 Separately conserved cosmological fluids

A noninteracting perfect fluid in general relativity has ${\nabla }_{\mu }{T}_i^{\mu \nu }=0$, so ${\dot{\rho }}_i+3H({\rho }_i+P_i)=0$. If energy is transferred between species, source terms $Q_i$ appear and only their sum vanishes. The Friedmann equation still involves the sum of all component stress tensors because all components share one spacetime metric.