Scale-dependent halo bias from scale-dependent growth

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 Sloan Digital Sky Survey measurements of the clustering of luminous red galaxies to constrain the theory's parameters.