Making inflation work : Damping of density perturbations due to Planck energy cut-off

Abstract

In this paper we propose an alternative method for the computation of classical density perturbations from a quantum field in an inflationary scenario. We compute the power spectrum of density perturbations directly from vacuum Auctuations of the "time-time" component of the energy momentum tensor. We compute the inhornogeneous part of~ the correlation function (0~ T o(x, t)T 0(y, t) ~0) for a massless minimally coupled scalar field in de Sitter space. The Fourier transform of this two-point function leads to the scale-invariant spectrum of perturbations, but is ultraviolet divergent. This expression can be made finite by introducing an (ad hot.") small-distance cutoff' in the proper length. We argue that this cutoff'should be of the order of the Planck length, and show that, in such a case, the density Auctuations have the acceptable magnitude (-10 ) for the case of primordial inflation. Thus the inflationary scenario can be made to work without any