Apparent Phantom Crossing in Gauss-Bonnet Gravity

The recent observations of the Dark Energy Spectroscopic Instrument (DESI) indicated the possibility that the dark energy equation of state parameter $w$ might change from $w<-1$ to $w>-1$ when the redshift $z\sim 0.5$, which is called the inverse phantom crossing. In this paper, we investigate the possibility of the phantom crossing, and we construct realistic models realizing the crossing in the framework of the scalar--Einstein--Gauss-Bonnet gravity and ghost-free $f(\mathcal{G})$ gravity. We also investigate the scenario of the apparent phantom crossing, where dark matter energy density decreases more slowly than usually expected, which might explain the DESI observations. In the scenarios developed, the energy conditions are not violated by any component of the cosmic fluid. In the framework of the apparent phantom crossing, we also propose a new scenario, where the particle corresponding to the scalar field in the scalar--Einstein--Gauss-Bonnet gravity is dark matter. The mass of the particle might increase due to the coupling with the Gauss-Bonnet invariant, which makes the decrease of the dark matter energy density slower. This last scenario may suggest that the inverse phantom crossing might be related to the transition from the decelerating expansion of the Universe to the accelerating expansion.