SELF-REGENERATING INFLATIONARY UNIVERSE IN HIGHER-ORDER GRAVITY IN ARBITRARY DIMENSION

We present a discussion of self-regenerating, self-reproducing inflationary universe in the context of higher-order gravity theories in an arbitrary number of dimensions taking into account quantum fluctuations during the time of inflation. Using the conformal equivalence theorem, we analyse the scalar field dynamics induced by quantum fluctuations in an effective potential which is typically an exponential function of the field. We find that, as in the usual eternal inflation model based on chaotic inflation, space-time foam regions are likely to exist today for some choices of the gravitational lagrangian. These include all theories with space-time dimension greater than twice the order of the leading term in the gravitational lagrangian. However, when the number of space-time dimensions is less or equal to twice the order of the leading term in the lagrangian, eternal inflation does occur and space-time foam regions are not likely to exist today.