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