Integrable scalar cosmologies: II. Can they fit into Gauged Extended Supergravity or be encoded in [formula omitted] superpotentials?

P Fré,A.S Sorin,M Trigiante

doi:10.1016/j.nuclphysb.2014.01.024

P Fré, A.S Sorin + Show 1 more

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https://doi.org/10.1016/j.nuclphysb.2014.01.024

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Abstract

The question whether the integrable one-field cosmologies classified in a previous paper by Fré, Sagnotti and Sorin can be embedded as consistent one-field truncations into Extended Gauged Supergravity or in N=1 supergravity gauged by a superpotential without the use of D-terms is addressed in this paper. The answer is that such an embedding is very difficult and rare but not impossible. Indeed, we were able to find two examples of integrable models embedded in supergravity in this way. Both examples are fitted into N=1 supergravity by means of a very specific and interesting choice of the superpotential W(z). The question whether there are examples of such an embedding in Extended Gauged Supergravity remains open. In the present paper, relying on the embedding tensor formalism we classified all gaugings of the N=2 STU model, confirming, in the absence on hypermultiplets, the uniqueness of the stable de Sitter vacuum found several years ago by Fré, Trigiante and Van Proeyen and excluding the embedding of any integrable cosmological model. A detailed analysis of the space of exact solutions of the first supergravity-embedded integrable cosmological model revealed several new features worth an in-depth consideration. When the scalar potential has an extremum at a negative value, the Universe necessarily collapses into a Big Crunch notwithstanding its spatial flatness. The causal structure of these Universes is quite different from that of the closed, positive curved, Universe: indeed, in this case the particle and event horizons do not coincide and develop complicated patterns. The cosmological consequences of this unexpected mechanism deserve careful consideration.

Highlights

In a recent paper [1] some of us have addressed the question of classifying integrable one-field cosmological models based on a slightly generalized ansatz for the spatially flat metric, ds 2 = e2B(t) dt 2 − a 2 (t) dx · dx, (1.1)and on a suitable choice of a potential V (φ) for the unique scalar field φ, whose kinetic term is supposed to be canonical: √Lkin (φ) = ∂μ φ∂ μ φ −g. (1.2)The suitable potential functions V (φ) that lead to exactly integrable Maxwell–Einstein field equations were searched within the family of linear combinations of exponential functions exp βφ or rational functions thereof
The N = 2 model that we have been considering is not integrable, its Friedman equations can be integrated numerically providing a qualitative understanding of the nature of the solutions In Fig. 1 we show the behavior of both the scale factor and the scalar field for any regular initial conditions
In the present paper we have addressed two questions (A) Whether any of the integrable one-field cosmological models classified in [1] can be fitted into Gauged Supergravity based on constant curvature scalar manifolds G/H as consistent truncations to one-field of appropriate multi-field models

Summary

Introduction

The suitable potential functions V (φ) that lead to exactly integrable Maxwell–Einstein field equations were searched within the family of linear combinations of exponential functions exp βφ or rational functions thereof. The motivations for such a choice were provided both with string and supergravity arguments and a rather remarkable bestiary of exact cosmological solutions was uncovered, endowed with quite interesting mathematical properties. Some of these solutions have some appeal as candidate models of the inflationary scenario, capable of explaining the structure of the primordial power spectrum.

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