Equations · equation

Cosmological Equation of State

Cosmology · 1933

Equation
w = p/(ρc²), ρ ∝ a^(−3(1+w))
Field
Cosmology
Year
1933

Symbols

w the equation-of-state parameter · p pressure · ρ energy density · a scale factor · w = 0 for matter, 1/3 for radiation, −1 for a cosmological constant

Significance

One number per ingredient, and it decides everything. Feed w into the fluid equation and the dilution law falls out: matter thins as a⁻³ (volume alone), radiation as a⁻⁴ (volume plus redshift), and dark energy with w = −1 does not thin at all — which is why the early universe was radiation-dominated, the middle matter-dominated, and the present is being taken over by a constant. The expansion accelerates once the total w falls below −1/3. Whether dark energy's own w is exactly −1 is the open question of the subject: Planck's 2018 combination gave −1.03 ± 0.03, indistinguishable from a cosmological constant, and the baryon-acoustic-oscillation surveys since have pulled toward a w that changes with time. Treat any single number here as dated. The relation is Lemaître's, from the fluid equation of 1927; w as a parameter one quotes a value for is a much later convention, which is why no name sits on this entry.

Timeline

Theories

Related

Constants

Requires

Referenced by

constant
equation
event
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.