The cosmic curvature ${\mathrm{\Omega }}_K$ is an important parameter related to the inflationary cosmology and the ultimate fate of the universe. In this work, we adopt the noncosmic microwave background (CMB) observations to constrain ${\mathrm{\Omega }}_K$ in the $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model and its extensions. The DESI baryon acoustic oscillation, DES type Ia supernova, cosmic chronometer, and strong gravitational lensing time delay data are considered. We find that the data combination favors an open universe in $\mathrm{\Lambda }\mathrm{CDM}$, specifically ${\mathrm{\Omega }}_K=0.106\pm 0.056$ at the $1\sigma$ level, which is in $2.6\sigma$ tension with the Planck CMB result supporting our Universe being closed. In the $\mathrm{\Lambda }\mathrm{CDM}$ extensions, the data combination is consistent with a flat universe. It is noteworthy that when the cosmic chronometer data is excluded, the derived constraints demonstrate increased statistical preference for an open universe. Specifically, ${\mathrm{\Omega }}_K=0.146\pm 0.060$ in $\mathrm{\Lambda }\mathrm{CDM}$, which is in $3.1\sigma$ tension with the CMB result, and the flat universe scenario can be ruled out at $>1\sigma$ level in the $\mathrm{\Lambda }\mathrm{CDM}$ extensions. The constraining power mainly stems from DESI’s distance measurements. Given the advantages of the full-shape power spectrum in ${\mathrm{\Omega }}_K$ measurements and the support for a closed universe from previous full-shape analyses, it is necessary to validate our findings with DESI’s full-shape data. We adopt the Akaike information criterion to compare different cosmological models. The result shows that nonflat models fit the observational data better than the flat $\mathrm{\Lambda }\mathrm{CDM}$ model, which indicates that flat $\mathrm{\Lambda }\mathrm{CDM}$ may not be the ultimate model of cosmology.

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• Cosmological parameters
• Cosmology
• Dark energy