Galaxy density contrast (${\delta }_g=(n_g-{\bar{n}}_g)/{\bar{n}}_g$)

The galaxy density contrast measures a fractional departure of galaxy number density from its ensemble or survey mean. Linear galaxy bias relates its large-scale three-dimensional component to the matter density contrast by ${\delta }_g=b_g{\delta }_m$. An angular sample averages this field with its normalized redshift selection; a probability density $p(z)$ per unit cosmological redshift corresponds to a distance kernel $H(z)p(z)/c$ in a spatially flat background.