One Loop Back Reaction On Chaotic Inflation

Authors
Publication Date
Nov 30, 1998
Identifiers
DOI: 10.1103/PhysRevD.60.044010
OAI: oai:arXiv.org:astro-ph/9811430
Source
CERN Document Server
Keywords
Language
English
We extend, for the case of a general scalar potential, the inflaton-graviton Feynman rules recently developed by Iliopoulos {\it et al.} As an application we compute the leading term, for late co-moving times, of the one loop back reaction on the expansion rate for $V(\phi) = \frac12 m^2 \phi^2$. This is expressed as the logarithmic time derivative of the scale factor in the coordinate system for which the expectation value of the metric has the form: $<0 | g_{\mu\nu}({\bar t},{\vec x}) | 0 > dx^{\mu} dx^{\nu} = - d{\bar t}^2 + a^2({\bar t}) d{\vec x} \cdot d{\vec x}$. This quantity should be a gauge independent observable. Our result for it agrees exactly with that inferred from the effect previously computed by Mukhanov {\it et al.} using canonical quantization. It is significant that the two calculations were made with completely different schemes for fixing the gauge, and that our computation was done using the standard formalism of covariant quantization. This should settle some of the issues recently raised by Unruh.