A new parameter in attractor single-field inflation

Abstract

We revisit the notion of slow-roll in the context of general single-field inflation. As a generalization of slow-roll dynamics, we consider an inflaton $\varphi$ in an attractor phase where the time derivative of $\varphi$ is determined by a function of $\varphi$, $\dot{\varphi }=\dot{\varphi }(\varphi )$. In other words, we consider the case when the number of $e$-folds $N$ counted backward in time from the end of inflation is solely a function of $\varphi$, $N=N(\varphi )$. In this case, it is found that we need a new independent parameter to properly describe the dynamics of the inflaton field in general, in addition to the standard parameters conventionally denoted by $ϵ$, $\eta$, $c_s^2$ and $s$. Two illustrative examples are presented to discuss the non-slow-roll dynamics of the inflaton field consistent with observations.

Comments: (v1) 11 pages; (v2) 12 pages, discussions improved including the running, to appear in Physics Letters B