Cosmological Evolution of Linear Bias

Abstract

Using linear perturbation theory and the Friedmann-Lemaitre solutions of the cosmological field equations, we derive analytically 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 semi-analytic model of Mo & White, which utilises the Press-Schechter formalism and the 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 even up to large redshifts.