Modified gravity or imperfect dark matter: a model-independent discrimination

TL;DR

This paper develops a model-independent framework to distinguish between modified gravity and imperfect dark matter by analyzing their effects on cosmological observables, focusing on the sub-Hubble regime and using Fisher forecasts.

Contribution

It introduces a parametrization of dark matter perturbations with five functions and identifies three observable combinations to discriminate between gravity modifications and dark matter imperfections.

Findings

Observable signals differ for gravity modifications versus dark matter imperfections.

Three key parameter combinations can be constrained to distinguish models.

Fisher forecast demonstrates potential to identify shear viscosity effects.

Abstract

We analyze how to parametrize general modifications of the dark matter perturbations equations in a model-independent way. We prove that a general model with an imperfect and non-conserved dark matter fluid with bulk and shear viscosities and heat flux in a modified gravity scenario can be described with five general functions of time and scale. We focus on the sub-Hubble regime within the quasi-static approximation and calculate the observable power spectra of the galaxy distribution, galaxy velocities and weak lensing and find that these observables are only sensitive to three combinations of the initial five functions. Deviations of these three observable functions with respect to $\mathrm{\Lambda CDM}$ give us different characteristic signals which allow us to determine in which cases it is possible to discriminate a modification of gravity from an imperfect or non-conserved dark matter. Finally, we perform a Fisher forecast analysis for these three parameters and show an example for a particular model with shear viscosity.