= Flat matter-radiation conformal solution
{title2=$a(\eta)=H_0\sqrt{\Omega_{R,0}}\eta+\Omega_{M,0}H_0^2\eta^2/4$}
For a spatially flat <FLRW metric> containing conserved <pressureless matter> and <radiation in cosmology>, with $a_0=1$ and <conformal time> zero at the <Big Bang>, the <Friedmann equation> gives $a'^2=H_0^2(\Omega_{M,0}a+\Omega_{R,0})$. Separating the positive square root gives the displayed <scale factor>. At <matter-radiation equality>, $a_{\rm eq}=\Omega_{R,0}/\Omega_{M,0}$ and $\eta_{\rm eq}=2(\sqrt2-1)\sqrt{\Omega_{R,0}}/(H_0\Omega_{M,0})$. Here the prime denotes differentiation with respect to $\eta$, not $c\eta$.
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