 Total and relative density modes of two pressureless matter fluids

ID: total-and-relative-density-modes-of-two-pressureless-matter-fluids

f_{B}, f_{D}

S = f_{B} Δ_{B} + f_{D} Δ_{D}

obeys the usual self-gravitating growth equation, while

D = Δ_{D} - Δ_{B}

obeys

\ddot{D} + 4 \dot{D} / (3 t) = 0

. Thus

S = A t^{2/3} + B t^{- 1}

and

D = C + E t^{- 1/3}

. The individual contrasts are

Δ_{B} = S - f_{D} D

and

Δ_{D} = S + f_{B} D

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