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Alexander Friedmann derived evolving homogeneous cosmological solutions of the Einstein field equations. The Friedmann equations relate cosmic expansion to energy density, pressure, spatial curvature and the cosmological constant.

The conceptual change is that general relativity permits the scale of a homogeneous universe to evolve, rather than requiring a static geometry. Observational evidence and the choice of matter content are additional inputs needed to identify which mathematical solution describes the Universe.^[ref]

The Friedmann equations, named for Alexander Friedmann, apply the Einstein field equations to an FLRW metric. Using natural units with $c=1$, energy density $\rho$, pressure $p$ and cosmological constant $\Lambda$, they readHere $a$ is the scale factor, $H=\dot{a}/a$ the Hubble parameter, and $k$ specifies spatial curvature. The cosmological continuity equation completes the fluid description. For a flat universe with $\Lambda =0$, pressureless matter gives $a\propto t^{2/3}$ and radiation in cosmology gives $a\propto t^{1/2}$.^[ref]