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Friedmann Equations

A set of equations governing the expansion of a homogeneous and isotropic universe, central to inflationary cosmology.

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The statement of the theorem

Consider a homogeneous and isotropic universe described by the metric

ds^2 = -c^2 dt^2 + a(t)^2 (dx^2 + dy^2 + dz^2)

. The first Friedmann equation relates the Hubble parameter

H = \dot{a}/a

to the total energy density

\rho

and the spatial curvature

k

: \n

\left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3c^2} \rho - \frac{kc^2}{a^2}

Source: Wikipedia