Phantom-Crossing Dark Energy and the $Ω_m$ Tug-of-War

Abstract

Recent analyses combining data from the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and Type Ia supernovae (SN) have revealed a tentative observational preference for phantom crossing in the dark energy equation of state $w$. We argue that this preference is a natural consequence of the $Ω_m$ tensions that arise when these datasets are individually fit to $Λ$CDM, specifically because of the ordering $Ω_m^\mathrm{BAO} < Ω_m^\mathrm{CMB} < Ω_m^\mathrm{SN}$. We show both theoretically and empirically that models with phantom crossing can shift all of these inferred $Ω_m$ values toward mutual alignment. In contrast, quintessence theories restricted to $w \geq -1$ can alleviate the tensions with SN data but only at the cost of exacerbating the BAO-CMB discrepancy. We therefore conclude that it is the BAO and CMB measurements - not the SN data - that drive the preference for phantom crossing over quintessence in joint analyses. Moreover, we point out that SN data exhibit greater tensions with the other datasets when fit to phantom-crossing models than when fit to quintessence, causing the preference for phantom crossing to be weaker in joint CMB+BAO+SN analyses than in analyses of CMB+BAO data alone.

Figures (7)

• Figure 1: Observational constraints on the CPL (left) and Padé-w (right) parameter spaces, colored in accordance with observationally compatible values of $\Omega_m$ (colorbars are shared within columns). The top row shows constraints from CMB data, the middle row shows constraints from BAO data, and the bottom row shows constraints from SN data (using the DES-Dovekie supernova sample SN$_\mathrm{D}$). The individual plotted points represent MCMC samples with at least 5% of the maximum 2D posterior density (which generalizes the $2\sigma$ region of a Gaussian distribution). Dashed lines are drawn to cross at the $\Lambda$CDM limit of the CPL parameter space; the $\Lambda$CDM limit corresponds to $\epsilon_0 = 0$ for Padé-w.
• Figure 2: MCMC constraints from DESI DR2 BAO on two toy models, in which $w(z)$ is a piecewise-constant function that is allowed to deviate from $w = -1$ in either the "low-$z$" regime ($z < 0.4$) or the "high-$z$" regime ($z > 0.4$). Dashed lines indicate the $\Lambda$CDM limit with DESI's best-fit $\Omega_m^\mathrm{BAO} = 0.297$. The inferred value of $\Omega_m$ increases as $w$ increases in the low-$z$ regime, but the reverse is true as $w$ increases in the high-$z$ regime.
• Figure 3: CMB- and BAO-based correlations between $\Omega_m$ and either the CPL parameter $w_0$ (left panel) or the Padé-w parameter $\epsilon_0$ (right panel) controlling deviations from $\Lambda$CDM. For visual clarity, the parameters $w_a$ and $\eta_0$ have not been varied independently (see text for further explanation). The $\Lambda$CDM limit in the left panel ($w_0=-1$) is marked with a dashed line; in the right panel, this limit corresponds to $\epsilon_0 = 0$. Notice that in phantom-crossing (CPL) models, deviations from $\Lambda$CDM can alleviate the CMB-BAO tension in $\Omega_m$, whereas in thawing quintessence (Padé-w) models, deviations from $\Lambda$CDM only exacerbate it.
• Figure 4: Marginalized posterior distributions of $\Omega_m$ in $\Lambda$CDM (left panel), in the best-fit Padé-w model to CMB+BAO+SN data (middle panel), and in the best-fit CPL model to CMB+BAO+SN data (right panel). For the purposes of illustration, we only show results using the DES-Dovekie supernova sample (SN$_\mathrm{D}$). Notice that the $\Lambda$CDM tension between BAO and SN data is resolved in both types of dynamical dark energy models, but the BAO-CMB tension cannot be alleviated in thawing quintessence (Padé-w) models, since $\Omega_m^\mathrm{CMB}$ increases at least as much as $\Omega_m^\mathrm{BAO}$ (as discussed in section \ref{['s_bao']}). Only the phantom-crossing (CPL) models can bring all three inferences of $\Omega_m$ into agreement.
• Figure 5: MCMC results showing joint 68% and 95% credible regions for the matter fraction $\Omega_m$ and either the CPL parameters $\{w_0, w_a\}$ (top row) or the Padé-w parameters $\{\epsilon_0, \eta_0\}$ (bottom row). Dashed lines are drawn to indicate the values of $w_0$ and $w_a$ in the $\Lambda$CDM limit. Supernova-based constraints are presented as shaded contours and contrasted against the (non-shaded) CMB+BAO constraints. Notice that in CPL models, SN datasets (especially DES-Dovekie) exhibit greater tensions with the CMB+BAO constraints than in the Padé-w parameter space.