Cosmological adiabatic sound speed ($c_a^2={\bar{P}}^{\prime }/{\bar{\rho }}^{\prime }$)

The squared adiabatic sound speed is the ratio of background pressure and energy-density time derivatives. For a barotropic equation of state it is $dP/d\rho$. The non-adiabatic pressure perturbation is the difference $\delta P-c_a^2\delta \rho$; in a general field or multicomponent model this background quantity need not equal the rest-frame propagation speed.