Gauged Supergravities, de Sitter Space and Cosmology

TL;DR

This paper analyzes scalar potentials in gauged supergravities, finding that de Sitter vacua are unstable and unsuitable for inflation, but these models may still describe the universe's current accelerated expansion and include flat directions with cosmological implications.

Contribution

It provides a detailed study of scalar potentials in gauged supergravities, highlighting their instability and potential cosmological applications, including flat directions and fast-roll inflation possibilities.

Findings

De Sitter extrema are unstable maxima or saddle points.

Potential is unbounded from below in analyzed models.

Possible use in describing current accelerated universe expansion.

Abstract

We have studied scalar potentials V of gauged N=8,4,2 supergravities in d=4. Extrema of these potentials may correspond to de Sitter, anti de Sitter and Minkowski vacua. All de Sitter extrema that we have studied correspond to unstable maximum/saddle points with negative curvature |V''|=2V for the fields canonically normalized at the extremum. This is equivalent to the relation |m^2| =|R|/2 = 6H^2 for the tachyonic mass m, the curvature scalar R, and the Hubble constant H. This prevents the use of de Sitter extrema for slow-roll inflation in the early universe, which would require |V''| \ll V . Moreover, in all models that we were able to analyse the potential is unbounded from below. On the other hand, barring the question how realistic such models could be, one can use them for the description of the accelerated expansion of the universe at the present epoch. This is related to a novel possibility of the fast-roll inflation with |V''| > V . We also display some potentials that have flat directions with vanishing cosmological constant, and discuss their possible cosmological implications.