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 ΛCDM model by a cosmological constant (Λₛ) that switches sign at a certain redshift z_, and we call this model ΛₛCDM. We discuss the construction and theoretical features of this model in detail and find out that, when the consistency of the ΛₛCDM model with the cosmic microwave background (CMB) data is ensured, (i) z_1.1 is implied by the condition that the Universe monotonically expands, (ii) H₀ and MB (type Ia supernovae absolute magnitude) values are inversely correlated with z_ and reach H₀≈74.5 km s^-1 Mpc^-1 and MB≈-19.2 mag for z_=1.5, in agreement with the SH0ES measurements, and (iii) $H(z)$ presents an excellent fit to the Ly-α measurements provided that z_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 CMB+BAO data set favors the sign switch of Λₛ, providing the constraint z_=2.44±0.29 (68% C.L.). Our analysis reveals that the lower and upper limits of z_ are controlled by the Galaxy and Ly-α BAO measurements, respectively, and the larger z_ values imposed by the Galaxy BAO data prevent the model from achieving the highest local H₀ measurements. In general, the ΛₛCDM model (i) relaxes the H₀ tension while being fully consistent with the tip of the red giant branch measurements, (ii) relaxes the MB tension, (iii) removes the discrepancy with the Ly-α measurements, (iv) relaxes the S₈ 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 ΛₛCDM and ΛCDM models. However, interesting and promising features of the ΛₛCDM model, which we describe in our study, provide an advantage over ΛCDM.