Scalar measure of the local expansion rate

L. R. Abramo and R. P. Woodard
Phys. Rev. D 65, 043507 – Published 15 January 2002
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Abstract

We define a scalar measure of the local expansion rate based on how astronomers determine the Hubble constant. Our observable is the inverse conformal d’Alembertian acting on a unit “standard candle.” Because this quantity is an integral over the past light cone of the observation point it provides a manifestly causal and covariant technique for averaging over small fluctuations. For an exactly homogeneous and isotropic spacetime our scalar gives minus one-half times the inverse square of the Hubble parameter. Our proposal is that it be assigned this meaning generally and that it be employed to decide the issue of whether or not there is a significant quantum gravitational back reaction on inflation. Several techniques are discussed for promoting the scalar to a full invariant by giving a geometrical description for the point of observation. We work out an explicit formalism for evaluating the invariant in perturbation theory. The results for two simple models are presented in subsequent papers.

  • Received 18 September 2001

DOI:https://doi.org/10.1103/PhysRevD.65.043507

©2002 American Physical Society

Authors & Affiliations

L. R. Abramo*

  • Theoretische Physik, Ludwig Maximilians Universität, Theresienstrasse 37, D-80333 München, Germany

R. P. Woodard

  • Department of Physics, University of Florida, Gainesville, Florida 32611

  • *Email address: abramo@theorie.physik.uni-muenchen.de
  • Email address: woodard@phys.ufl.edu

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Vol. 65, Iss. 4 — 15 February 2002

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