Geometric Determinations Of Characteristic Redshifts From DESI-DR2 BAO and DES-SN5YR Observations: Hints For New Expansion Rate Anomalies

In this work, we perform a model-agnostic reconstruction of the cosmic expansion history by combining DESI-DR2 BAO and DES-SN5YR data, with a focus on geometric determination of characteristic redshifts where notable tensions in the expansion rate are found to emerge. Employing Gaussian process regression alongside knot-based spline techniques, we reconstruct cosmic distances and their derivatives to pinpoint these characteristic redshifts and infer $E(z)$. Our analysis reveals significant deviations of approximately 4 to 5$\sigma$ from the Planck 2018 $\Lambda$CDM predictions, particularly pronounced in the redshift range $z \sim 0.35-0.55$. These anomalies are consistently observed across both reconstruction methods and combined datasets, indicating robust late-time departures that could signal new physics beyond the standard cosmological framework. The joint use of BAO and SN probes enhances the precision of our constraints, allowing us to isolate these deviations without reliance on specific cosmological assumptions. Our findings underscore the role of characteristic redshifts as sensitive indicators of expansion rate anomalies and motivate further scrutiny with forthcoming datasets from DESI-5YR BAO, Euclid, and LSST. These future surveys will tighten constraints and help distinguish whether these late-time anomalies arise from new fundamental physics or unresolved systematics in the data.

A New $\sim 5σ$ Tension at Characteristic Redshift from DESI DR1 and DES-SN5YR observations

We perform a model-independent reconstruction of the angular diameter distance ($D_{A}$) using the Multi-Task Gaussian Process (MTGP) framework with DESI-DR1 BAO and DES-SN5YR datasets. We calibrate the comoving sound horizon at the baryon drag epoch $r_d$ to the Planck best-fit value, ensuring consistency with early-universe physics. With the reconstructed $D_A$ at two key redshifts, $z\sim 1.63$ (where $D_{A}^{\prime} =0$) and at $z\sim 0.512$ (where $D_{A}^{\prime} = D_{A}$), we derive the expansion rate of the Universe $H(z)$ at these redshifts. Our findings reveal that at $z\sim 1.63$, the $H(z)$ is fully consistent with the Planck-2018 $\Lambda$CDM prediction, confirming no new physics at that redshift. However, at $z \sim 0.512$, the derived $H(z)$ shows a more than $5\sigma$ discrepancy with the Planck-2018 $\Lambda$CDM prediction, suggesting a possible breakdown of the $\Lambda$CDM model as constrained by Planck-2018 at this lower redshift. This emerging $\sim 5\sigma$ tension at $z\sim 0.512$, distinct from the existing ``Hubble Tension'', may signal the first strong evidence for new physics at low redshifts.