Ups and Downs in Dark Energy: phase transition in dark sector as a proposal to lessen cosmological tensions

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-Λ Cold Dark Matter": ΛΛCDM. 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. ΛΛCDM has its maximum likelihood for a_t= 0.916^+0.055_-0.0076 and H_0= 72.8± 1.6. This result shows no inconsistency between early and late time measurements of Hubble parameter in ΛΛCDM model. In comparison to ΛCDM, our model has better fit to data such that Δχ^2=-11 and even if we take care of two additional degrees of freedom we do have better AIC quantity ΔAIC=-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.