Testing a Sign-Switch Cosmological Model with Curvature through Latest Planck 2018, DESI DR2 and PantheonPlus\&SH0ES Observational Data

Abstract

We investigate the spatial geometry of the Universe within the framework of a sign-switch dark energy scenario by extending the recently proposed $\Lambda_{\rm s}$CDM model to include a free curvature parameter $\Omega_k$.In this framework, the effective cosmological constant undergoes a transition from a negative to a positive value at a characteristic redshift $z_{\dagger}$. Using the latest Planck 2018 cosmic microwave background (CMB) data, DESI DR2 baryon acoustic oscillation (BAO) measurements, and the PantheonPlus\&SH0ES Type Ia supernova sample, we derive joint constraints on the spatial curvature parameter $\Omega_k$ and other cosmological parameters. We find that Planck data itself slightly favors a closed universe within both the $\Lambda_{\rm s}$CDM$+\Omega_k$ and $\Lambda$CDM$+\Omega_k$ frameworks, although spatial flatness remains well within the allowed uncertainties. When low-redshift probes were included, the curvature constraints were significantly tightened. In particular, the full Pk18+DR2+PP\&SH0ES dataset yields $\Omega_k = 0.0001 \pm 0.0014$ for the $\Lambda_{\rm s}$CDM model, indicating a universe that is remarkably consistent with spatial flatness. We further analyzed the correlations between $\Omega_k$, $H_0$, and $S_8$, finding that the inclusion of curvature and a sign-switch dark energy component helps stabilize cosmological parameter estimates while remaining compatible with current observational constraints. Model comparison using AIC and Bayesian evidence shows that the $\Lambda_{\rm s}$CDM model receives inconclusive/weak observational support relative to $\Lambda$CDM.