S15 Pressure and Energy Density Evolution SOLUTIONS

Exercise 15.1.1

Answer

The equation is

\[a\frac{d\rho}{da} = -3(P/c^2+\rho) \nonumber\]

Plugging in \(\rho \propto a^n\) we get \(n\rho = -3(P/c^2 + \rho)\). Solving for \(P\) for \(n=-3, -4, 0\) we find \(P=0\), \(P=\rho c^2/3\), and \(P = -\rho c^2\) respectively.