Scale-Dependent Gravitational Couplings in Parameterised Post-Newtonian 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.