Recovering the Inflationary Potential

Abstract

A procedure is developed for the recovery of the inflationary potential over the interval that affects astrophysical scales ($\approx 1\text{Mpc}-10^4\text{Mpc}$). The amplitudes of the scalar and tensor metric perturbations and their power-spectrum indices, which can in principle be inferred from large-angle CBR anisotropy experiments and other cosmological data, determine the value of the inflationary potential and its first two derivatives. From these, the inflationary potential can be reconstructed in a Taylor series and the consistency of the inflationary hypothesis tested. A number of examples are presented, and the effect of observational uncertainties is discussed.

Comments: 13 pages LaTeX, 6 Figs. available on request, FNAL-Pub-93/182-A