The Hubble tension as an effect of the renormalization of fundamental constants and cosmological parameters

Abstract

In this Letter we propose an interpretation of the Hubble tension as an effect of the scale-running of cosmological parameters and fundamental constants, as the Newton's constant $G$ and the cosmological constant $\Lambda$. Namely, the tension between $H_0$ measurements by CMB and Supernovae observations would be a consequence of the fact that the value of $H_0$ depends (due to the running of $G$ and $\Lambda$) on the scale at which it is measured. Indeed, the two different values of the Hubble parameter today correspond to the two different cosmological scales at which Supernovae and CMB measurements probe our universe. We discuss some possible theoretical scenarios in which the running of $G$ and $\Lambda$ can occur. We stress that one should interpret such a running as a scale-dependence of the cosmological parameters and fundamental constants at the same time rather than a time dependence, as it is usually considered in the literature.