Deriving Oscillating Universe Result: Need Help

[p.p]

Does anyone know how to derive the result for an oscillating universe?

R(t)= sqrt(3/lambda)sin(sqrt((3/lambda)ct)

I would appreciate the help on this one

 

[phsopher]

I'm not sure what particular derivation you're after, but presumably in the RW metric there are such K and rho that give such a universe as a solution. You have the solution so why not plug it into the Friedmann equation and solve for K and rho? I think K=-1 and rho=lambda/3 would give this solution.

 

[p.p]

From integral( dR/(sqrt(lambda*R^2/3) - K) = ct
derivation has the initial conditions;
lambda<0
K=-1

Leading to the oscillating universe

 

[phsopher]

Sorry, the answer I gave you is not correct. lambda can't be negative because then the argument inside sine would be imaginary and thus it wouldn't be an oscillating solution. But the method should work. Just plug your solution inside the Friedmann eq and find K and rho. There can be many pairs of K and rho that give such a solution.