The cosmological constant in Supergravity

We propose a supersymmetrisation of the cosmological constant in ordinary $N=1$ supergravity that breaks supersymmetry spontaneously by a constant Fayet-Iliopoulos (FI) term associated to a $U(1)$ symmetry. This term is a variation of a new gauge invariant FI term proposed recently, which is invariant under K\"{a}hler transformations and can be written even for a gauged R-symmetry on top of the standard FI contribution. The two terms are the same in the absence of matter but differ in its presence. The proposed term is reduced to a constant FI-term up to fermion interactions that disappear in the unitary gauge in the absence of any F-term supersymmetry breaking. The constant FI term leads to a positive cosmological constant, uplifting the vacuum energy from the usual anti-de Sitter supergravity to any higher value.