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Friedmann equation

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For a test mass on the surface of a uniform sphere of radius $R$ and mass $M=4\pi\rho R^3/3$, zero Newtonian specific energy gives
$$
\frac12\dot R^2-\frac{GM}{R}=0.
$$
With $R\propto a$, this becomes the spatially flat <Friedmann equation> $H^2=8\pi G\rho/3$.

Newtonian derivation of the flat Friedmann equation

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 41 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 9B / Solution

Newtonian derivation of the flat Friedmann equation

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Newtonian derivation of the flat Friedmann equation

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