S-dual inflation and the string swampland

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 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 similar to O(10(-1)) and c' similar to 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 O(1) when measured as a distance in the target space geometry, we further restrict c similar to O(10(-2)), while the constraint on c' remains unchanged. We comment on how to accommodate the required small values of c and c'.

Automated summary

The swampland de Sitter conjecture, combined with upper limits on the tensor-to-scalar ratio r derived from observations of the cosmic microwave background, challenges the paradigm of slow-roll single-field inflation. By reexamining single-field inflationary potentials with S-duality symmetry and computing r at next-to-leading order, it is found that certain values of c and c' can accommodate experimental constraints. Further restrictions are imposed by requiring a minimum number of e-folds of inflation and an effective field theory description valid only over a certain field displacement in the target space geometry.