Hint towards inconsistency between BAO and Supernovae Dataset: The Evidence of Redshift Evolving Dark Energy from DESI DR2 is Absent

The combination of independent cosmological datasets is a route towards precision and accurate inference of the cosmological parameters if these observations are not contaminated by systematic effects. However, the presence of unknown systematics present in differrent datasets can lead to a biased inference of the cosmological parameters. In this work, we test the consistency of the two independent tracers of the low-redshift cosmic expansion, namely the supernovae dataset from Pantheon$+$ and the BAO dataset from DESI DR2 using the distance duality relation which is a cornerstone relation in cosmology under the framework of General Relativity. We find that these datasets violate the distance duality relation and show a signature of redshift evolution, hinting toward unaccounted physical effects or observational artifacts. Coincidentally this effect mimics a redshift evolving dark energy scenario when supernovae dataset and DESI datasets are combined without accounting for this inconsistency. Accounting for this effect in the likelihood refutes the previous claim of evidence of non-cosmological constant as dark energy model from DESI DR2, and shows a result consistent with cosmological constant with $w_0= -0.92\pm 0.08$ and $w_a= -0.49^{+0.33}_{-0.36}$. This indicates that the current conclusion from DESI DR2 in combination with Pantheon$+$ is likely due to the combination of two inconsistent datasets resulting in precise but inaccurate inference of cosmological parameters. In the future, tests of this kind for the consistency between different cosmological datasets will be essential for robust inference of cosmological parameters and for deciphering unaccounted physical effects or observational artifacts from supernovae and BAO datasets.