Vacuum structure in a chiral R+R^n modification of pure supergravity

Abstract

We discuss an $\mathcal{R}+{\mathcal{R}}^n$ class of modified $\mathcal{N}=1$, D=4 supergravity models where the deformation is a monomial ${\mathcal{R}}^n{|}_F$ in the chiral scalar curvature multiplet $\mathcal{R}$ 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 $R+R^n$ 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 $n\ge 3$ 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.

15 pages, 2 figures, v2: typos corrected, published in Phys. Lett. B

References in corpus (14)

• Universality Class in Conformal Inflation
• Minimal Supergravity Models of Inflation
• Superconformal generalizations of the Starobinsky model
• Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity
• No-Scale Supergravity Realization of the Starobinsky Model of Inflation
• Non-minimal Inflationary Attractors
• On the Starobinsky Model of Inflation from Supergravity
• Multi-field Conformal Cosmological Attractors
• Embedding (R+R^2)-Inflation into Supergravity
• Integrable Scalar Cosmologies I. Foundations and links with String Theory
• On the Supersymmetric Completion of $R+R^2$ Gravity and Cosmology
• Higher Order Corrections in Minimal Supergravity Models of Inflation
• Old-minimal supergravity models of inflation
• Chaotic inflation in F(R) supergravity

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