A practical approach to cosmological perturbations in modified gravity

TL;DR

This paper proposes a simplified, polynomial-based parametrization for testing deviations from General Relativity in cosmological surveys, enabling more efficient data analysis of modified gravity models.

Contribution

It introduces a polynomial ratio framework for linear perturbations in local gravity theories, reducing the complexity of model constraints from two variables to one.

Findings

Functions are ratios of second-degree even polynomials in k.

Five functions of a single variable suffice for constraints.

Non-parametric fitting with smoothness priors is feasible.

Abstract

The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations, departures from the growth in the LCDM model can be quantified in terms of two functions of time and Fourier number k. We argue that in local theories of gravity, in the quasi-static approximation, these functions must be ratios of polynomials in k, with the numerator of one function being equal to the denominator of the other. Moreover, the polynomials are even and of second degree in practically all viable models considered today. This means that, without significant loss of generality, one can use data to constraint only five functions of a single variable, instead of two functions of two variables. Furthermore, since the five functions are expected to be slowly varying, one can fit them to data in a non-parametric way with the aid of an explicit smoothness prior. We discuss practical application of this parametrization to forecasts and fits.