Minimizing the tensor-to-scalar ratio in single-field inflation models

TL;DR

This paper explores how simple single-field inflation models can be modified with higher order operators to produce negligible tensor-to-scalar ratios, potentially below future observational sensitivities, while maintaining consistency with observed spectral indices.

Contribution

It explicitly constructs corrected quadratic hilltop potentials using effective field theory and demonstrates their ability to minimize the tensor-to-scalar ratio using MCMC and optimization techniques.

Findings

Potential to lower r below CMB-S4 sensitivity

Minimum r scales as a power law with expansion order

Minimum r asymptotes around 10^{-11}

Abstract

We revisit a class of simple single-field inflation models and demonstrate that they can readily produce a negligible tensor/scalar ratio $r$. Motivated by recent work suggesting the need to introduce higher order operators to stabilise unregulated potentials, as well as by work indicating that such terms can have significant effects on observable predictions, we explicitly construct corrected versions of the quadratic hilltop potential that are motivated by an effective field theory expansion. We employ Markov Chain Monte Carlo (MCMC) methods and optimization techniques to sample viable models and minimize $r$. We find that such potentials can readily lower $r$ values below projected CMB-S4 sensitivity, while still remaining within observable constraints on $n_s$. Furthermore, we find that the minimum $r$ reached for each order of the expansion considered is well-described by a power law $r_{min}(q) \propto q^{-B}$ before asymptoting to a value of $r_{min} \sim 10^{-11}$, where $q$ is the order to which the expansion of $V(\phi)$ is carried out.