Rescaled Einstein–Hilbert gravity: Inflation and the Swampland criteria

Abstract

In this work, we shall study a class of [Formula: see text] gravity models which during the inflationary era, which is the large curvature regime, result to an effective inflationary Lagrangian that contains a rescaled Einstein–Hilbert term [Formula: see text] in the presence of a canonical minimally coupled scalar field. The dimensionless parameter [Formula: see text] is chosen to take values in the range [Formula: see text] and the main motivation for studying these rescaled Einstein–Hilbert [Formula: see text] gravities, is the fact that the rescaled action may render an otherwise incompatible canonical scalar field theory with the Swampland criteria, to be compatible with the Swampland criteria and specifically the distance conjecture and the de Sitter conjecture, without considering the refined de Sitter conjecture however. As we will show, by studying a large number of inflationary potentials appearing in the 2018 Planck collaboration paper for the constraints on inflation, the simultaneous compatibility with both the Planck constraints and the aforementioned two Swampland criteria is achieved for some models, and the main characteristic of the models for which this is possible is the small value that the parameter [Formula: see text] must take.