D=4 pure (anti)-de Sitter supergravity revisited

By considering that N = 2 during the supersymmetrization process and by imposing the N=1 condition only at the end, D=4, N=1 pure (anti)-de Sitter supergravity is revisited in an heterodox way that can be used to derive D=4 pure de Sitter supergravity without having to introduce any other field than those of the graviton and the gravitino.

About the theory

Supergravity (SUGRA in short) is a wonderful achievement at the crossroads between the works of A. Einstein and P. Dirac. Noteworthily, almost since its discovery forty-five years ago, D=4, N=1 pure supergravity is known to be anti-de Sitter with a negative cosmological constant when no other field than the bosonic field of the graviton and the fermionic field of the gravitino are considered. It is only recently that D=4, N=1 pure de Sitter supergravity with a positive cosmological constant has been derived by adding a nilpotent Goldstino fermionic field to ensure the local supersymmetry and then by eliminating it through supersymmetry breaking.

Given the no-go theorems on the subject, it is clear that hoping to derive pure de Sitter supergravity requires an unusual approach. This paper presents such an approach that consists in doubling the usual number of Majorana spinors for both the gravitino field and the supersymmetry parameter, which allows to construct spinor-ansatzes that cancel the usual quartic fermion terms appearing in the supersymmetrization process.

The theory

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