Equations · equation

Second Friedmann Equation

Cosmology · 1922

Equation
ä/a = −4πG(ρ + 3p/c²)/3 + Λc²/3
Field
Cosmology
Named After
Alexander Friedmann
Year
1922

Symbols

a the scale factor of the universe · ä its second time derivative, the acceleration of the expansion · G gravitational constant · ρ energy density · p pressure — it is the 3p term that makes radiation slow the expansion harder than matter does, and a negative enough p that reverses the sign · Λ the cosmological constant · c speed of light

Significance

Whether the expansion speeds up or slows down. Matter and pressure put on the brakes; the cosmological constant steps on the gas — exactly what the 1998 supernova surveys found the universe doing.

Timeline

Theories

Related

Instruments

Constants

Requires

Referenced by

constant
equation
event
instrument
theory

Open on the Equations shelf — the interactive card, the filters, and everything alongside it.

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.