Relaxing cosmological tensions with a sign switching cosmological constant

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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model by a cosmological constant (${\mathrm{\ensuremath{\Lambda}}}_{s}$) that switches sign at a certain redshift ${z}_{\ifmmode\dagger\else\textdagger\fi{}}$, and we call this model ${\mathrm{\ensuremath{\Lambda}}}_{s}\mathrm{CDM}$. We discuss the construction and theoretical features of this model in detail and find out that, when the consistency of the ${\mathrm{\ensuremath{\Lambda}}}_{s}\mathrm{CDM}$ model with the cosmic microwave background (CMB) data is ensured, (i) ${z}_{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\gtrsim}1.1$ 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 ${z}_{\ifmmode\dagger\else\textdagger\fi{}}$ and reach ${H}_{0}\ensuremath{\approx}74.5\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ and ${M}_{B}\ensuremath{\approx}\ensuremath{-}19.2\text{ }\text{ }\mathrm{mag}$ for ${z}_{\ifmmode\dagger\else\textdagger\fi{}}=1.5$, in agreement with the SH0ES measurements, and (iii) $H(z)$ presents an excellent fit to the Ly-$\ensuremath{\alpha}$ measurements provided that ${z}_{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\lesssim}2.34$. 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 ${z}_{\ifmmode\dagger\else\textdagger\fi{}}$, but the $\mathrm{CMB}+\mathrm{BAO}$ data set favors the sign switch of ${\mathrm{\ensuremath{\Lambda}}}_{s}$, providing the constraint ${z}_{\ifmmode\dagger\else\textdagger\fi{}}=2.44\ifmmode\pm\else\textpm\fi{}0.29$ (68% C.L.). Our analysis reveals that the lower and upper limits of ${z}_{\ifmmode\dagger\else\textdagger\fi{}}$ are controlled by the Galaxy and Ly-$\ensuremath{\alpha}$ BAO measurements, respectively, and the larger ${z}_{\ifmmode\dagger\else\textdagger\fi{}}$ values imposed by the Galaxy BAO data prevent the model from achieving the highest local ${H}_{0}$ measurements. In general, the ${\mathrm{\ensuremath{\Lambda}}}_{s}\mathrm{CDM}$ 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-$\ensuremath{\alpha}$ 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 ${\mathrm{\ensuremath{\Lambda}}}_{s}\mathrm{CDM}$ and $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ models. However, interesting and promising features of the ${\mathrm{\ensuremath{\Lambda}}}_{s}\mathrm{CDM}$ model, which we describe in our study, provide an advantage over $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$.