eta}{\eta_*})}{\eta_*^2 a^4} \right] [/tex]Not sure how to show this equals RHS..