Observational constraint of non-scalar phantom dark energies

Recent observation of DESI strongly disfavors cosmological constant. Given the lack of constraint regarding the fundamental field that constitutes a dynamical dark energy, people traditionally resort on a hypothetical scalar field. We instead consider minimally coupled non-spinless field as alternative, specifically the extended Proca-Nuevo theory (spin-1) and 3-form field (spin-3). Both theories at the background level permit pure phantom (w < -1) and phantom crossing (w < -1 to w > -1) scenarios. Furthermore, with reasonable choice of EFT parameters we can decouple the scalar perturbation of the dark energy from the matter sector. However, the Lorentz constraint within the higher-spin field inevitably modifies the response of the scalar potential to the matter perturbation. This leads to an enhancement of the matter power spectrum most obvious in BAO fullshape analysis. We then perform MCMC analysis and show that the Hubble tension is alleviated, and the non-spin-0 models are preferred marginally over a cosmological constant.