Horizon angle at matter-radiation equality (source code)

= Horizon angle at matter-radiation equality
{title2=$\theta_{\rm eq}\simeq\tau_{\rm eq}/(\tau_0-\tau_{\rm eq})$}

A horizon-length patch on the <matter-radiation equality> surface has physical size $a_{\rm eq}\tau_{\rm eq}$ in a flat universe with <conformal time> measured from the <Big Bang>. Dividing by its <angular diameter distance> $a_{\rm eq}(\tau_0-\tau_{\rm eq})$ gives its small angular size. For the <radiation-matter scale factor in conformal time>, this is $(\sqrt2-1)\sqrt{\Omega_{r,0}}/[1-\sqrt{2\Omega_{r,0}}]$. A patch diameter is twice the angle associated with one horizon radius. The <particle horizon> is an integral over past evolution and must not be silently replaced by the instantaneous <Hubble radius>.