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 $\Lambda$CDM model by a cosmological constant ($\Lambda_{\rm s}$) that switches sign at a certain redshift $z_\dagger$, and we call this model $\Lambda_{\rm s}$CDM. We discuss the construction and theoretical features of this model and find out that, when the consistency of $\Lambda_{\rm s}$CDM with the CMB data is ensured, (i) $z_\dagger\gtrsim1.1$ 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 $z_\dagger$ and reach $H_0\approx74.5~{\rm km\, s^{-1}\, Mpc^{-1}}$ and $M_B\approx-19.2\,{\rm mag}$ for $z_\dagger=1.5$, in agreement with the SH0ES measurements, and (iii) $H(z)$ presents an excellent fit to the Ly-$\alpha$ measurements provided that $z_\dagger\lesssim 2.34$. We further investigate the model constraints by using the full Planck CMB data set, with and without BAO data. We find that the CMB data alone does not constrain $z_\dagger$, but the CMB+BAO data set favors the sign switch of $\Lambda_{\rm s}$ providing the constraint: $z_\dagger=2.44\pm0.29$ (68% C.L.). Our analysis reveals that the lower and upper limits of $z_\dagger$ are controlled by the Galaxy and Ly-$\alpha$ BAO measurements, respectively, and the larger $z_{\dagger}$ values imposed by the Galaxy BAO data prevent the model from achieving the highest local $H_0$ measurements. In general, $\Lambda_{\rm s}$CDM (i) relaxes the $H_0$ tension while being fully consistent with the TRGB 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 BBN constraints on the physical baryon density. [Abridged]