In this work we shall investigate the phenomenological implications of the constant-roll condition on a k -Inflation theory of gravity .
The latter theories are particularly promising , since these remained robust to the results of GW170817 , since these have a gravitational wave speed c _ { T } = 1 in natural units .
We shall mainly focus on the phenomenology of the k -Inflation models , with the only assumption being the slow-roll condition imposed on the first and fourth slow-roll parameters , and the constant-roll condition for the evolution of the scalar field .
We present in detail the final form of the gravitational equations of motion that control the dynamics of the cosmological system , with the constant-roll condition imposed , and by using a conveniently , from the perspective of analytical manipulations , chosen potential , we express the slow-roll indices and the resulting observational indices of the theory as functions of the e -foldings number .
The results of our analysis indicate that the constant-roll k -Inflation theory can be compatible with the Planck 2018 data , for a wide range of the free parameters .
Also we examine in a quantitative way the effects of the constant-roll condition on the parameter f _ { NL } ^ { equil } on which the bispectrum is proportional , in the equilateral momentum approximation , and we demonstrate that the effect of the constant-roll condition is non-trivial .
In effect , non-Gaussianities in the theory may be enhanced , a phenomenon which is known to be produced by constant-roll scalar theories of gravity in general .