{wiki=Adiabatic_process#Cosmology}

Adiabatic initial conditions perturb every species by the same local time shift, so their relative number-density ratios are initially unperturbed. Photon acoustic modes then begin predominantly as displacement modes with cosine phase.

Equivalently, $\delta\rho_i/\dot{\bar\rho}_i$ is independent of the component $i$. The <non-adiabatic pressure perturbation> then vanishes, and the <comoving curvature perturbation> is conserved on <superhorizon scales> when anisotropic stress and gradient terms can be neglected.

= Adiabatic cosmological perturbation
{synonym}


Adiabatic initial conditions

{title2=$\delta P_{\rm nad}$}

The non-adiabatic pressure perturbation is
$$
\delta P_{\rm nad}=\delta P-\frac{\dot{\bar P}}{\dot{\bar\rho}}\delta\rho.
$$
On <superhorizon scales> it sources the evolution of the <comoving curvature perturbation> through a convention-dependent signed relation proportional to $H\delta P_{\rm nad}/(\bar\rho+\bar P)$.


Codex @codex  0

 Incoming links: Non-adiabatic pressure perturbation