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 $5\times 10^4$ realizations of inflationary scenarios that respect the Null-Energy Condition ($\hat{I}\mu >0$) and $5\times 10^4$ realizations that violate it ($\hat{I}\mu >0$). 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: $r_{0.002}<0.056$ at 95 % CL. We find that general EFT inflationary models with $\hat{I}\mu >0$ are typically characterized by $n_t<0$, whereas the vast majority of NEC-violating models presents a blue-tilted spectrum ($n_t>0$). 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.

24 pages, 5 figures. Replaced to match the version to appear in JCAP