Anybody like to help a physics student who did their BSc six years ago and has forgotten all their maths! Its a problem from Andrew Liddle's Introduction to cosmology 5.5 The Friedmann eqn is (a'/a)2 = 8TTG/3 P - k/a2 Consider the case k>o, with the universe containing matter only, so that p =p0/a3 Demonstrate that the parametric solution a(y) = 4 TT G p0/3k (1-cos y) ; t(y) = 4TTGp0/3k3/2 (y-siny) solves this equation where y runs from 0 to 2TT Sorry about the crassness..I hope you can deciphere my symbols... I know I should differentiate them and use the chain rule..but really my maths is rubbish!! Any fellow physicists I would much appreciate it...maybe I shouldn't be doing my masters..I need to dig out my old calculus book...
You need to show some work before we can help you. (This really belongs in the homework section too). You are correct that you need to differentiate and use the chain rule. Perhaps you should have a go and post what you get.
Ok, so either you're not coming back, or you still can't attempt the problem. I'll give you a few hints: You vasically have two parametric functions a(y)=L(1-cos(y)) and t(y)=M(y-sin(y)), for some constants L and M. In the Friedmann equation, we have a term [itex]a'=\frac{da}{dt}[/itex]. Using the chain rule we can write [tex]\frac{da}{dt}=\frac{da/dy}{dt/dy}[/tex] from which you should be able to solve.