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‖(x,t) (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 (∼) for the case of primordial inflation. Thus the inflationary scenario can be made to work without any fine-tuning.
- Received 28 July 1988
DOI:https://doi.org/10.1103/PhysRevD.39.2100
©1989 American Physical Society