Equations · equation

Critical Density

Cosmology · 1932

Equation
ρ_c = 3H² / (8πG)
Field
Cosmology
Named After
Georges Lemaître · Howard Robertson
Year
1932

Symbols

ρ_c the density that makes space exactly flat · H the Hubble parameter at that epoch · G gravitational constant · densities are quoted against it as Ω = ρ/ρ_c

Significance

The tipping-point density: above it space curves closed, below it open, exactly at it flat. Today it is about 8.5 × 10⁻²⁷ kg/m³ taking H₀ = 67 km/s/Mpc — five hydrogen atoms per cubic metre, a better vacuum than any laboratory can make, and yet the density that decides the shape of the cosmos. Take H₀ = 73 instead and it rises to 10 × 10⁻²⁷, which is one more way of saying the Hubble tension is not a small argument. Measurements put the total at Ω = 1.000 ± 0.002, flat to a fifth of a percent, which is the observation inflation was invented to explain.

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From the Equations database in Notion, last edited 2026-08-26. This page is the row, rendered by the build; nothing on it is written by hand.