Hadamard and boundary conditions for the Big Bang quantum vacuum

TL;DR

This paper explores initial vacuum states in early universe cosmology using boundary conditions inspired by the Weyl curvature hypothesis, with implications for dark matter production.

Contribution

It introduces a method to construct Hadamard states for quantum fields in the early universe based on boundary conditions at the Big Bang.

Findings

Constructed preferred vacuum states using boundary conditions at the Big Bang.

Derived Hadamard states consistent with the Weyl curvature hypothesis.

Discussed implications for dark matter production in cosmology.

Abstract

General relativity predicts final-type singularities inside black holes, as well as a cosmological initial-type singularity. Cosmic censorship protects external observers from black hole singularities, while Penrose's Weyl curvature hypothesis protects the smoothness of the initial (Big Bang) singularity. We discuss a simple realization of the Weyl curvature hypothesis by assuming a very early radiation-dominated universe and analytically extending the expansion factor to negative values of conformal time. We impose time-reversal conditions at the Big Bang to characterize a natural set of preferred vacuum states for quantized matter fields. We implement the prescription of States of Low Energy constructed around the Big Bang obtaining Hadamard states. We also explore the physical implications of these vacua for cosmological dark matter production.