NO COSMOLOGICAL D=11 SUPERGRAVITY

We show, in two complementary ways, that D = 11 supergravity - in cont rast to all its lower dimensional versions forbids a cosmological exte nsion. First, we linearize the putative model about an Anti de Sitter background and show that it cannot even support a ''global'' supersymm etry 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 a rgument, starting from the original full nonlinear theory, establishes the absence of deformations involving spin 3/2 mass and cosmological terms. In both approaches, it is the form field that is responsible fo r the obstruction. ''Dualizing'' the cosmological constant to an Ii-fo rm field also fails. (C) 1997 Elsevier Science B.V.