Galilean constant-roll inflation

The constant-roll inflation in the context of Galilean inflation or G-inflation is analyzed. By considering some coupling function G(φ,χ) associated with the model of G-inflation, we find different inflationary solutions in the context of the constant roll scenario. In order to present an analytical discussion, we work with two specific cases of the general function G(φ,χ)∝g(φ)χⁿ, e.g. (i) G(φ,χ)∝φ when g(φ)=φ and n=0 and (ii) G(φ,χ)∝χ when g(φ)= constant and n=1/2. Also, we introduce a new function G(φ,χ) associated with both variables φ and χ. We reconstruct the potential of the scalar field for the considered cases of the function G in the context of the constant-roll approach and then we study the corresponding cosmological perturbations of the model. Eventually, we use the recent observations datasets in order to constrain the parameter-space of the model.