Phenomenological Gravitational Phase Transition: Early and Late Modifications

In this work we generalize the idea of a gravitational phase transition or GPT at late times to allow for a modified gravity scenario in the early universe as well. The original GPT was shown to simultaneously relax the $H_0$ and $\sigma_8$ tensions and {\it Planck} internal inconsistencies. However, the primary results from GPT predictions implied disagreement with the data from the baryonic acoustic oscillations (BAO). Here we investigate whether the generalized GPT scenario could address the Hubble tension in the presence of the BAO data as well. We find that, despite the vastly enlarged gravitational parameter space, the BAO data strongly prefer the $\Lambda$CDM paradigm with a low inferred Hubble constant, $68.03\pm 0.76 $ km/s/Mpc, in tension with the local $H_0$ measurements from Riess et al., $H_0=74.03\pm 1.42$ km/s/Mpc. This failure of the generalized GPT scenario to host the P18-BAO-R19 trio is of significance and noticeably shrinks the space of possible gravitational solutions to the Hubble tension.