Can varying the gravitational constant alleviate the tensions ?

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$\pm 0.04$ (resp. $\pm 0.01$) 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.

Swiflty accepted and published in JCAP. Minor changes and references added in this version after proof reading. 18 pages, 9 figures

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