On Viability of Inflation in Nonminimal Kinetic Coupling Theory

We consider the initial conditions for inflation in the nonminimal kinetic coupling theory. If inflation is driven solely by the kinetic term with no potential, the resulting number of e-folds depends only on the 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 an exponentially big initial \(\dot{\phi}\). When the scalar field potential is taken into account, a double inflation scenario arises, where the first inflation is kinetic term driven, while the second one is potential term driven. In this case, we need not a very large \(\dot{\phi}\) to start with for 60 e-folds, on the other hand, some initial conditions lead to a physically inadmissible eternal inflation. We show numerically that in the measure used in the present paper only a smaller part of initial conditions leads to eternal inflation for reasonable values of the coupling constant.