A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension

TL;DR

The paper introduces PEDE, a simple emergent dark-energy model with no extra degrees of freedom, where dark energy is negligible in the early universe and rises at late times. The PEDE density follows $ ilde{ ho}_{DE}(z)= ho_{DE,0}[1- anh( ext{log}_{10}(1+z))]$, yielding an evolving equation of state that approaches $w=-1$ in the far future while starting near $-1-rac{2}{3 ext{ln}10}$. By applying hard priors on the local H0 measurement and combining SN Ia, BAO, Lyα BAO, and CMB data, PEDE substantially improves statistical fit over ΛCDM (and over CPL in some cases), with large reductions in DIC and substantial χ^2 gains, indicating a potential resolution to H0-related tensions. However, without H0 priors the gains diminish and some tension in Ωm persists, underscoring the pivotal role of the H0 prior in distinguishing models. The results motivate further theoretical development of emergent dark-energy scenarios as viable alternatives to the cosmological constant in the current cosmological paradigm.

Abstract

Motivated by the current status of the cosmological observations and significant tensions in the estimated values of some key parameters assuming the standard $Λ$CDM model, we propose a simple but radical phenomenological emergent dark energy model where dark energy has no effective presence in the past and emerges at the later times. Theoretically, in this phenomenological dark energy model with zero degree of freedom (similar to a $Λ$CDM model), one can derive that the equation of state of dark energy increases from $-\frac{2}{3 {\rm{ln}}\, 10} -1$ in the past to $-1$ in the future. We show that by setting a hard-cut 2$σ$ lower bound prior for the $H_0$ that associates with $97.72\%$ probability from the recent local observations~\citep{riess2019large}, this model can satisfy different combinations of cosmological observations at low and high redshifts (SNe Ia, BAO, Ly{$α$} BAO and CMB) substantially better than the concordance $Λ$CDM model with $Δχ^2_{bf} \sim -41.08$ and $Δ\,{\rm{DIC}} \sim-35.38$. If there are no substantial systematics in SN Ia, BAO or Planck CMB data and assuming reliability of the current local $H_0$ measurements, there is a very high probability that with slightly more precise measurement of the Hubble constant our proposed phenomenological model rules out the cosmological constant with decisive statistical significance and is a strong alternative to explain combination of different cosmological observations. This simple phenomenologically emergent dark energy model can guide theoretically motivated dark energy model building activities.

Figures (4)

• Figure 1: The upper plot shows the evolution of dark energy density $\Omega_{\rm{DE}}(z)$ from early times to the far future and the bottom plot presents the evolution of Equation of State of Dark Energy $w(z)$ for $\Lambda$CDM and PEDE models. This figure is only for demonstrating the behavior of this model in comparison with cosmological constant and flatness and $\Omega_m\,=\,0.3$ is assumed for both $\rm{\Lambda}CDM$ and PEDE models.
• Figure 2: 2-D regions and 1-D marginalized distributions with 1$\sigma$ and 2$\sigma$ contours for $\rm{\Lambda}CDM$ model from different observations. From left to right, we use No $H_0$ prior, 2$\sigma$ hard-cut $H_0$ prior and 1$\sigma$ hard-cut $H_0$ prior from riess2019large, respectively. The black curves/contours denote for the constraints from Pantheon+BAO and the blue ones are derived with Pantheon+BAO+Ly$\alpha$+CMB data combination.
• Figure 3: 2-D regions and 1-D marginalized distributions with 1$\sigma$ and 2$\sigma$ contours for PEDE model from different observations. From left to right, we use No $H_0$ prior, 2$\sigma$ hard-cut $H_0$ prior and 1$\sigma$ hard-cut $H_0$ prior from riess2019large, respectively. The black curves/contours denote for the constraints from Pantheon+BAO and the blue ones are derived with Pantheon+BAO+Ly$\alpha$+CMB data combination.
• Figure 4: The histograms of $\chi^2$ distribution from the converged MCMC chains for $\Lambda$CDM model, CPL and PEDE are presented. The left plots shows the $\chi^2$ distribution for the Pantheon+BAO combination and the right plots are obtained with Pantheon+BAO+Ly$\alpha$+CMB combination. Upper plots are derived with setting 2$\sigma$$H_0$ hard-cut prior and lower plots are derived with setting 1$\sigma$ hard-cut $H_0$ prior. Combining all the data, there is hardly an overlap between the $\chi^2$ distribution of the PEDE model and $\Lambda$CDM model that explains the huge difference we derived for their DIC.