S-dual inflation and the string swampland

Luis A. Anchordoqui , Ignatios Antoniadis (1) , Dieter Lüst , Jorge F. Soriano

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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 $\mathcal{O}(1)$ constants $c$ and $c^{\prime }$. 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 $c\sim \mathcal{O}({10}^{-1})$ and $c^{\prime }\sim \mathcal{O}({10}^{-2})$ can accommodate the 95% C.L. upper limit on $r$. By imposing at least $50e$-folds of inflation with the effective field theory description valid only over a field displacement $\mathcal{O}(1)$ when measured as a distance in the target space geometry, we further restrict $c\sim \mathcal{O}({10}^{-2})$, while the constraint on $c^{\prime }$ remains unchanged. We comment on how to accommodate the required small values of $c$ and $c^{\prime }$.

Mots clés: higher-order: 1; inflation; slow-roll approximation; de Sitter; cosmic background radiation; effective field theory; S-duality; geometry; string model: landscape

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Astrophysique [astro-ph]; Physique des Hautes Energies - Phénoménologie [hep-ph]

Luis A. Anchordoqui, Ignatios Antoniadis, Dieter Lüst, Jorge F. Soriano. S-dual inflation and the string swampland. Physical Review D, 2021, 103 (12), pp.123537. ⟨10.1103/PhysRevD.103.123537⟩. ⟨hal-03186218⟩