Tensor Einstein Equations

The Einstein equations tell us that the tensor metric source is governed by

$$\ddot H + 2{\dot a \over a} \dot H + k^2 H = 8\pi G a^2 [ p_f^{\vphantom{{(2)}}} \pi^{{(2)}}_f + \pi^{{(2)}}_s]\, ,$$ (60)

where note that the photon contribution is $\pi^{(2)}_\gamma = {8 \over 5}\Theta_2^{(2)}$.