States of Low Energy on Bianchi I spacetimes

Abstract

States of Low Energy are a class of exact Hadamard states for free quantum fields on cosmological spacetimes whose structure is fixed at {\it all} scales by a minimization principle. The original construction was for Friedmann-Lemaître geometries and is here generalized to anisotropic Bianchi I geometries relevant to primordial cosmology. In addition to proving the Hadamard property, systematic series expansions in the infrared and ultraviolet are developed. The infrared expansion is convergent and induces in the massless case a leading spatial long distance decay that is always Minkowski-like but anisotropy modulated. The ultraviolet expansion is shown to be equivalent to the Hadamard property, and a non-recursive formula for its coefficients is presented.

44 pages

References in corpus (11)

• Generalized Robertson-Walker space times, a survey
• States of Low Energy on Robertson-Walker Spacetimes
• The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes
• States of Low Energy in bouncing inflationary scenarios in Loop Quantum Cosmology
• WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Low Energy States and CPT invariance at the Big Bang
• Any spacetime has a Bianchi type I spacetime as a limit
• Bianchi I "asymptotically Kasner" solutions of the Einstein scalar field equations
• States of low energy in the Schwinger effect
• Modified Green-Hyperbolic Operators