Recovering the inflationary potential

Abstract

A procedure is developed for the recovery of the inflationary potential over the interval that affects astrophysical scales (≈1 Mpc to ${10}^4$ Mpc). The amplitudes of the scalar and tensor metric perturbations and their power-spectrum indices, which in principle can be inferred from large-angle CBR anisotropy 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. Examples are presented, and the effect of observational uncertainties is discussed.