Generalizing the constant-roll condition in scalar inflation

In this work we generalize the constant-roll condition for minimally coupled canonical scalar field inflation. Particularly, shall assume that satisfies $\ddot{\phi}=\alpha (\phi) V'(\phi)$, and derive equations under assumption. We call framework extended framework. Accordingly calculate inflationary indices corresponding observational of order to demonstrate viability, choose three potentials are problematic in context slow-roll dynamics, namely chaotic, linear power-law exponential inflation, by choosing a simple form smooth function $\alpha (\phi)$, show framework, models compatible with latest 2018 Planck constraints on also justify appropriately why called new V'(\phi)$ is equivalent $\ddot{\phi}=\beta H \dot{\phi}$, latter being generalization condition. Finally, examine an interesting physical situation, which general model required satisfy cosmological tracker used quintessence models. contrast ordinary cases, case not neither or conditions, can be This feature leads phenomenological essential features develop brief.