Abstract
We discuss an R+Rn class of modified N=1, D=4 supergravity models where the deformation is a monomial Rn|F in the chiral scalar curvature multiplet R of the “old minimal” auxiliary field formulation. The scalaron and goldstino multiplets are dual to each other in this theory. Since one of them is not dynamical, this theory, as recently shown, cannot be used as the supersymmetric completion of R+Rn gravity. This is confirmed by investigating the scalar potential and its critical points in the dual standard supergravity formulation with a single chiral multiplet with specific Kähler potential and superpotential. We study the vacuum structure of this dual theory and we find that there is always a supersymmetric Minkowski critical point which however is pathological for n⩾3 as it corresponds to a corner (n=3) and a cusp (n>3) point of the potential. For n>3 an anti-de Sitter regular supersymmetric vacuum emerges. As a result, this class of models are not appropriate to describe inflation. We also find the mass spectrum and we provide a general formula for the masses of the scalars of a chiral multiplet around the anti-de Sitter critical point and their relation to osp(1,4) unitary representations.
Highlights
Motivated by the latest Planck mission data [1, 2], there has been recently a renewed interest in R + R2 bosonic theories, which realize the Strarobinsky model of inflation
As there are two such minimal extensions, old and new minimal supergravity, there are two inequivalent ways to supersymmetrize the bosonic R+R2 theory. This has been done originally in [3] in the old minimal supergravity framework and in [4] in new minimal formulation. These theories have the common feature of adding to pure supergravity four bosonic and four fermionic degrees of freedom, two chiral multiplets in old minimal [3] and a massive vector multiplet in new minimal [4], in accordance with the linearized analysis given in [14]
We have discuss here a particular F(R) supergravity [12, 13], namely the F (R) = R + Rn class of supergravity models. We found that this theory is not the supersymmetric completion of R + Rn, since it does not contain two chiral multiplets
Summary
Motivated by the latest Planck mission data [1, 2], there has been recently a renewed interest in R + R2 bosonic theories, which realize the Strarobinsky model of inflation. These theories have the common feature of adding to pure supergravity four bosonic and four fermionic degrees of freedom, two chiral multiplets in old minimal [3] and a massive vector multiplet in new minimal [4], in accordance with the linearized analysis given in [14] These theories have been considered [5,6,7,8,9,10,11] in the light of the new constraints set by the Planck mission on inflation [2].
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