Anero, JesúsPérez Martín, CarmeloSantos García, Raquel2023-06-162023-06-162020-031475-751610.1088/1475-7516/2020/03/006https://hdl.handle.net/20.500.14352/6269© 2020 IOP Publishing. We are very much indebted to Prof. E. Alvarez for countless enlightening discussions on unimodular supergravity. This work has been partially supported by the Spanish Ministerio de Ciencia, Innovacion y Universidades through grant PGC2018-095382-B-I00. This work has also received funding from the Spanish Research Agency (Agencia Estatal de Investigacion) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, and the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grants agreement No. 674896 and No. 690575. We also have been partially supported by FPA2016-78645-P (Spain). RSG is supported by the Spanish FPU Grant No. FPU16/01595.We put forward a unimodular N = 1; d = 4 anti-de Sitter supergravity theory off shell. This theory, where the Cosmological Constant does not couple to gravity, has a unique maximally supersymmetric classical vacuum which is Anti-de Sitter spacetime with radius given by the equation of motion of the auxiliary scalar field, i.e., S = 3/kappa L. However, we see that the non-supersymmetric classical vacua of the unimodular theory are Minkowski and de Sitter spacetimes as well as anti-de Sitter spacetime with radius l not equal L.engjournal articlehttps://iopscience.iop.org/article/10.1088/1475-7516/2020/03/006https://iopscience.iop.org/open access53Cosmological constatGravity.Física (Física)22 Física