On viability of inflation in non-minimal kinetic coupling theory

TL;DR

This paper investigates the conditions for successful inflation in non-minimal kinetic coupling theories, highlighting the dependence on initial scalar field velocity and the impact of potential inclusion on inflation duration and eternal inflation.

Contribution

It provides explicit formulas for e-folds based on initial conditions and analyzes the likelihood of eternal inflation within this theoretical framework.

Findings

Inflation driven solely by kinetic term requires very large initial velocities.

Including potential reduces the required initial velocity for sufficient inflation.

Numerical analysis shows only a small subset of initial conditions lead to eternal inflation.

Abstract

We consider initial conditions for inflation in non-minimal kinetic coupling theory. If inflation is driven solely by kinetic term with no potential, the resulting number of e-folds depends only upon initial velocity of the scalar field $\dot \phi$. We write down the expression for the number of e-folds explicitly, and show that for physically reasonable values of the coupling constant, we can get 60 e-folds only for exponentially big initial $\dot \phi$. When the scalar field potential is taken into account, on the other hand, we need not very large $\dot \phi$ to start with for 60 e-folds, on the other hand, some initial condition lead to physically inadmissible eternal inflation. We show numerically that in the measure used in the present paper only smaller part of initial conditions lead to eternal inflation for reasonable values of the coupling constant.