Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local $\mathcal{N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent Goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and Goldstino, no scalars. In the global limit when the supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where the Goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.

• Received 30 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.085040