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When Dark Energy Turns On: Constraints on a Critical Emergence Model

Mahdi Najafi, Mahdi Habibollahi, Masoume Reyhani, Eleonora Di Valentino, Supriya Pan, Javad T. Firouzjaee, Weiqiang Yang

Abstract

We investigate a specific emergent dark energy scenario, known as critically emergent dark energy (CEDE), in which dark energy is effectively absent in the early Universe and becomes dynamically relevant only after a critical cosmic epoch through a phase transition. We constrain this model using recent cosmological observations, including cosmic microwave background (CMB) data from \emph{Planck} 2018, baryon acoustic oscillation (BAO) measurements from SDSS and DESI DR2, and two independent Type Ia supernova compilations, PantheonPlus and Union3. Our results show that within the CEDE framework a dark energy phase transition is not ruled out. In particular, CMB-only, CMB+SDSS, and CMB+DESI datasets provide evidence for a nonzero transition scale factor and, according to standard statistical indicators such as $Δχ^2$ and Bayesian evidence, can favor CEDE over the $Λ$CDM model. At the same time, we find that CEDE does not fully resolve the Hubble constant tension. Overall, our analysis indicates that dark energy models featuring a phase transition remain a viable and phenomenologically interesting extension of the standard cosmological framework. Upcoming high-precision cosmological surveys will be essential to further assess whether such emergent dark energy scenarios represent a genuine departure from $Λ$CDM or an effective description of current data.

When Dark Energy Turns On: Constraints on a Critical Emergence Model

Abstract

We investigate a specific emergent dark energy scenario, known as critically emergent dark energy (CEDE), in which dark energy is effectively absent in the early Universe and becomes dynamically relevant only after a critical cosmic epoch through a phase transition. We constrain this model using recent cosmological observations, including cosmic microwave background (CMB) data from \emph{Planck} 2018, baryon acoustic oscillation (BAO) measurements from SDSS and DESI DR2, and two independent Type Ia supernova compilations, PantheonPlus and Union3. Our results show that within the CEDE framework a dark energy phase transition is not ruled out. In particular, CMB-only, CMB+SDSS, and CMB+DESI datasets provide evidence for a nonzero transition scale factor and, according to standard statistical indicators such as and Bayesian evidence, can favor CEDE over the CDM model. At the same time, we find that CEDE does not fully resolve the Hubble constant tension. Overall, our analysis indicates that dark energy models featuring a phase transition remain a viable and phenomenologically interesting extension of the standard cosmological framework. Upcoming high-precision cosmological surveys will be essential to further assess whether such emergent dark energy scenarios represent a genuine departure from CDM or an effective description of current data.
Paper Structure (5 sections, 18 equations, 6 figures, 5 tables)

This paper contains 5 sections, 18 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Critically Emergent Dark Energy
  3. Statistical methodology and observational datasets
  4. Results
  5. Summary and Discussions

Figures (6)

  • Figure 1: Redshift evolution of the dimensionless DE density $\widetilde{\Omega}_{\rm DE}(z)$ in the CEDE model for different values of the critical redshift $z_c$, compared with the PEDE and $\Lambda$CDM models. In all cases, we fix the present-day DE density to $\Omega_{\rm DE,0}=0.7$.
  • Figure 2: Evolution of the growth-rate observable $f\sigma_8(z)$ for the CEDE model, compared with the PEDE and $\Lambda$CDM scenarios. The curves are shown alongside observational measurements from various large-scale structure surveys. The vertical grey line indicates the redshift at which the dark energy equation of state $w_{\rm DE}$ diverges in the CEDE model.
  • Figure 3: One-dimensional marginalized posterior distributions and two-dimensional joint confidence contours for selected CEDE model parameters, obtained using the combined CMB, SDSS BAO, PantheonPlus, and Union3 datasets.
  • Figure 4: One-dimensional marginalized posterior distributions and two-dimensional joint confidence contours for selected CEDE model parameters, obtained using the combined CMB, DESI BAO, PantheonPlus, and Union3 datasets.
  • Figure 5: Rescaled Hubble parameter $H(z)/(1+z)$ showing the 68% and 95% confidence regions for the CEDE model obtained from CMB+SDSS (upper panel) and CMB+DESI (lower panel), compared with the corresponding SDSS and DESI BAO measurements eBOSS_DR16_cosmoDESI:2025zgx.
  • ...and 1 more figures