NONPERTURBATIVE MODELS FOR THE QUANTUM GRAVITATIONAL BACK-REACTION ONINFLATION

We consider a universe in which inflation commences because of a posit ive cosmological constant, the effect of which is progressively screen ed by the interaction between virtual gravitons that become trapped in the expansion of spacetime. Perturbative calculations have shown that screening becomes nonperturbatively large at late times. In this pape r we consider effective field equations which can be evolved numerical ly to provide a non-perturbative description of the process. The induc ed stress tensor is that of an effective scalar field which is a non-l ocal functional of the metric. We use the known perturbative result, c onstrained by general principles and guided by a physical description of the screening mechanism, to formulate a class of ansatze for this f unctional. A scheme is given for numerically evolving the field equati ons which result from a simple ansatz, from the beginning of inflation past the time when it ends. We find that inflation comes to a sudden end, producing a system whose equation of state rapidly approaches tha t of radiation. Explicit numerical results are presented. (C) 1998 Aca demic Press.