Cosmic Microwave Background Observables of Small Field Models of Inflation

TL;DR

This work challenges the common view that small-field inflation cannot yield observable gravitational waves by introducing a class of small-field models with a non-monotonic slow-roll parameter $\epsilon(\phi)$, capable of producing both a measurable tensor-to-scalar ratio $r$ and a negative running $\alpha$. The authors construct a five-parameter potential that interpolates between large- and small-field behaviors and compute the resulting CMB observables by solving the Mukhanov-Sasaki equation numerically, finding that significant running can accompany a detectable $r$ with a sub-Planckian field excursion. An effective field theory analysis ties the running to a high inflation scale and a sizeable GW signal, requiring a small trilinear coupling $\lambda_3$ and a potential scale $\Lambda$ close to the UV cutoff, with $\Lambda \sim 10^{16}\,\text{GeV}$ for plausible $r$. The model makes a distinctive prediction of enhanced small-scale power and offers running as a key discriminator among inflationary scenarios, while predicting negligible non-Gaussianity in single-field setups, a testable hallmark for upcoming observations. Overall, the paper provides a coherent framework linking RUN, GW detectability, and EFT constraints in a class of small-field inflation models.

Abstract

We construct a class of single small field models of inflation that can predict, contrary to popular wisdom, an observable gravitational wave signal in the cosmic microwave background anisotropies. The spectral index, its running, the tensor to scalar ratio and the number of e-folds can cover all the parameter space currently allowed by cosmological observations. A unique feature of models in this class is their ability to predict a negative spectral index running in accordance with recent cosmic microwave background observations. We discuss the new class of models from an effective field theory perspective and show that if the dimensionless trilinear coupling is small, as required for consistency, then the observed spectral index running implies a high scale of inflation and hence an observable gravitational wave signal. All the models share a distinct prediction of higher power at smaller scales, making them easy targets for detection.