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

We study the cosmological constant ($\mathrm{\ensuremath{\Lambda}}$) in the standard $\mathrm{\ensuremath{\Lambda}}$ cold dark matter model by introducing the graduated dark energy (gDE) characterized by a minimal dynamical deviation from the null inertial mass density of the $\mathrm{\ensuremath{\Lambda}}$ in the form ${\ensuremath{\rho}}_{\text{inert}}\ensuremath{\propto}{\ensuremath{\rho}}^{\ensuremath{\lambda}}<0$ with $\ensuremath{\lambda}<1$ being a ratio of two odd integers, for which its energy density $\ensuremath{\rho}$ dynamically takes negative values in the finite past. For large negative values of $\ensuremath{\lambda}$, it creates a phenomenological model described by a smooth function that approximately describes the $\mathrm{\ensuremath{\Lambda}}$ spontaneously switching sign in the late Universe to become positive today. We confront the model with the latest combined observational datasets of $\mathrm{Planck}+\mathrm{baryon}\text{ }\mathrm{acoustic}\text{ }\mathrm{oscillations}+\mathrm{supernova}+H$. It is striking that the data predict bimodal posterior probability distributions for the parameters of the model along with large negative $\ensuremath{\lambda}$ values; the new maximum significantly excludes the $\mathrm{\ensuremath{\Lambda}}$, and the old maximum contains the $\mathrm{\ensuremath{\Lambda}}$. The improvement in the goodness of fit for the $\mathrm{\ensuremath{\Lambda}}$ reaches highly significant levels, $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}_{\mathrm{min}}^{2}=6.4$, for the new maxima, while it remains at insignificant levels, $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}_{\mathrm{min}}^{2}\ensuremath{\lesssim}0.02$, for the old maxima. We show that, in contrast to the old maxima, which do not distinguish from the $\mathrm{\ensuremath{\Lambda}}$, the new maxima agree with the model-independent ${H}_{0}$ measurements, high-precision $\mathrm{Ly}\text{\ensuremath{-}}\ensuremath{\alpha}$ data, and model-independent $Om{h}^{2}$ 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 anti-de Sitter vacua to de Sitter vacua, at a redshift $z\ensuremath{\approx}2.32$, and triggered the late-time acceleration, and suggests looking for such mechanisms in string theory constructions.