Can varying the gravitational constant alleviate the tensions ?

TL;DR

This study investigates whether allowing the gravitational constant to vary over redshift can resolve existing tensions in cosmological parameters, using CMB and galaxy clustering data, but finds no significant alleviation.

Contribution

It introduces a framework to treat the gravitational constant as a free, possibly dynamical parameter in cosmological models and tests its impact on parameter tensions.

Findings

Varying G does not resolve H0 and σ8 tensions with current data.

Constraints on G remain close to the local value, within 1-4%.

Allowing G to run does not significantly alter cosmological conclusions.

Abstract

Constraints on the cosmological concordance model parameters from observables at different redshifts are usually obtained using the locally measured value of the gravitational constant $G_N$. Here we relax this assumption, by considering $G$ as a free parameter, either constant over the redshift range or dynamical but limited to differ from fiducial value only above a certain redshift. Using CMB data and distance measurements from galaxy clustering BAO feature, we constrain the cosmological parameters, along with $G$, through a MCMC bayesian inference method. Furthermore, we investigate whether the tensions on the matter fluctuation $\sigma_8$ and Hubble $H_0$ parameter could be alleviated by this new variable. We used different parameterisations spanning from a constant $G$ to a dynamical $G$. In all the cases investigated in this work we found no mechanism that alleviates the tensions when both CMB and BAO data are used with $\xi_{\mathrm{g}} = G / G_N$ constrained to 1.0$\pm0.04$ (resp. $\pm0.01$) in the constant (resp. dynamical) case. Finally, we studied the cosmological consequences of allowing a running of the spectral index, since the later is sensitive to a change in $G$. For the two parameterisations adopted, we found no significant changes to the previous conclusions.