Old-minimal supergravity models of inflation

Abstract

We study three types of the old-minimal higher-derivative supergravity theories extending the $f(R)$ gravity, towards their use for the inflationary model building in supergravity, by using both superfields and their field components. In the curved superspace all those theories are described in terms of a single chiral scalar curvature superfeld $\mathcal{R}$. Each of those theories can be dualized into a matter-coupled supergravity without higher derivatives. The first type is parametrized by a single non-holomorphic potential $N(\mathcal{R},\bar{\mathcal{R}})$, and gives rise to the dual matter-coupled supergravities with two dynamical chiral matter superfields having a no-scale Kähler potential. We find that a generic potential $N(\mathcal{R},\bar{\mathcal{R}})$ generates both the $(R+R^2)$ gravity and the non-minimal coupling of the propagating complex scalar field to the $R$, needed for the Starobinsky and Higgs inflation, respectively. We find the general conditions for the Starobinsky inflation and compute the inflaton mass. The second type is given by the chiral supergravity actions whose superfield Lagrangian $F(\mathcal{R},\Sigma (\bar{\mathcal{R}}))$ also depends upon the chiral projection $\Sigma$ of the anti-chiral superfield $\bar{\mathcal{R}}$. We find that the actions of the second type always give rise to ghosts. We also revisit the $F(\mathcal{R})$ supergravity actions of the third type (without the $\Sigma$-dependence) with the reduced number of the extra physical degrees of freedom, comprising a single chiral matter superfeld with a no-scale Kähler potential. We confirm that the pure $F(\mathcal{R})$ supergravity is insufficient for realization of the Starobinsky inflation, though by the reason different from those proposed in the recent literature.

LaTeX, 24 pages, no pictures; Sections 3 and 4 expanded, references added, typos corrected

References in corpus (18)

• The Standard Model Higgs boson as the inflaton
• Minimal Supergravity Models of Inflation
• Inflation scenario via the Standard Model Higgs boson and LHC
• 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
• New models of chaotic inflation in supergravity
• General inflaton potentials in supergravity
• On the Starobinsky Model of Inflation from Supergravity
• Embedding (R+R^2)-Inflation into Supergravity
• On the Supersymmetric Completion of $R+R^2$ Gravity and Cosmology
• Higher Order Corrections in Minimal Supergravity Models of Inflation
• Superstring-inspired supergravity as the universal source of inflation and quintessence
• Slow-roll inflation in (R+R*4) gravity
• Vacuum structure in a chiral R+R^n modification of pure supergravity
• Chaotic inflation in F(R) supergravity
• Scalar potential in F(R) supergravity
• Cosmological properties of a generic (\cal R)^2-supergravity

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• Primordial black holes from modified supergravity
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• Reheating processes after Starobinsky inflation in old-minimal supergravity
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• Ghostbusters in higher derivative supersymmetric theories: who is afraid of propagating auxiliary fields?
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• Deforming the Starobinsky model in ghost-free higher derivative supergravities
• Supersymmetry, Cosmological Constant and Inflation: Towards a fundamental cosmic picture via "running vacuum"
• Higher Curvature Supergravity, Supersymmetry Breaking and Inflation
• Volkov-Akulov-Starobinsky supergravity revisited
• $\alpha$-attractors from supersymmetry breaking
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• Gravity Rainbow Effects on Higher Curvature Modification of R2 inflation
• Gauging the R-symmetry of old-minimal $R+R^2$ supergravity
• Exploring the parameter space of modified supergravity for double inflation and primordial black hole formation
• Evaporation and Antievaporation instabilities