Phase transition in the 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-Lambda Cold Dark Matter: (sic)CDM. The phase transition occurred because of (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 datasets including cosmic microwave background (CMB), Baryon acoustic oscillations (BAO) distances, and R19 data points. (sic)CDM has its maximum likelihood for a= 0.851. This result shows no inconsistency between early and late time measurements of the Hubble parameter in the (sic)CDM model. In comparison to Lambda CDM, our model has better fit to data with Delta = -16 and we even have a better Akaike information criterion (AIC) quantity Delta AIC = -12, where our model is penalized because of two more degrees of freedom. We conclude that a phase transition in the behavior of dark energy can address H tension successfully and may be responsible for the other cosmological tensions.