S-dual Inflation and the String Swampland

TL;DR

This paper investigates S-dual inflation models within the string swampland constraints, showing they can satisfy observational limits on tensor-to-scalar ratio and de Sitter conjecture conditions with specific parameter ranges.

Contribution

It computes next-to-leading order predictions for S-dual inflation potentials and analyzes their compatibility with swampland and observational constraints.

Findings

S-dual potentials can meet the 95% CL upper limit on r.

Parameter ranges c ~ 10^{-1} to 10^{-2} are compatible with constraints.

Imposing 50 e-folds restricts c to around 10^{-2}.

Abstract

The Swampland de Sitter conjecture in combination with upper limits on the tensor-to-scalar ratio $r$ derived from observations of the cosmic microwave background endangers the paradigm of slow-roll single field inflation. This conjecture constrains the first and the second derivatives of the inflationary potential in terms of two ${\cal O} (1)$ constants $c$ and $c'$. In view of these restrictions we reexamine single-field inflationary potentials with $S$-duality symmetry, which ameliorate the unlikeliness problem of the initial condition. We compute $r$ at next-to-leading order in slow-roll parameters for the most general form of $S$-dual potentials and confront model predictions to constraints imposed by the de Sitter conjecture. We find that $c \sim {\cal O} (10^{-1})$ and $c' \sim {\cal O} (10^{-2})$ can accommodate the 95\% CL upper limit on $r$. By imposing at least 50 $e$-folds of inflation with the effective field theory description only valid over a field displacement ${\cal O} (1)$ when measured as a distance in the target space geometry, we further restrict $c \sim {\cal O} (10^{-2})$, while the constraint on $c'$ remains unchanged. We comment on how to accommodate the required small values of $c$ and $c'$.