# A question of separation: disentangling tracer bias and gravitational nonlinearity with counts-in-cells statistics

## TL;DR

This paper develops a model linking dark matter and tracer densities using counts-in-cells statistics, validated with simulations, and enabling joint estimation of dark matter variance and bias parameters for future galaxy surveys.

## Contribution

It introduces a quadratic bias model combined with large deviation theory to accurately predict tracer density statistics from dark matter models.

## Key findings

- Excellent agreement with Horizon Run 4 simulation data.
- Effective joint estimation of dark matter variance and bias parameters.
- Applicability to upcoming galaxy surveys like Euclid and WFIRST.

## Abstract

Starting from a very accurate model for density-in-cells statistics of dark matter based on large deviation theory, a bias model for the tracer density in spheres is formulated. It adopts a mean bias relation based on a quadratic bias model to relate the log-densities of dark matter to those of mass-weighted dark haloes in real and redshift space. The validity of the parametrised bias model is established using a parametrisation-independent extraction of the bias function. This average bias model is then combined with the dark matter PDF, neglecting any scatter around it: it nevertheless yields an excellent model for densities-in-cells statistics of mass tracers that is parametrised in terms of the underlying dark matter variance and three bias parameters. The procedure is validated on measurements of both the one and two point statistics of subhalo densities in the state-of-the-art Horizon Run 4 simulation showing excellent agreement for measured dark matter variance and bias parameters. Finally, it is demonstrated that this formalism allows for a joint estimation of the nonlinear dark matter variance and the bias parameters using solely the statistics of subhaloes. Having verified that galaxy counts in hydrodynamical simulations sampled on a scale of 10 Mpc/h closely resemble those of subhaloes, this work provides important steps towards making theoretical predictions for density-in-cells statistics applicable to upcoming galaxy surveys like Euclid or WFIRST.