Graduated dark energy: Observational hints of a spontaneous sign switch in the cosmological constant

TL;DR

The paper tackles LambdaCDM tensions by proposing graduated dark energy (gDE), a minimal extension where the inertial mass density obeys $\rho_{\rm inert} = \gamma\rho_0(\rho/\rho_0)^{\lambda}$, allowing the effective vacuum energy to become negative and to switch sign. The authors derive the gDE background evolution, express it with $\rho/\rho_0 = \text{sgn}[1 - \Psi\ln a]|1 - \Psi\ln a|^{1/(1-\lambda)}$ and $\Psi = -3\gamma(\lambda-1)$, and show that for $\lambda<1$, $\gamma<0$, the DE density can cross zero at $z_* = e^{-1/\Psi} - 1$, approaching a step-function behavior as $|\lambda|$ grows. Using a modified SimpleMC with PLK+BAO+SN+$H$ data, they find bimodal posteriors for $\lambda \le -4$, with a new maximum ($\gamma \neq 0$) yielding substantial improvements in fit (e.g., $\Delta\chi^2_{\min} \approx 6.4$) and a robust pole location at $z_* \approx 2.32$, while the old maximum near $\gamma=0$ remains statistically disfavored. The favored solution aligns with model-independent $H_0$ and Omh^2 estimates and can alleviate Ly-$\alpha$ BAO tensions by causing a rapid change in $H(z)$ around $z \sim 2.3$, potentially signaling a spontaneous sign switch of the cosmological constant and suggesting a string-theory realization of an AdS→dS transition. Overall, the work demonstrates that a sign-switching DE can reconcile late-time cosmological tensions and carries implications for fundamental physics and the nature of dark energy.

Abstract

We study the cosmological constant ($Λ$) in the standard $Λ$CDM model by introducing the \textit{graduated dark energy} (gDE) characterised by a minimal dynamical deviation from the null inertial mass density of the $Λ$ in the form $ρ_{\rm inert}\propto ρ^λ<0$ with $λ<1$ being a ratio of two odd integers, for which its energy density $ρ$ dynamically takes negative values in the finite past. For large negative values of $λ$, it creates a phenomenological model described by a smooth function that approximately describes the $Λ$ spontaneously switching sign in the late universe to become positive today. We confront the model with the latest combined observational data sets of PLK+BAO+SN+$H$. It is striking that the data predict bimodal posterior probability distributions for the parameters of the model along with large negative $λ$ values; the new maximum significantly excludes the $Λ$, and the old maximum contains the $Λ$. The improvement in the goodness of fit for the $Λ$ reaches highly significant levels, $Δχ_{\rm min}^2=6.4$ for the new maxima, while it remains at insignificant levels, $Δχ_{\rm min}^2\lesssim0.02$, for the old maxima. We show that, in contrast to the old maxima, which do not distinguish from the $Λ$, the new maxima agree with the model-independent $H_0$ measurements, high-precision Ly-$α$ data, and model-independent $Omh^2$ diagnostic estimates. Our results provide strong hints of a spontaneous sign switch in the cosmological constant and lead us to conjecture that the universe has transitioned from AdS vacua to dS vacua, at a redshift $z\approx 2.32$ and triggered the late-time acceleration, and suggests looking for such mechanisms in string theory constructions.

Figures (7)

• Figure 1: We use $\Omega_{{\rm m},0}=0.30$ and, for gDE-CDM, $\gamma=-0.03$ along with $\lambda=-10$ (green). $H(z)/(1+z)$ vs. $z$ for the gDE-CDM (green) and $\Lambda$CDM (black). $H_{0}=70{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ (solid) and $H_{0}=73{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ (dashed). $H_0= 69.8 \pm 0.8\, {\rm km\,s}^{-1}{\rm Mpc}^{-1}$ from the TRGB $H_0$Freedman:2019jwv, $H(z=0.57) = 97.9 \pm 3.4\,{\rm km\,s}^{-1}{\rm Mpc}^{-1}$Anderson:2013zyy, and $H(z=2.34) = 222.4 \pm 5.0\,{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ from the latest BAO data Delubac:2014aqe. $H_0 = 73.52 \pm 1.62{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ is independent measurement from Gaia parallaxes Riess:2018byc.
• Figure 2: 1D marginalised posterior distributions for the graduated $\gamma$ parameter (top left panel), $\Psi \equiv 3\gamma(1-\lambda)$ (right) and the redshift location of the pole (if present) given by Eqn. (\ref{['eq:redshift']}). For a better display we have included some particular cases of $\lambda$ values.
• Figure 3: Top panel: 1D marginalised posterior distributions of $\Psi$, along with (bottom panel) 2D posterior distributions of {$\Psi$, $h_0$} colour coded by the $\gamma$ parameter.
• Figure 4: Means values along with $1\,\sigma$ error bars from the 1D marginalised posterior distributions of $H_0 [{\rm km\,s}^{-1}{\rm Mpc}^{-1}]$. Green error bars are associated with the peak containing $\Psi\sim 0$ ($\Lambda$CDM), whereas red with the new peak stable at $\Psi\sim -0.86$.
• Figure 5: Graduated Dark energy model with varying the $\lambda$ parameter. Left panel: 3D marginalised posterior distributions for the graduated $\lambda$ and $\Psi$ parameters, coloured coded by the $\gamma$ parameter. Right panel: 1D marginalised posterior of the redshift position given by the pole. The vertical line is the mean value $z_*=2.32$.