Higher derivatives in quantum cosmology: (I). The isotropic case

This paper is the first in a series that investigates the effects on cosmology of curvature-squared terms which are bound to appear in the effective action whether or not gravity is perturbatively finite, is cut off by nonperturbative effects, or is made renormalisable by the addition of curvature squared terms to the bare action. We examine how these terms affect the recent proposal that the quantum state of the universe is defined by a path integral over compact metrics. In this paper we consider a simple minisuperspace model of an isotropic universe. In such a model the C-squared term in the action plays no role while the R-squared term behaves like a massive scalar field. The wave function of the universe can be interpreted as corresponding in the classical limit to a family of solutions that start out with a long period of exponential expansion and then go over to a matter dominated era.