Homework Help: P=(\rho)/3 in the RW universe

1. Jan 11, 2010

Altabeh

1. The problem statement, all variables and given/known data

A space-time has metric $$ds^2=-dt^2+R^2(dx^2+dy^2+dz^2)$$, where R is a function of t only. Assume that the space-time is filled with an ideal gas, with energy-momentum tensor $$T_{\mu\nu} = pg_{\mu\nu}+ (p+\rho)u_{\mu}u_{\nu}$$, where u is the four-vector of gas particles vector, and p and $$\rho$$ are functions of t. If $$R(t) = \sqrt{t/t_0}$$ where t_0 is a constant, prove that p = $$\rho$$ /3.

3. The attempt at a solution

I can only show this when the second derivative of R is zero. What should I do to prove this under the circumstances described in the problem statement?

Thanks,
AB