RECONSTRUCTING THE INFLATON POTENTIAL - AN OVERVIEW

The authors review the relation between the inflationary potential and the spectra of density waves (scalar perturbations) and gravitational waves (tensor perturbations) produced, with particular emphasis on th e possibility of reconstructing the inflaton potential from observatio ns. The spectra provide a potentially powerful test of the inflationar y hypothesis; they are not independent but instead are linked by consi stency relations reflecting their origin from a single inflationary po tential. To lowest order in a perturbation expansion there is a single , now familiar, relation between the tensor spectral index and the rel ative amplitude of the spectra. The authors demonstrate that there is an infinite hierarchy of such consistency equations, though observatio nal difficulties suggest only the first is ever likely to be useful. T hey also note that since observations are expected to yield much bette r information on the scalars than on the tensors, it is likely to be t he next-order version of this consistency equation that will be approp riate, not the lowest-order one. If inflation passes the consistency t est, one can then confidently use the remaining observational informat ion to constrain the inflationary potential, and the authors survey th e general perturbative scheme for carrying out this procedure. Explici t expressions valid to next-lowest order in the expansion are presente d. The prospects for future observations' reaching the quality require d are then briefly assessed and simulated data sets motivated by this outlook are considered.