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 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.