CAN ASYMPTOTIC SERIES RESOLVE THE PROBLEMS OF INFLATION

We discuss a cosmological scenario in which inflation is driven by a p otential which is motivated by an effective Lagrangian approach, to gr avity. We exploit the recent arguments that an effective Lagrangian L- eff which, by definition, contains operators of arbitrary dimensionali ty, is in general not a convergent but rather an asymptotic series wit h factorially growing coefficients. The potential we use is obtained b y resumming this series. It provides a natural realization of the infl ationary scenario. By caking into account a cosmological infrared cuto ff, we propose a mechanism which simultaneously provides a graceful ex it from inflation and relaxes to zero the contribution to the cosmolog ical constant which stems from the inflation Lagrangian.