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

In this talk, I will focus on a set of seven characteristic redshifts in the range $0.3 \leq z \leq 1.7$, identified as sensitive probes of the Universe’s expansion history. At each of these redshifts, we reconstruct the normalized expansion rate $E(z)$, employing two complementary methods: multi-task Gaussian process framework and knot-based spline techniques, applied to the DESI-DR2 BAO and DES-SN5YR datasets. The comoving sound horizon at the baryon drag epoch $r_d$ is calibrated to the Planck value to ensure consistency with early-universe physics. Our reconstruction of cosmic distances and their derivatives reveals significant deviations—at the $4\sigma$ to $5\sigma$ level—from the Planck 2018 $\Lambda$CDM predictions, most prominently in the redshift range $z \sim 0.35$–0.55. These anomalies are robust across both reconstruction methods and datasets, indicating a late-time tension in the expansion rate that is distinct from the traditional Hubble tension. I will discuss the implications of these findings, potential interpretations including new physics or unaccounted systematics, and the outlook for confirmation with upcoming datasets, including DESI-5YR, Euclid, and LSST.