Abstract
Abstract We revisit and clarify the supersymmetric versions of R + R 2 gravity, in view of the renewed interest to these models in cosmology. We emphasize that the content of the dual standard supergravity theory in the old minimal formulation necessarily includes two massive chiral multiplets, that we call the inflaton and the goldstino. We point out that the presence of these multiplets is model independent in the old minimal formulation and therefore any theory that contains a single chiral multiplet fails to be a supersymmetric generalization of the R + R 2 gravity. The supergravity interactions of the two chiral multiplets are encoded in a superpotential mass term and an arbitrary Kähler potential for the goldstino multiplet. The implication for cosmology of the supersymmetric R + R 2 gravity is also discussed.
Highlights
We emphasize that the content of the dual standard supergravity theory in the old minimal formulation necessarily includes two massive chiral multiplets, that we call the inflaton and the goldstino
We point out that the presence of these multiplets is model independent in the old minimal formulation and any theory that contains a single chiral multiplet fails to be a supersymmetric generalization of the R + R2 gravity
The supergravity interactions of the two chiral multiplets are encoded in a superpotential mass term and an arbitrary Kahler potential for the goldstino multiplet
Summary
In the old minimal supergravity the most general R + R2 theory is given by a Lagrangian of the form [2] This action has a manifest superconformal symmetry, and we write it using notations of superconformal calculus, reviewed in [7]. Since the equation of motion for the auxiliary field X following from (3.4) is algebraic, one solves X(x) in terms of R(x) and in approximation of high curvature one produces the non-linear in R(x) action of the form. The supersymmetric action (3.1) has some extra terms beyond the ones in (3.4) depending on Aμ, an auxiliary field of supergravity. The complete bosonic part of the supersymmetric action (3.1) does not lead to an algebraic equation of motion for X, this field is not auxiliary anymore, it is propagating, and is the only propagating complex scalar degree of freedom
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