Parametrizing theories of gravity on large and small scales in cosmology

TL;DR

This paper establishes a theoretical link between large-scale and small-scale parametrizations of gravity in cosmology, reducing the complexity of testing gravity across different regimes by expressing key functions in terms of four time-dependent parameters.

Contribution

It introduces a novel framework connecting gravity parametrizations on vastly different scales using only theoretical consistency, simplifying multi-scale observational tests.

Findings

Derived relations for slip and Newton's constant in terms of four functions of time.

Generalized post-Newtonian parameters to cosmological scales.

Reduced degrees of freedom needed for consistent gravity testing.

Abstract

We present a link between parametrizations of alternative theories of gravity on large and small scales in cosmology. This relationship is established using theoretical consistency conditions only. We find that in both limits the "slip" and "effective Newton's constant" can be written in terms of a set of four functions of time, two of which are direct generalizations of the $\alpha$ and $\gamma$ parameters from post-Newtonian physics. This generalizes previous work that has constructed frameworks for testing gravity on small scales, and is to the best of our knowledge the first time that a link between parametrizations of gravity on such very different scales has been established. We expect our result to facilitate the imposition of observational constraints, by drastically reducing the number of functional degrees of freedom required to consistently test gravity on multiple scales in cosmology.