On the Supersymmetric Completion of $R+R^2$ Gravity and Cosmology

Understand

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 Kahler potential for the goldstino multiplet.