G-constant-roll inflation

Abstract: The constant-roll inflation in the context of Galilean inflation or G-inflation is analyzed. By considering a coupling function $G(\varphi,\chi)\propto g(\varphi)\,\chi^n$ for the model of G-inflation, we find different expressions for a suitable development of a model inflationary in the context of constant roll inflation. In order to obtain analytical solutions, we analyze two specific cases; $g(\varphi)=\varphi$ and $n=0$, i.e., $G(\varphi,\chi)\propto\,\varphi$ and when $g(\varphi)=$ constant and $n=1$ with which $G(\varphi,\chi)\propto\,\chi$. In both cases, we find different expressions for the reconstruction of the background variables and the cosmological perturbations in the framework the constant roll inflation. We utilize recent astronomical observations to constrain the different parameters appearing in the stage of constant roll condition as well in the coupling function $G(\varphi,\chi)$.