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 ” : \mathop { \hbox to 0.0 pt { $ \Lambda$ } \mkern 2.0 mu \makebox [ 7.499886 pt ] { $ \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 . \mathop { \hbox to 0.0 pt { $ \Lambda$ } \mkern 2.0 mu \makebox [ 7.499886 pt ] { $ \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 \mathop { \hbox to 0.0 pt { $ \Lambda$ } \mkern 2.0 mu \makebox [ 7.499886 pt ] { $ \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 .