Tensor Einstein Equations

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

$$\ddot H + 2{\dot a \over a} \dot H + (k^2 + 2K) H = 8\pi G a^2 [ p_f^{\vphantom{{(2)}}} \pi^{{(2)}}_f + \pi^{{(2)}}_s]\, ,$$ (49)

for all gauges.