Gauged supergravities, de Sitter space, and cosmology

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Abstract
We study 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. We find that all known de Sitter extrema correspond to unstable maximum or saddle points with negative curvature |V″|=2V for the fields canonically normalized at the extremum. This is equivalent to the relation |m2|=|R|/2=6H2 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″|≪V. Moreover, in all models that we are able to analyze the potential is unbounded from below. On the other hand, barring the question of 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 the novel possibility of the fast-roll inflation with |V″|≳V. We also display some potentials that have flat directions with a vanishing cosmological constant, and discuss their possible cosmological implications.