Cosmological dynamics of Cuscuta–Galileon gravity

We study cosmological dynamics of the Cuscuta–Galileon gravity with a potential term by using the dynamical system approach. This model is galileon generalization of the cuscuton gravity where we add a potential term to the theory in order to obtain the radiation and matter dominated eras. The exponential potential can provide the sequence of the thermal history of the Universe correctly, i.e. starting from radiation dominance, passing through matter dominant era, and then approaching de Sitter expansion stage. This model has no ghosts and the Laplacian instability for both scalar and tensor perturbations. We also discuss the observational constraints on the model parameters. It turns out that the model actually has three degrees of freedom unlike the original cuscuton theory.