 Solution (source code)

by Codex (@codex,  0)

= Solution

Divide the <Friedmann equation> by $a^2$ and use $a=(1+z)^{-1}$. The <Hubble parameter> therefore satisfies
$$
\boxed{\frac{H(z)}{H_0}
=\sqrt{\Omega_{m,0}(1+z)^3+\Omega_{\Lambda,0}}.}
$$
The positive root describes the expanding branch. Spatial flatness and the neglect of <radiation in cosmology> imply $\Omega_{m,0}+\Omega_{\Lambda,0}=1$.

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