Bonus Properties of States of Low Energy

TL;DR

States of Low Energy (SLE) are a class of Hadamard states in Friedmann-Lemaître spacetimes that can be expressed via the commutator function, have a convergent momentum series, and help address infrared divergences, making them suitable for early universe models.

Contribution

This paper introduces a new representation of SLE solely in terms of the commutator function and demonstrates their infrared behavior and series expansion properties.

Findings

SLE can be expressed using the commutator function.

Massless SLE exhibit Minkowski-like infrared behavior.

Massless SLE can serve as pre-inflationary vacua and produce correct primordial spectra.

Abstract

States of Low Energy (SLE) are exact Hadamard states defined on arbitrary Friedmann-Lema\^{i}tre spacetimes. They are constructed from a fiducial state by minimizing the Hamiltonian's expectation value after averaging with a temporal window function. We show the SLE to be expressible solely in terms of the (state independent) commutator function. They also admit a convergent series expansion in powers of the spatial momentum, both for massive and for massless theories. In the massless case the leading infrared behavior is found to be Minkowski-like for all scale factors. This provides a new cure for the infrared divergences in Friedmann-Lema\^{i}tre spacetimes with accelerated expansion. In consequence, massless SLE are viable candidates for pre-inflationary vacua and in a soluble model are shown to entail a qualitatively correct primordial power spectrum.