Oscillatory dark energy with phantom crossings in Einstein-Gauss-Bonnet gravity

Abstract: Recent baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument (DESI), combined with supernova observations, show a mild preference for an evolving dark-energy equation of state, in which dark energy remains phantom-like at higher redshift while a transition toward the quintessence regime emerges around $z\lesssim0.5$. Beyond the monotonic evolution of the equation of state, an oscillatory dark-energy scenario provides a potential alternative realization of dynamical dark energy. We study such an oscillatory scenario within the Einstein-scalar-Gauss-Bonnet gravity framework, where a scalar field with a hybrid exponential-quadratic potential couples nonminimally to the Gauss-Bonnet (GB) invariant. We choose a Gaussian GB coupling function localized around the minimum of the potential. During the late-time epoch, the field thereby oscillates around the potential minimum and eventually exits toward a stable de Sitter attractor phase. In the minimally coupled limit, the effective equation of state oscillates in the quintessence regime at low redshift, $z\sim0$, without crossing the phantom divide. The nonminimal coupling amplifies the oscillations and drives the effective equation of state across the phantom divide multiple times. Although a sufficiently strong coupling can induce negative scalar and tensor sound speeds, rendering the perturbation modes unstable. We identify a region of parameter space in which the model undergoes multiple phantom crossings while remaining free of ghost and gradient instabilities and approaching a stable de Sitter attractor in the future.