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Abstract

We extend the model orignally proposed by Unruh and Jheeta in [6] in two ways. First we derive the complex action to third order in the slope of the slow-roll potential and find that it depends on precisely which endpoint is chosen in complex T space, and that it also has phase contributions to the semi-classical wave function. Secondly, we derive the reduced Hamiltonian action to second order in classical, non-homogenous scalar metric and matter fluctuations about an arbitrary FRW background. We analyze the I = 1 mode for the closed FRW universe and prove it is a gauge mode. We find a contour in T space for which this reduced action has a simple character. We use this character to make an argument concerning the appropriateness of using Linde's or Hawking's sign in determining the amplitude contribution to the wave-function from these classical fluctuations.