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Linear cosmological density perturbation

Density contrast

For a pressureless fluid with
$$
\rho=\bar\rho+\epsilon\,\delta\rho,
\qquad
\mathbf v=\epsilon\,\delta\mathbf v,
$$
the first-order <density contrast> $\delta=\delta\rho/\bar\rho$ obeys
$$
\dot\delta=-\frac1a\nabla\cdot\delta\mathbf v.
$$

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Linearized cosmological continuity equation

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Linearized cosmological continuity equation

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