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

TL;DR

The paper tackles the H0 and related cosmological tensions by introducing a phase-transition in the dark-energy sector, modeled as a two-valued cosmological constant $Λ$ with a transition at $a_t$. The approach draws on critical phenomena (Ising-like two-state dynamics) and imposes two Friedmann evolutions pre-transition, converging to standard $Λ$CDM post-transition; perturbations remain standard. Using Planck TT, BAO, LSS, and R19 data, the authors find $a_t≈0.916$ and $H_0≈72.8$, with a significantly better fit than $Λ$CDM ($Δχ^2≈-11$, $Δ$AIC≈-7) and apparent resolution of the H0 tension. The work suggests dark-energy microstructure could address multiple cosmological tensions and outlines future directions to generalize the phase-transition framework.

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-$Λ$ Cold Dark Matter": $ΛΛ$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. $ΛΛ$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 $ΛΛ$CDM model. In comparison to $Λ$CDM, 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 $Δ$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.

Figures (8)

• Figure 1: Here we sketch Ising model and our approximation of it in a cartoon. In line a we can see that Ising model in high temperatures sees two states (here we showed them by black and white small boxes) randomly. However when we are close to the critical temperature then one of the states becomes dominant (here the black states). Then if the temperature goes to absolute zero all the states will be black. In our approximation, line b, we assumed before the transition scale factor we have black and white states one by one and after the transition scale factor we switch to black states. Note that in our cosmological scenario increasing scale factor $a$ means decreasing temperature and a transition scale factor $a_t$ corresponds to the critical temperature.
• Figure 2: We have plotted the order parameter versus temperature. In a real Ising model the order parameter (in this case the magnetization) which is zero for above $T_c$ starts to take either a positive or negative value. In our approximation this transition is assumed to be sharp as it is demonstrated in FIG. \ref{['fig:demonst']}. Physically, it means our system transits from the critical temperature very quickly.
• Figure 3: $\mathop{ \hbox{$\Lambda$} \mkern2mu \hbox{$\Lambda$} }$CDM (with non-trivial $a_t$) $68\%$ and $95\%$ parameter constraint contours from two sets of data points both including CMB and BAO but the green one has R19 in addition. We have also added a marker in $H_0$ posterior distribution and corresponding contours to show the value of $H_0$ data point. we have to emphasize that $\mathop{ \hbox{$\Lambda$} \mkern2mu \hbox{$\Lambda$} }$CDM model prediction for $H_0$ for only CMB+BAO dataset is consistent with R19. This is very important to reach to this consistency before adding R19 as a data point since for sure adding R19 is in favor of higher $H_0$.
• Figure 4: Comparison between the inferred $H_0$ posteriors from two models, $\Lambda$CDM and $\mathop{ \hbox{$\Lambda$} \mkern2mu \hbox{$\Lambda$} }$CDM when all the data points (TT+BAO+R19) are used and that of directly measured by R19. It is clear that our model solves the $H_0$ tension since $\mathop{ \hbox{$\Lambda$} \mkern2mu \hbox{$\Lambda$} }$CDM posterior for $H_0$ parameter has overlap with the same posterior from $\Lambda$CDM model in $2\sigma$ region. In addition R19 is obviously compatible with $\mathop{ \hbox{$\Lambda$} \mkern2mu \hbox{$\Lambda$} }$CDM model prediction.
• Figure 5: The metric distance, $D_M(z)$, normalized to $\Lambda$CDM best fit values prediction.