Minimal parameterizations for modified gravity

TL;DR

This paper introduces a new, flexible parameterization of modified gravity using two functions of time and scale, enabling systematic testing of deviations from general relativity with cosmological data.

Contribution

It proposes a novel approach linking modifications to gravity directly with field equations, improving observational confrontability and comparison with existing parameterizations.

Findings

New parameterization linked to field equations

Comparison with existing methods like PPF and bc,b3b4

Illustration with toy model showing qualitative features

Abstract

The increasing precision of cosmological data provides us with an opportunity to test general relativity (GR) on the largest accessible scales. Parameterizing modified gravity models facilitates the systematic testing of the predictions of GR, and gives a framework for detecting possible deviations from it. Several different parameterizations have already been suggested, some linked to classifications of theories, and others more empirically motivated. Here we describe a particular new approach which casts modifications to gravity through two free functions of time and scale, which are directly linked to the field equations, but also easy to confront with observational data. We compare our approach with other existing methods of parameterizing modied gravity, specifically the parameterized post-Friedmann approach and the older method using the parameter set $\{\mu,\gamma\}$. We explain the connection between our parameters and the physics that is most important for generating cosmic microwave background anisotropies. Some qualitative features of this new parameterization, and therefore modifications to the gravitational equations of motion, are illustrated in a toy model, where the two functions are simply assumed to be constant parameters.