= Flat dust-vacuum Hubble parameter
{title2=$H(z)=H_0[\Omega_{m0}(1+z)^3+\Omega_{\Lambda0}]^{1/2}$}
For <pressureless matter>, a positive <cosmological constant>, flat spatial geometry and negligible <radiation>, the <continuity equation> gives $\rho_m\propto a^{-3}$. Substitution in the <Friedmann equation> yields the displayed <Hubble parameter>, with $\Omega_{m0}+\Omega_{\Lambda0}=1$. <radiation> must be restored at early epochs; the formula does not require matter to be the largest present-day density component.
Back to article page
