The time-evolution of bias

TL;DR

This paper addresses how the bias factor $b$ and the mass–galaxy correlation $r$ evolve with cosmic time in a simple analytic framework that couples galaxy formation to the gravitational growth of structure. Using a two-variate Gaussian description of mass and luminous-density fluctuations and linear perturbation theory, the authors derive exact evolution relations for the post-formation covariance and show that gravitational clustering tends to drive Bias metrics toward unity, even with ongoing galaxy formation. They extend the model to include a time-dependent galaxy formation rate, a birth bias, and a memory term for random formation events, showing that debiasing is robust and that large initial biases can be produced by stochastic formation but fade as the number of uncorrelated formation epochs increases. The results have implications for interpreting large redshift surveys and for constraining cosmology, suggesting that the time evolution of $b$ and $r$ can be a test of gravitational instability predictions and may be largely cosmology-insensitive when viewed through the growth factor $D$.

Abstract

We study the evolution of the bias factor b and the mass-galaxy correlation coefficient r in a simple analytic model for galaxy formation and the gravitational growth of clustering. The model shows that b and r can be strongly time-dependent, but tend to approach unity even if galaxy formation never ends as the gravitational growth of clustering debiases the older galaxies. The presence of random fluctuations in the sites of galaxy formation relative to the mass distribution can cause large and rapidly falling bias values at high redshift.