Cosmological optical depth (source code)

= Cosmological optical depth
{title2=$\tau(\eta)$}

The optical depth from conformal time $\eta$ to observation at $\eta_0$ is
$$
\tau(\eta)=\int_\eta^{\eta_0}\Gamma(\eta')\,d\eta'.
$$
The factor $e^{-\tau(\eta)}$ is the probability that a photon travels from $\eta$ to the observer without another scattering.