Relaxing cosmological tensions with a sign switching cosmological constant

Inspired by the recent conjecture originated from graduated dark energy that Universe has recently transitioned anti-de Sitter vacua to de vacua, we extend $\Lambda$CDM model a cosmological constant ($\Lambda_{\rm s}$) switches sign at certain redshift $z_\dagger$, and call this $\Lambda_{\rm s}$CDM. We discuss construction theoretical features of find out that, when consistency s}$CDM with CMB data is ensured, (i) $z_\dagger\gtrsim1.1$ implied condition monotonically expands, (ii) $H_0$ $M_B$ (type Ia supernovae absolute magnitude) values are inversely correlated $z_\dagger$ reach $H_0\approx74.5~{\rm km\, s^{-1}\, Mpc^{-1}}$ $M_B\approx-19.2\,{\rm mag}$ for $z_\dagger=1.5$, in agreement SH0ES measurements, (iii) $H(z)$ presents an excellent fit Ly-$\alpha$ measurements provided $z_\dagger\lesssim 2.34$. further investigate constraints using full Planck set, without BAO data. alone does not constrain but CMB+BAO set favors switch s}$ providing constraint: $z_\dagger=2.44\pm0.29$ (68% C.L.). Our analysis reveals lower upper limits controlled Galaxy respectively, larger $z_{\dagger}$ imposed prevent achieving highest local measurements. In general, relaxes tension while being fully consistent TRGB tension, removes discrepancy (iv) $S_8$ (v) finds better BBN on physical baryon density. [Abridged]