No cosmological D = 11 supergravity

We show, in two complementary ways, that D = 11 supergravity — in contrast to all its lower dimensional versions — forbids a cosmological extension. First, we linearize the putative model about an Anti de Sitter background and show that it cannot even support a “global” supersymmetry invariance; hence there is no Noether construction that can lead to a local supersymmetry. This is true with the usual 4-form field as well as for a “dual”, 7-form, starting point. Second, a cohomology argument, starting from the original full nonlinear theory, establishes the absence of deformations involving spin 32 mass and cosmological terms. In both approaches, it is the form field that is responsible for the obstruction. “Dualizing” the cosmological constant to an 11-form field also fails.