  Based on tensions between the early and late time cosmology, we proposed a
double valued cosmological constant which could undergo a phase transition in
its history. It is named "double-$\Lambda$ Cold Dark Matter":
$\Lambda\Lambda$CDM. An occurred phase transition results in (micro-)
structures for the dark sector with a proper (local) interaction. In this
paper, inspired by the physics of critical phenomena, we study a simplified
model such that the cosmological constant has two values before a transition
scale factor, $a_t$, and afterwards it becomes single-valued. We consider both
the background and perturbation data sets including CMB, BAO distances and R19
data point. $\Lambda\Lambda$CDM has its maximum likelihood for $a_t=
0.916^{+0.055}_{-0.0076}$ and $H_0= 72.8\pm 1.6$. This result shows no
inconsistency between early and late time measurements of Hubble parameter in
$\Lambda\Lambda$CDM model. In comparison to $\Lambda$CDM, our model has better
fit to data such that $\Delta\chi^2=-11$ and even if we take care of two
additional degrees of freedom we do have better AIC quantity $\Delta$AIC$=-7$.
We conclude that a phase transition in the behavior of dark energy can address
$H_0$ tension successfully and may be responsible for the other cosmological
tensions.
