# S-dual Inflation and the String Swampland

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 $c'$.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03186218
Contributor : Inspire Hep <>
Submitted on : Tuesday, March 30, 2021 - 10:33:01 PM
Last modification on : Tuesday, April 13, 2021 - 10:30:05 PM

### Citation

Luis A. Anchordoqui, Ignatios Antoniadis, Dieter Lüst, Jorge F. Soriano. S-dual Inflation and the String Swampland. 2021. ⟨hal-03186218⟩

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