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We exploit a new numerical technique for evaluating the tree ordercontributions to the primordial scalar and tensor power spectra for scalarpotential models of inflation. Among other things we use the formalism todevelop a good analytic approximation which goes beyond generalized slow rollexpansions in that (1) it is not contaminated by the physically irrelevantphase, (2) its 0th order term is exact for constant first slow roll parameter,and (3) the correction is multiplicative rather than additive. These featuresallow our formalism to capture at first order, effects which are higher orderin other expansions. Although this accuracy is not necessary to compare currentdata with any specific model, our method has a number of applications owing tothe simpler representation it provides for the connection between the powerspectra and the expansion history of a general model.

Precision Predictions for the Primordial Power Spectra of Scalar Potential Models of Inflation