Scale-Dependent Gravitational Couplings in Parameterised Post-Newtonian Cosmology

TL;DR

This paper extends the Parameterised Post-Newtonian Cosmology framework to include scale-dependent gravitational couplings, verifying its predictions for scalar-tensor theories and assessing the impact of interpolation methods on cosmological observables.

Contribution

It introduces the first investigation of scale-dependent gravitational couplings within the PPNC framework and evaluates simple interpolation functions for transitioning between small and large scales.

Findings

Theoretical predictions of PPNC are verified with high accuracy.

Simple interpolating functions perform well in the transition region.

Study advances the use of PPNC for testing gravity evolution in cosmology.

Abstract

Parameterised Post-Newtonian Cosmology (PPNC) is a theory-agnostic framework for testing gravity in cosmology, which connects gravitational physics on small and large scales in the Universe. It is a direct extension of the Parameterised Post-Newtonian (PPN) approach to testing gravity in isolated astrophysical systems, and therefore allows constraints on gravity from vastly different physical regimes to be compared and combined. We investigate the application of this framework to a class of example scalar-tensor theories of gravity in order to verify theoretical predictions, and to investigate for the first time the scale-dependence of the gravitational couplings that appear within its perturbation equations. In doing so, we evaluate the performance of some simple interpolating functions in the transition region between small and large cosmological scales, as well as the uncertainties that using such functions would introduce into the calculation of observables. We find that all theoretical predictions of the PPNC framework are verified to high accuracy in the relevant regimes, and that simple interpolating functions perform well (but not perfectly) between these regimes. This study is an important step towards being able to use the PPNC framework to analyse cosmological datasets, and to thereby test if/how the gravitational interaction has changed as the Universe has evolved.