Cosmological Evolution of Linear Bias

Abstract

Using linear perturbation theory and the Friedmann-Lemaitre solutions of the cosmological field equations, we analytically derive a second-order differential equation for the evolution of the linear bias factor, b(z), between the background matter and a mass-tracer fluctuation field. We find b(z) to be a strongly dependent function of redshift in all cosmological models. Comparing our analytical solution with the semianalytic model of Mo & White, which utilizes the Press-Schechter formalism and gravitationally induced evolution of clustering, we find an extremely good agreement even at large redshifts, once we normalize to the same bias value at two different epochs, one of which is the present. Furthermore, our analytic b(z) function agrees well with the outcome of N-body simulations.