Phenomenological Gravitational Phase Transition: Reconciliation between
  the Late and Early Universe
  In this work we investigate whether a certain phenomenological extension to
the general relativity (GR), in the form of a gravitational phase transition
(GPT) in the Universe, can reduce the external $Planck$ tensions with the local
Hubble measurements and the distribution of matter, characterized by
$\sigma_8$, as well as its internal inconsistencies in the lensing amplitude
and the low--high $\ell$ parameter estimates. We introduce new degrees of
freedom into the background and the two scalar perturbation equations in the
Newtonian gauge, with simultaneous transitions from an early gravitational
phase equivalent to GR toward a late phase. We model the transition as a "tanh"
parametrized by the transition redshift $z_{\rm t}$ and width $\alpha$, with
amplitudes $\Lambda(z)$ and $(\mu(z),\gamma(z))$ for the background and
perturbations respectively. We verify the consistency of the datasets used in
this work in the GPT framework and confirm that the individual tensions do not
require conflicting transitions. We find that the joint datasets prefer a
recent transition at $z_{\rm t}\approx 0.9$ in the background and perturbed
Einstein equations, driven mainly by the local Hubble measurement. This
transition relaxes all the tensions considered in this work.
