Comparing Mass-Varying Neutrino Dark Energy Models with DESI DR2: Cosmological Constraints and Bayesian Evidence
We investigate late-time cosmic acceleration in mass-varying neutrino (MaVaN) dark energy scenarios, where the neutrino mass is coupled to a dynamical quintessence field through a conformal interaction. Starting from the coupled conservation equations, we derive the corresponding background evolution equations for three related scenarios: a constant dark-energy equation of state with a constant coupling (Case-I), an exponential neutrino mass linked to an exponential potential under an adiabatic minimum-tracking approximation (Case-II), and a CPL-type time-varying equation of state with constant coupling (Case-III). For each case we obtain the neutrino and dark energy density evolution and the corresponding Hubble parameter, and use an MCMC analysis (emcee) to test the models against DESI DR2 BAO data, the compressed Planck CMB likelihood, and three supernova compilations (Pantheon+, DES-SN5YR, Union3), taken one at a time. Across the three cases, $H_0$ and $Ω_{m0}$ move together in a way set mainly by which supernova sample is used, following the pattern already seen in other DESI DR2 analyses. A nonzero coupling stays consistent with the data in most fits, though its size, and sometimes its sign, depend on how it enters the model and on the priors chosen for the underlying parameters. The resulting neutrino mass bounds range from about $0.06$ to $0.3\,\mathrm{eV}$, depending on the case and dataset combination. Comparing the Bayesian evidence of each case with flat $Λ$CDM gives a mixed picture, with no case preferred throughout, so we regard these results as suggestive rather than firm evidence for a coupling between neutrinos and dark energy.