= Synchronous perfect-fluid density equation
{title2=$\delta'=(1+w)(k^2\theta-h'/2)$}
For constant $P=w\rho$ and <velocity potential> $v_i=ik_i\theta$, <stress-energy conservation> gives the displayed density equation in <synchronous gauge in cosmology>. Here $h$ is the trace of the spatial metric perturbation, and primes denote <conformal time>. In particular cold baryons obey $\delta_b'=k^2\theta_b-h'/2$. A positive sign in front of $k^2\theta_b$ on the left contradicts this potential convention.
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