Abstract
AbstractWe consider \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} =2 $\end{document} supergravity theories that have the same spectrum as the R + R2 supergravity, as predicted from the off‐shell counting of degrees of freedom. These theories describe standard \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} =2 $\end{document} supergravity coupled to one or two long massive vector multiplets. The central charge is not gauged in these models and they have a Minkowski vacuum with \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} =2 $\end{document} unbroken supersymmetry. The gauge symmetry, being non‐compact, is always broken. α‐deformed inflaton potentials are obtained, in the case of a single massive vector multiplet, with α = 1/3 and 2/3. The α = 1 potential (i.e. the Starobinsky potential) is also obtained, but only at the prize of having a single massive vector and a residual unbroken gauge symmetry. The inflaton corresponds to one of the Cartan fields of the non‐compact quaternionic‐Kähler cosets.
Highlights
One of the attractive features of the inflaton potential of the Starobinsky model is its dual relation to a pure R + R2 gravitational theory, where a physical scalar, the scalaron, emerges from the higher derivative theory
To understand this phenomenon in the context of supergravity, an off-shell formulation is needed, and two versions of the R + R2 N = 1 supergravity were constructed [1, 2]. In these theories the inflaton is embedded in a massive chiral multiplet or in a massive vector multiplet [3, 4]
The more recent results of BICEP2 [7] seem to be at odds with the PLANCK ones and to disfavor Starobinsky-like models pointing towards more general, supergravity inspired inflationary scenarios
Summary
One of the attractive features of the inflaton potential of the Starobinsky model is its dual relation to a pure R + R2 gravitational theory, where a physical scalar, the scalaron, emerges from the higher derivative theory. Each multiplet contains a spin 1, four spin 1/2 and five scalar fields, and the N = 2 analogue of the Stuckelberg formulation of massive vector states should be based on a gauging of two abelian isometries of a two-dimensional quaternionic Kahler manifold [12], which provides the supersymmetric Higgs mechanism This is the gravity analogue of the N = 2 Higgs effect, which was first studied by Fayet at the birth of N = 2 supersymmetry [13]. In this paper we analyze possible cosmological potentials that follow from this scenario Note that in this massive theory the vector multiplet should have non-vanishing mass for all vanishing values of the scalar fields, which can only occur if the corresponding isometries are non-compact.
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