Making inflation work: damping of density perturbations due to Planck energy cutoff

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 fluctuations of the "time-time" component of the energy-momentum tensor. We compute the inhomogeneous part of the correlation function <0‖T₀⁰(x,t) T₀⁰(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 hoc) 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 fluctuations have the acceptable magnitude (∼10^-4) for the case of primordial inflation. Thus the inflationary scenario can be made to work without any fine-tuning.