Revisiting slow-roll dynamics and the tensor tilt in general single-field inflation

Abstract

We explore the possibility of a blue-tilted gravitational wave spectrum from potential-driven slow-roll inflation in the Horndeski theory. In Kamada et al. (2012), it was claimed that a blue gravitational wave spectrum cannot be obtained from stable potential-driven slow-roll inflation within the Horndeski framework. However, it has been demonstrated that the spectrum of primordial gravitational waves can be blue in inflation with the Gauss-Bonnet term, where the potential term is dominant and slow-roll conditions as well as the stability conditions are satisfied. To fill in this gap, we clarify where the discrepancy is coming from. We extend the formulation of Kamada et al. (2012) and show that a blue gravitational wave spectrum can certainly be generated from stable slow-roll inflation if some of the conditions previously imposed on the form of the free functions in the Lagrangian are relaxed.