= Redshift evolution of the Lyman-alpha forest
The <Lyman-alpha forest> becomes denser and more opaque towards higher <cosmological redshift>, for a fixed absorption selection over the ordinary post-reionization range. The incidence is often parametrized as $d\mathcal N/dz=A(1+z)^\gamma$, with the index depending on the <column density> threshold and epoch. The evolution flattens at low redshift as the declining <cosmic ionizing background> partly offsets dilution of the <intergalactic medium>. For optically thin gas at fixed overdensity, <photoionization equilibrium> gives approximately $n_{\rm HI}\propto\alpha(T)(1+z)^6/\Gamma$, illustrating why density, temperature and ionizing radiation all matter.
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