New insights on a sign-switching $\Lambda$

The proposal for a sudden sign-switching cosmological constant $\Lambda$ in the local universe, emulating a phase transition from anti-de Sitter (AdS) to de Sitter (dS) space, has markedly revamped the fit to observational data and lays out a propitious framework for ameliorating major cosmological tensions, such as the $H_0$ and $S_8$ tensions. This proposal is widely known as $\Lambda_s$CDM. We investigate the possibility that $\Lambda$ does not only flip sign at the transition but has also different curvature radii in the AdS and dS phases. We show that the critical redshift of the transition $z_c$ is strongly correlated with the vacuum energy in the AdS phase $\Omega_{\Lambda_-}$, and that these two variables do not correlate strongly with the other cosmological parameters. We also show that the cost of adding an additional parameter to the $\Lambda_s$CDM cosmological model does not improve the goodness of fit. Armed with our findings, we demonstrate that for a proper choice of $z_c$, the vacuum energy in the dS phase may not necessarily be $-\Omega_{\Lambda_-}$, for comparable degree of conformity between the model prediction and experimental data.