Covariant Vacuum Polarizations on de Sitter Background

Abstract

We derive covariant expressions for the one loop vacuum polarization induced by a charged scalar on de Sitter background. Two forms are employed: one in which two covariant derivatives act on de Sitter invariant basis tensors multiplied by scalar structure functions, and the other in which four covariant derivatives act on a single basis tensor times a structure function. The second representation permits the correction to dynamical photons to be expressed as a surface integral, which raises the important question of what sorts of effects can be absorbed into corrections of the initial state. Results are obtained for charged, minimally coupled scalars which are either massless or else light. The former show de Sitter breaking whereas the latter are de Sitter invariant. However, the de Sitter invariant formulation does not seem useful, even when it is possible. Our work has important implications for representations of the graviton self-energy on de Sitter.

arXiv comment30 pages, 3 figures, 2 tables, uses LaTeX 2e

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• Electrodynamic Effects of Inflationary Gravitons
• Graviton Loop Corrections to Vacuum Polarization in de Sitter in a General Covariant Gauge
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• One loop graviton corrections to dynamical photons in de Sitter
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• Representing the Graviton Self-Energy on de Sitter Background
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• One-loop Graviton Corrections to Conformal Scalars on a de Sitter Background
• One loop corrected conformally coupled scalar mode equations during inflation
• Photon propagator for inflation in the general covariant gauge
• Photon quantization in cosmological spaces
• A photon propagator on de Sitter in covariant gauges