Cosmic stellar mass density (${\rho }_{\ast }^{\mathrm{com}}={\int }_0^{\infty }{M}_{\ast }{n}_{\ast }(M_{\ast })d{M}_{\ast }$)

The cosmic stellar mass density is the mass moment of a galaxy stellar mass function in a stated volume convention. With a comoving mass function it is mass per comoving volume, while proper density is larger by $(1+z{)}^3$. Comparing it to a critical or matter density requires keeping the epoch and volume convention explicit.