Ambiguous Tests of General Relativity on Cosmological Scales

TL;DR

This paper examines how different parameterizations of modified gravity theories impact constraints on General Relativity on cosmological scales, emphasizing the importance of choosing appropriate frameworks for accurate testing.

Contribution

It demonstrates that the choice of parameterization significantly affects constraints on GR and argues for using either highly flexible or theory-specific modifications.

Findings

Alternative parameterizations alter constraints substantially

Insufficiently flexible models tighten constraints artificially

Modifications should either be highly general or directly theory-mapped

Abstract

There are a number of approaches to testing General Relativity (GR) on linear scales using parameterized frameworks for modifying cosmological perturbation theory. It is sometimes assumed that the details of any given parameterization are unimportant if one uses it as a diagnostic for deviations from GR. In this brief report we argue that this is not necessarily so. First we show that adopting alternative combinations of modifications to the field equations significantly changes the constraints that one obtains. In addition, we show that using a parameterization with insufficient freedom significantly tightens the apparent theoretical constraints. Fundamentally we argue that it is almost never appropriate to consider modifications to the perturbed Einstein equations as being constraints on the effective gravitational constant, for example, in the same sense that solar system constraints are. The only consistent modifications are either those that grant near-total freedom, as in decomposition methods, or ones which map directly to a particular part of theory space.