This work revisits D=4, N=1 (anti)-de Sitter supergravity within a deliberately unconventional framework aiming to show that D=4, N=1 de Sitter supergravity can be derived only with the graviton and the gravitino fields, and therefore without a Goldstino field, a scalar sector, or spontaneous supersymmetry breaking.
Supergravity is a wonderful achievement at the crossroads between the works of A. Einstein and P. Dirac. Noteworthily, almost since its discovery fifty years ago, D=4, N=1 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 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 D=4, N=1 de Sitter supergravity without adding a nilpotent Goldstino fermionic field requires an unusual approach. This paper presents such an approach that consists in using the Majorana conjugate to construct bilinears of Weyl spinors and introducing the hyperbolic unit in the fermionic terms related to a positive cosmological constant.
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