Constraints on the spectral index for the inflation models in the string landscape

Abstract

We conjecture that the inflation models with trans-Planckian excursions in the field space should be in the swampland. We check this conjecture in a few examples and investigate the constraints on the spectral index for the slow-roll inflation model in the string landscape where the variation of the inflaton during the period of inflation is less than the Planck scale ${M}_{p}$. A red primordial power spectrum with a lower bound on the spectral index is preferred. Both the tensor-scalar ratio and the running can be ignored.