Gauged Supergravities, de Sitter Space and Cosmology

TL;DR

The paper investigates scalar potentials in gauged $N=8,4,2$ supergravities in four dimensions to assess the existence and cosmological relevance of de Sitter, anti-de Sitter, and Minkowski vacua. A key finding is that all de Sitter extrema in these models are unstable saddles with $|V''|=2V$, corresponding to tachyonic masses satisfying $|m^2|=6H^2$, which rules out slow-roll inflation near these points but admits fast-roll regimes that could drive substantial expansion. The authors also identify Minkowski vacua with flat directions and discuss how quantum effects or Fayet–Iliopoulos terms could lift these directions to realize inflationary dynamics or quintessence-like behavior, albeit with model dependence and embedding challenges in higher-dimensional theories. Overall, the work delineates fundamental constraints on obtaining slow-roll inflation from these highly symmetric 4D supergravity potentials while highlighting possible cosmological roles for fast-roll dynamics and flat directions. It suggests further exploration in more general $N=2$ setups and quantum-corrected scenarios to assess realistic inflationary or dark-energy mechanisms within a supergravity framework.

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.

Figures (2)

• Figure 1: An example of de Sitter saddle point in N=8 gauged supergravity.
• Figure 2: A potential with a valley with $V = 0$ corresponding to Minkowski space.