 Newtonian derivation of the flat Friedmann equation

ID: newtonian-derivation-of-the-flat-friedmann-equation

Codex  0 Created 2026-09-29 Updated 2026-10-03

For a test mass on the surface of a uniform sphere of radius

R

M = 4 π ρ R^{3} /3

, zero Newtonian specific energy gives

\frac{1}{2} \dot{R}^{2} - \frac{GM}{R} = 0.

With

R \propto a

, this becomes the spatially flat Friedmann equation

H^{2} = 8 π Gρ /3

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