Constraining Dark Energy Dynamics in Extended Parameter Space

TL;DR

This paper investigates dark-energy dynamics within a 12-parameter extension of ΛCDM, employing the $w(a)=w_0+(1-a)w_a$ parameterization to capture evolution and classify thawing vs freezing behavior. Using Planck 2015 data plus external priors and datasets (Riess et al. H0, BAO, JLA, WL, and CMB lensing), the authors constrain the $w_0$–$w_a$ plane and assess the impact of $A_{ m lens}$ and $\,\, ext{Ω}_k$. They find that Planck+R16 disfavors a cosmological constant and standard quintessence at >95% c.l., with BAO data partially restoring ΛCDM compatibility; the conclusion is robust across data combinations, though tensions remain with BAO. Varying $A_{ m lens}$ or allowing spatial curvature does not overturn the main result, though it can tighten constraints or shift degeneracies; overall, phantom dark energy scenarios (with $w<-1$) are often favored, highlighting the sensitivity of dark-energy inferences to data systematics and parameter space explored.

Abstract

Dynamical dark energy has been recently suggested as a promising and physical way to solve the 3.4 sigma tension on the value of the Hubble constant $H_0$ between the direct measurement of Riess et al. (2016) (R16, hereafter) and the indirect constraint from Cosmic Microwave Anisotropies obtained by the Planck satellite under the assumption of a $Λ$CDM model. In this paper, by parameterizing dark energy evolution using the $w_0$-$w_a$ approach, and considering a $12$ parameter extended scenario, we find that: a) the tension on the Hubble constant can indeed be solved with dynamical dark energy, b) a cosmological constant is ruled out at more than $95 \%$ c.l. by the Planck+R16 dataset, and c) all of the standard quintessence and half of the "downward going" dark energy model space (characterized by an equation of state that decreases with time) is also excluded at more than $95 \%$ c.l. These results are further confirmed when cosmic shear, CMB lensing, or SN~Ia luminosity distance data are also included. However, tension remains with the BAO dataset. A cosmological constant and small portion of the freezing quintessence models are still in agreement with the Planck+R16+BAO dataset at between 68\% and 95\% c.l. Conversely, for Planck plus a phenomenological $H_0$ prior, both thawing and freezing quintessence models prefer a Hubble constant of less than 70 km/s/Mpc. The general conclusions hold also when considering models with non-zero spatial curvature.

Figures (4)

• Figure 1: 68.3% and 95.4% confidence level constraints on the $w_0$--$w_a$ plane in a $12$ parameter extended space for the Planck+R16 data, and combined with several other datasets. Only in the case of Planck+R16+BAO (top right panel), is a cosmological constant within the 95.4% c.l. In all other cases a cosmological constant and the region ($w_0>-1$, $w_a>0$) is excluded at more than $95.4\%$ c.l.
• Figure 2: The effects of shifting the $H_0$ prior are illustrated for the Planck+$H_0$ prior set in the 12 parameter extended space. $68\%$ c.l. constraints on the $w_0$ vs $w_a$ plane are shown for five different $H_0$ priors.The steep magenta line shows the "mirage" line giving the main geometric CMB degeneracy. The shallower orange half line shows the $w_0$-$w_a$ relation that many thawing quintessence models follow.
• Figure 3: 68.3% and 95.4% constraints on the $w_0$--$w_a$ plane in an $11$ parameter extended space, fixing $A_{\rm lens}=1$. Only in the case of Planck+BAO (top right panel) is a cosmological constant still within 95.4% c.l. The allowed parameter space in the ($w_0>-1$, $w_a>0$) region is also reduced relative to the $12$-parameter case. For Planck+R16+JLA, the entire region with $w_a>0$ is now even more strongly excluded.
• Figure 4: 68.3% and 95.4% constraints on the $w_0$--$w_a$ plane in an $12$ parameter extended space, varying $\Omega_k$ but fixing $A_{\rm lens}=1$. The R16 prior is highly incompatible with the cosmological models preferred by the Planck+BAO and Planck+JLA datasets in this case. In the left panel, we see that from these data sets that the ($w_0>-1$, $w_a>0$) region is barely excluded. In the right panel we show constraints from the Planck+R16+lensing and Planck+R16+WL data sets. These constraints are significantly weaker with respect to the previous cases, but the ($w_0>-1$, $w_a>0$) region is still excluded at nearly $95 \%$ c.l..