Phenomenological Gravitational Phase Transition: Reconciliation between the Late and Early Universe

Understand

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.