Letters #1 Mathematical Physics 25:307 316, 1992. © 1992 Kluwer Academic Publishers. Printed #7 the Netherlands. 307 The Gravitational Anomalies in de Sitter Space MATTHIAS MAISCHAK* Institut fiir Theoretische Physik, Universitiit, Hannover, Appelstrafle 2, D-3000 Hannover 1, Germany (Received: 15 April 1992; revised: 10 June 1992) Abstract. All solutions to the consistency equations are determined which have to be satisfied by anomalies in gravitational theories with a de Sitter-invariant groundstate. They turn out to be identical with the solutions for a Poincar6-invariant groundstate. Mathematics Subject Classifications (1991). 81T50, 81T20. 1. Introduction Anomalies a have to satisfy the consistency condition [1] sa =0, a C sb, a = fd([qb]a, x), (1) where s is the nilpotent BRS transformation s 2 = 0 and the anomalies a (to lowest order in h) and b are local functionals. [~]a collectively denotes all fields • and their partial derivatives c?q5,c3#~ ..... The volume form (D-form) d depends polynomi- ally on x and [Oq~]a- Considered as a function of the undifferentiated fields as, the integrand d can be a formal series. For the integrand, the consistency condition (1) translates to s~' + d~ = 0, ~z ¢ sg~ + d~. (2) These consistency conditions cannot only be studied for ghost number 1 where their solutions correspond to all possible anomalies. For ghost number 0, the solutions determine all gauge invariant local actions and for ghost number 2 (in D- 1 dimensions), the solutions are related to Schwinger terms [2]. The solutions of (2) depend decisively on the set of fields qb and the way s acts on them and the domain of regularity of the action. In [3], Equation (2) was solved for Yang Mills theories for an arbitrary ghost number and, in [4], for the gravitational case with a Poincar6-invariant groundstate, i.e., with a flat back- ground. Here, (2) is analysed along the same lines as in [4] with the de Sitter space as the background. * Now at Institut ffir Angewandte Mathematik, Universitfit Hannover, Welfengarten 1, D-3000 Han- nover 1, Germany.