We study the cosmological constant ($\mathrm{\Lambda }$) in the standard $\mathrm{\Lambda }$ 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 $\mathrm{\Lambda }$ in the form ${\rho }_{\text{inert}}\propto {\rho }^{\lambda }<0$ with $\lambda <1$ being a ratio of two odd integers, for which its energy density $\rho$ dynamically takes negative values in the finite past. For large negative values of $\lambda$, it creates a phenomenological model described by a smooth function that approximately describes the $\mathrm{\Lambda }$ spontaneously switching sign in the late Universe to become positive today. We confront the model with the latest combined observational datasets of $\mathrm{Planck}+\mathrm{baryon}\mathrm{acoustic}\mathrm{oscillations}+\mathrm{supernova}+H$. It is striking that the data predict bimodal posterior probability distributions for the parameters of the model along with large negative $\lambda$ values; the new maximum significantly excludes the $\mathrm{\Lambda }$, and the old maximum contains the $\mathrm{\Lambda }$. The improvement in the goodness of fit for the $\mathrm{\Lambda }$ reaches highly significant levels, $\mathrm{\Delta }{\chi }_{\min }^2=6.4$, for the new maxima, while it remains at insignificant levels, $\mathrm{\Delta }{\chi }_{\min }^2\lesssim 0.02$, for the old maxima. We show that, in contrast to the old maxima, which do not distinguish from the $\mathrm{\Lambda }$, the new maxima agree with the model-independent $H_0$ measurements, high-precision $\mathrm{Ly}\text{−}\alpha$ 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 $z\approx 2.32$, and triggered the late-time acceleration, and suggests looking for such mechanisms in string theory constructions.

Inspired by the recent conjecture originated from graduated dark energy that the Universe has recently transitioned from anti–de Sitter vacua to de Sitter vacua, we extend the standard $\mathrm{\Lambda }\mathrm{CDM}$ model by a cosmological constant (${\mathrm{\Lambda }}_s$) that switches sign at a certain redshift $z_{†}$, and we call this model ${\mathrm{\Lambda }}_s\mathrm{CDM}$. We discuss the construction and theoretical features of this model in detail and find out that, when the consistency of the ${\mathrm{\Lambda }}_s\mathrm{CDM}$ model with the cosmic microwave background (CMB) data is ensured, (i) $z_{†}\gtrsim 1.1$ is implied by the condition that the Universe monotonically expands, (ii) $H_0$ and $M_B$ (type Ia supernovae absolute magnitude) values are inversely correlated with $z_{†}$ and reach $H_0\approx 74.5\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and $M_B\approx -19.2\mathrm{mag}$ for $z_{†}=1.5$, in agreement with the SH0ES measurements, and (iii) $H(z)$ presents an excellent fit to the Ly-$\alpha$ measurements provided that $z_{†}\lesssim 2.34$. We further investigate the model constraints by using the full Planck CMB data set, with and without baryon acoustic oscillation (BAO) data. We find that the CMB data alone does not constrain $z_{†}$, but the $\mathrm{CMB}+\mathrm{BAO}$ data set favors the sign switch of ${\mathrm{\Lambda }}_s$, providing the constraint $z_{†}=2.44\pm 0.29$ (68% C.L.). Our analysis reveals that the lower and upper limits of $z_{†}$ are controlled by the Galaxy and Ly-$\alpha$ BAO measurements, respectively, and the larger $z_{†}$ values imposed by the Galaxy BAO data prevent the model from achieving the highest local $H_0$ measurements. In general, the ${\mathrm{\Lambda }}_s\mathrm{CDM}$ model (i) relaxes the $H_0$ tension while being fully consistent with the tip of the red giant branch measurements, (ii) relaxes the $M_B$ tension, (iii) removes the discrepancy with the Ly-$\alpha$ measurements, (iv) relaxes the $S_8$ tension, and (v) finds a better agreement with the big bang nucleosynthesis constraints on the physical baryon density. We find no strong statistical evidence to discriminate between the ${\mathrm{\Lambda }}_s\mathrm{CDM}$ and $\mathrm{\Lambda }\mathrm{CDM}$ models. However, interesting and promising features of the ${\mathrm{\Lambda }}_s\mathrm{CDM}$ model, which we describe in our study, provide an advantage over $\mathrm{\Lambda }\mathrm{CDM}$.