Scale-dependent halo bias from scale-dependent growth

TL;DR

This paper derives a general expression for large-scale halo bias in theories with scale-dependent growth, including modified gravity and dark energy models, and applies it to constrain such theories using galaxy clustering data.

Contribution

It extends the excursion set formalism to include scale-dependent growth and accounts for mergers, providing a new analytic bias expression applicable to modified gravity models.

Findings

Derived a general formula for scale-dependent halo bias.

Applied the model to a Yukawa gravity modification.

Used SDSS data to constrain gravity model parameters.

Abstract

We derive a general expression for the large-scale halo bias, in theories with a scale-dependent linear growth, using the excursion set formalism. Such theories include modified gravity models, and models in which the dark energy clustering is non-negligible. A scale dependence is imprinted in both the formation and evolved biases by the scale-dependent growth. Mergers are accounted for in our derivation, which thus extends earlier work which focused on passive evolution. There is a simple analytic form for the bias for those theories in which the nonlinear collapse of perturbations is approximately the same as in general relativity. As an illustration, we apply our results to a simple Yukawa modification of gravity, and use SDSS measurements of the clustering of luminous red galaxies to constrain the theory's parameters.