Constant-roll approach to non-canonical inflation

The scenario of constant-roll inflation is studied where the inflaton is a scalar field with modified kinetic term, known as non-canonical scalar field. This modification leads to some changes in the slow-roll parameters, and also by taking the second slow-roll parameter as a constant, the differential equation for the Hubble parameter is altered as well. Assuming $\eta=\beta$ and reconsidering the perturbation equations makes it clear that there should be some modified terms in the scalar spectral index and amplitude of scalar perturbations. After finding the exact solution, the main perturbation parameters are obtained at the horizon crossing time. Then by plotting the $r-n_s$ diagram it is shown that for some specific values of $\beta$ one could find a good agreement with observational data. In addition, considering the attractor behavior of the model leads to this result that this feature could be appropriately satisfied.