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Cosmic-time matter density modes

In cosmic time during matter domination,

a (t) \propto t^{2/3}

and the pressureless density contrast obeys

\ddot{δ} + \frac{4}{3 t} \dot{δ} - \frac{2}{3 t ^{2}} δ = 0.

Its growing and decaying solutions are

t^{2/3}

and

t^{- 1}

.

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