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

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 ($epsilon > 0$) and $5 times 10^{4}$ realizations that violate it ($epsilon > 0$). 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 $epsilon > 0$ 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.