Let Effective Field Theory of inflation flow: stochastic generation of models with red/blue tensor tilt

Abstract

We extend the method of Flow Equations to the Effective Field Theory framework of inflation, in order to investigate the observable predictions of a very broad class of inflationary models. Focusing our attention on the gravitational-wave sector, we derive a general expression for the consistency relation for effective models and provide a numerical implementation which allows to study how the generated models populate the (r,nt) plane. We analyse 5 × 104 realizations of inflationary scenarios that respect the Null-Energy Condition (ϵ > 0) and 5 × 104 realizations that violate it (ϵ < 0). In both cases, 90 % of the viable models are below the most recent upper bound on the tensor-to-scalar ratio from Planck and BICEP2/Keck Array BK15 data: r0.002 < 0.056 at 95 % CL . We find that general EFT inflationary models with ϵ > 0 are typically characterized by nt < 0, whereas the vast majority of NEC-violating models presents a blue-tilted spectrum (nt > 0). Since a blue tensor spectral index implies more power on small scales, this result is of considerable interest in view of a possible direct detection of the primordial gravitational-wave background.