THE STRUCTURE OF PERTURBATIVE QUANTUM-GRAVITY ON A DESITTER BACKGROUND

Classical gravitation on de Sitter space suffers from a linearization instability. One consequence is that the causal response to a spatiall y localized distribution of positive energy cannot be globally regular . We use this fact to show that no causal Green's function can give th e correct linearized response to certain bilocalized distributions, ev en though these distributions obey the constraints of linearization st ability. We avoid the problem by working on the open submanifold spann ed by conformal coordinates. The retarded Green's function is first co mputed in a simple gauge, then the rest of the propagator is inferred by analyticity - up to the usual ambiguity about real, analytic and ho mogeneous terms. We show that the latter can be chosen so as to give a propagator which does not grow in any direction. The ghost propagator is also given and the interaction vertices are worked out.