Stress-testing the spatially flat Universe: nonparametric spatial curvature determination from DESI DR2

We present a nonparametric determination of spatial curvature using only late-time geometrical probes. Under a Gaussian Process smoothness prior, we jointly constrain the dimensionless expansion history and Ω K, combining three Type Ia Supernovae (SNeIa) samples with either DESI DR2 line-of-sight baryon acoustic oscillations (BAO) or cosmic chronometers (CC) data. From our baseline SNeIa+BAO analyses we find Ω K=0.219+0.110-0.111, Ω K=0.330+0.098-0.150 and Ω K=0.260+0.124-0.127 for the PantheonPlus, DES Dovekie and Union3 SNeIa samples respectively. These nonparametric results mildly favour an open Universe, supporting recent hints in this direction, and improve on the sensitivity of a previous application of the method by up to a factor of about 2.5. We find consistent constraints combining SNeIa and CC, whereas restricting SNeIa data to the redshift range covered by BAO somewhat weakens the constraints and shifts the PantheonPlus central value to Ω K<0. Our results depend only on late-time relative distances and expansion rates, making them insensitive to the absolute distance scale calibration, while relying neither on Cosmic Microwave Background data nor on a parametric dark energy model.