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

We investigate the spatial geometry of the Universe within the framework of a sign-switch dark energy scenario by extending the recently proposed ${\mathrm{\Lambda }}_{\mathrm{s}}$CDM model to include a free curvature parameter ${\mathrm{\Omega }}_k$.In this framework, the effective cosmological constant undergoes a transition from a negative to a positive value at a characteristic redshift $z_{†}$. 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 ${\mathrm{\Omega }}_k$ and other cosmological parameters. We find that Planck data itself slightly favors a closed universe within both the ${\mathrm{\Lambda }}_{\mathrm{s}}$CDM$+{\mathrm{\Omega }}_k$ and $\mathrm{\Lambda }$CDM$+{\mathrm{\Omega }}_k$ 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 ${\mathrm{\Omega }}_k=0.0001\pm 0.0014$ for the ${\mathrm{\Lambda }}_{\mathrm{s}}$CDM model, indicating a universe that is remarkably consistent with spatial flatness. We further analyzed the correlations between ${\mathrm{\Omega }}_k$, $H_0$, 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 ${\mathrm{\Lambda }}_{\mathrm{s}}$CDM model receives inconclusive/weak observational support relative to $\mathrm{\Lambda }$CDM.