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. *

Inflation with non-minimal kinetic and Gauss–Bonnet couplings

“…For the Higgs potential, for instance, in the framework of Galilean models one of the effects of the higher derivative terms is the reduction of the self coupling of the Higgs boson, so that the spectra of primordial density perturbations are consistent with the present observational data [52][53][54]. Different aspects aspects of Galilean-inflation have been considered in [52][53][54][55][56][57][58][59].…”

Imprint of inflationary gravitational waves and WIMP dark matter in pulsar timing array data

“…Let's also mention that although typical slow-roll inflation models cannot produce such BGW, many models beyond slow-roll predict tensor blue tilt, e.g., [36][37][38][39][40][41][42][43]. Because the PTA experiments such as NANOGrav continue to prefer a positive slope of the GW spectrum, GW with tensor blue tilt are one of the most favorable candidates [44][45][46][47][48].…”

Implication of pulsar timing array experiments on cosmological gravitational wave detection

“…Such a blue tensor spectrum may be realized in Ginflation [59][60][61] or Gauss-Bonnet inflation [62]. Both of them can be analyzed using the generalized G-inflation framework [63].…”