Model-independent consistency tests of DESI DR2 BAO and SN Ia

Abstract: Cosmic distances can be measured using two complementary probes: Type Ia supernovae (SN Ia), serving as standard candles, and baryon acoustic oscillations (BAO), serving as standard rulers. The luminosity distance derived from supernovae and the angular diameter distance obtained from BAO must be mutually consistent if these data are to be combined for cosmological inference. Hence, the existence of potential discrepancies, whether arising from systematics in either dataset or from violation of the cosmic duality relation (in an unconventional cosmology), remains an important issue to address. Testing consistency under a particular cosmological model can be limiting, as the model may not be sensitive to every kind of inconsistency possible in the data. Thus, in this work we use a model-independent Crossing Statistics framework to test the consistency, using DESI DR2 BAO, and the Pantheon+ and Union3 SN Ia datasets. We find adding up to two additional degrees of freedom, using Crossing Statistics on the LambdaCDM distance-redshift relation, to be statistically justified. In these cases, the two probes remain mutually consistent at the 1-2 sigma level. Having established this statistical consistency, we combine the datasets to reconstruct the expansion history of the Universe and the inferred evolution of dark energy. The reconstructions obtained using different crossing variables show compatible behaviour where the data constraints are strongest, particularly at low redshift. Overall, the results are suggestive of a dark energy component that is evolving at low redshift, compatible with results from other reconstruction methods.