Phase transition in the dark sector as a proposal to lessen cosmological tensions

Abstract

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-$\mathrm{\ensuremath{\Lambda}}$ Cold Dark Matter'': $\mathrm{\ensuremath{\Lambda}}\phantom{\rule[-0.0ex]{-0.45em}{0.0ex}}\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. 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. $\mathrm{\ensuremath{\Lambda}}\phantom{\rule[-0.0ex]{-0.45em}{0.0ex}}\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ has its maximum likelihood for ${a}_{t}=0.85{1}_{+0.027}^{+0.12}$ and gives ${H}_{0}={72.2}_{\ensuremath{-}1.5}^{+2.2}$. This result shows no inconsistency between early and late time measurements of the Hubble parameter in the $\mathrm{\ensuremath{\Lambda}}\phantom{\rule[-0.0ex]{-0.45em}{0.0ex}}\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. In comparison to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, our model has better fit to data with $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}=\ensuremath{-}16$ and we even have a better Akaike information criterion (AIC) quantity $\mathrm{\ensuremath{\Delta}}\mathrm{AI}\mathrm{C}=\ensuremath{-}12$, 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 ${H}_{0}$ tension successfully and may be responsible for the other cosmological tensions.