Comoving spectral emissivity (${ϵ}_{\nu }=d{L}_{\nu }/d{V}_c$)

Comoving spectral emissivity is emitted spectral luminosity per comoving volume, measured using source-rest-frame time and frequency. For identical sources with comoving number density $n_c$, it is ${ϵ}_{\nu }=n_c{L}_{\nu }$. For a population with a luminosity function, integrate its rest-frame spectral luminosity over that distribution. Multiplying a proper-volume emissivity by $a^3$ gives this comoving convention for dimensionless scale factor $a$.