 Matter growth equation as a function of scale factor

ID: matter-growth-equation-as-a-function-of-scale-factor

In a matter-plus-cosmological-constant universe, changing the independent variable from cosmic time to

a

gives

\frac{d ^{2} δ _{m}}{d a ^{2}} + (\frac{d l o g H}{d a} + \frac{3}{a}) \frac{d δ _{m}}{d a} - \frac{3 Ω _{m, 0} H _{0}^{2}}{2 a ^{5} H ^{2}} δ_{m} = 0.

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