Probing cosmic curvature with fast radio bursts and DESI DR2 data

The spatial curvature of the Universe remains a central question in modern cosmology. In this work, we explore the potential of localized Fast Radio Bursts (FRBs) as a novel tool to constrain the cosmic curvature parameter $Ω_k$ in a cosmological model-independent way. Using a sample of 120 FRBs with known redshifts and dispersion measures, we reconstruct the Hubble parameter $H(z)$ via artificial neural networks, and use it to obtain angular-diameter distances $D_A(z)$ through two complementary approaches. First, we derive the comoving distance $D_C(z)$ and $D_A(z)$ directly from FRBs without assuming a fiducial cosmology. Then, we combine the FRB-based $H(z)$ with Baryon Acoustic Oscillation (BAO) DESI DR2 measurements to infer $D_A(z)$. By comparing the FRB-derived and BAO+FRB-derived $D_A(z)$, we constrain spatial curvature. Our covariance-based likelihood (accounting for correlated uncertainties) yields $Ω_k = -0.31\pm0.57$, while a diagonal (Gaussian) treatment gives $Ω_k = -0.13\pm0.46$. Both estimations are consistent with spatial flatness at the $1σ$ level, albeit with a mild preference for negative curvature. Explicitly accounting for the full covariance broadens the intervals and avoids underestimation of uncertainties. These results highlight the growing relevance of FRBs in precision cosmology and their synergy with BAO as a powerful, cosmological model-independent probe of the large-scale geometry of the Universe.