Non-minimally coupled running curvaton for DESI-motivated dynamical dark energy

Abstract Recent DESI baryon-acoustic-oscillation measurements, when combined with CMB and supernova distance data, have renewed interest in dynamical dark energy whose effective equation of state can cross the phantom divide. We investigate whether such behavior can be embedded in the running-curvaton framework by adding a Jordan-frame non-minimal coupling, $$\xi \chi ^2R$$ ξ χ 2 R . The same field is used in two regimes: as a curvaton sector in the early universe and as a late-time dark-energy component. We show that the leading early-time curvaton predictions can be preserved by retuning the effective mass parameter, while the geometric terms in the late-time pressure allow phantom-crossing background histories without introducing a phantom kinetic term. We then perform a background-level likelihood analysis using numerical solutions of the model’s late-time homogeneous background equations, a reduced CMB prior on $$(\theta _*,\omega _b,\omega _{bc})$$ ( θ ∗ , ω b , ω bc ) , the official DESI DR2 BAO data vector with full covariance, and Pantheon+ supernovae without SH0ES calibration. This likelihood tests acoustic-scale, BAO-distance and supernova-distance consistency under the assumption that the curvaton/NMC sector is negligible near recombination. The MCMC analysis gives stable derived background parameters, with $$H_0=67.88^{+0.53}_{-0.61}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$$ H 0 = 67 . 88 - 0.61 + 0.53 km s - 1 Mpc - 1 , $$\Omega _m=0.3072^{+0.0059}_{-0.0054}$$ Ω m = 0 . 3072 - 0.0054 + 0.0059 , $$w_0=-0.922^{+0.055}_{-0.063}$$ w 0 = - 0 . 922 - 0.063 + 0.055 and $$w_a=-0.205^{+0.173}_{-0.182}$$ w a = - 0 . 205 - 0.182 + 0.173 . The microscopic non-minimal-coupling parameters remain broad, skewed and long-tailed in the marginalized posterior, reflecting degeneracies under background-level data. These results should not be interprete