  In this work we extend our earlier phenomenological model for a gravitational
phase transition (GPT) and its generalization to early times by letting the
modifications in the linearly-perturbed Einstein equations be scale-dependent.
These modifications are characterized as deviations of the parameters
$\mu(z,k)$ and $\gamma(z,k)$ from their values in general relativity (GR). The
scale-dependent amplitudes of modified $\mu(z,k)$ and $\gamma(z,k)$ and the
parameters defining the phase transition, along with the standard cosmological
parameters, are measured by various data combinations. Out of the perturbation
parameters, we construct gravity eigenmodes which represent patterns of
perturbations best detectable by data. We detect no significant deviation from
GR in these parameters. However, the larger parameter space produced due to the
new degrees of freedom allows for the reconciliation of various datasets which
are in tension in $\Lambda$CDM. In particular, we find $H_0=71.9\pm 9.2$ from
anisotropies of the Cosmic Microwave Background as measured by Planck and
various measurements of the Baryonic Acoustic Oscillations, in agreement with
local Hubble measurements. We also find that the $\sigma_8$ tension between the
measurements of Dark Energy Survey and Planck is reduced to less than
$1\sigma$.
