Effective Phantom Divide Crossing with Standard and Negative Quintessence

TL;DR

The paper demonstrates that an effective crossing of the phantom divide seen in background dark-energy reconstructions can be achieved without violating single-field no-crossing theorems by modeling dark energy as a composite of a standard quintessence field and a negative quintessence field (SQ+NQ) with opposite-sign kinetic terms. Using quadratic potentials and carefully chosen masses, the two-field system evolves such that the total DE density rises at intermediate redshifts and then dilutes, producing a peak around $z\sim0.4$–$0.5$ while keeping each component below the phantom boundary. They fit Planck+DESI+DES-Y5 data and compare to $\Lambda$CDM and CPL, finding that SQ+NQ improves the fit by about $\chi^2_{\min}\approx18$ over $\Lambda$CDM and is competitive with CPL, with $\Omega_m^0$, $H_0$, and the field parameters tightly constrained. The analysis highlights the potential importance of exotic fields in the low-energy universe and motivates further study of perturbations, growth, and comparisons with other beyond-$\Lambda$CDM models. The results emphasize that a peak in $f_{\rm DE}$ need not imply a true phantom crossing and that composite DE scenarios can accommodate current observations while remaining testable with future data.

Abstract

Cosmic microwave background data from the {\it Planck} satellite, combined with baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument and Type Ia supernovae from various samples, provide hints of dynamical dark energy (DE). These results indicate a peak in the DE density around $z\sim 0.4-0.5$, with the highest significance observed when using the supernovae from the Dark Energy Survey. In this {\it Letter}, we show that this peak does not necessarily imply a true crossing of the phantom divide if the measured effective DE is not a single component, but a combination of standard and negative quintessence. The latter is characterized by negative energy density and positive pressure, both decreasing in absolute value and tending to 0 in the future. For appropriate values of the parameters, negative quintessence is relevant at intermediate redshifts and becomes subdominant in front of standard quintessence around $z\sim 0.4-0.5$, giving rise to the aforementioned peak in the DE density. We find that our model is preferred over $Λ$CDM at a $3.26σ$ CL, which is comparable to the level of exclusion found with the Chevallier-Polarski-Linder parametrization. Our analysis leaves open the possibility of negative quintessence and other exotic fields existing in the low-energy universe, potentially playing a significant role in cosmic dynamics.

Figures (2)

• Figure 1: EoS diagram. The pink and orange regions correspond to the SQ ($-1\leq w\leq-1/3$) and phantom ($w\leq-1$) DE regimes, respectively. In the white region the strong energy condition is fulfilled, i.e., $\rho+3p\geq 0$ and $\rho+p\geq 0$. In particular, non-relativistic matter ($w=0$) and radiation ($w=1/3$) lie within this region, satisfying $p,\rho\geq 0$. Phantom matter ($w\leq -1$) as well, with $\rho<0$ and $p>0$Grande:2006nnMavromatos:2021urxGomez-Valent:2024tdbGomez-Valent:2024ejh. The blue region is the one for species with negative energy density and decreasing absolute value. Within that region, the triangular area bounded by the "closed universe" line and the edge of the "phantom matter" region represents the domain of the NQ scenario.
• Figure 2: Right plots: Profile distributions for $M_1$ and $M_2$. A wide range of masses lead to low values of $\chi^2$; Left and central plots: In addition to the reconstructions obtained with Planck+DESI+DES-Y5 Gonzalez-Fuentes:2025lei for the relevant background quantities (shown in light blue), we display several curves associated to SQ+NQ models with varying ability to describe the data. We use models corresponding to different points on the profile likelihood of M2, with the best-fit model shown as a black dot-dashed line. For the $\Lambda$CDM $H^\Lambda(z)$ we set $\Omega_{\rm m}^0=0.315$ and $H_0=67.26$ km/s/Mpc Rosenberg:2022sdy. In the central upper plot, we show the SQ and NQ densities that contribute to the total DE density in solid and dashed curves, respectively.