The Impact of the Hubble Tension on the Evidence for Dynamical Dark Energy

Abstract: Recent findings from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) favor a dynamical dark energy characterized by a phantom crossing feature. This result also implies a lower value of the Hubble constant, thereby intensifying the so-called Hubble tension. To alleviate the Hubble tension, we consider the early dark energy and explore its impact on the evidence for dynamical dark energy including the Hubble constant calibrated by the SH0ES collaboration. We find that incorporating SH0ES prior with CMB, DESI DR2 BAO and Pantheon Plus/Union3/DESY5 data reduces the preference to dynamical dark energy to $1.5\sigma/1.4\sigma/2.4\sigma$ level, respectively. Our results suggest a potential tension between the Hubble constant $H_0$ of the SH0ES measurement and the phantom-to-quintessence transition in dark energy favored by DESI DR2 BAO data.