Non-equilibrium Quantum Field Theory and Axion Electrodynamics in curved spacetimes

TL;DR

The thesis investigates axions as both solutions to the Strong CP problem and dark matter candidates, focusing on non-equilibrium quantum field theory in curved spacetimes and axion electrodynamics. It develops Green's-function methods and 2PI-style approaches to study axion dynamics, time- and space-dependent backgrounds, and their observable consequences, including modified Casimir energies and domain-wall dynamics. The work combines rigorous QFT in FLRW backgrounds with axion cosmology (misalignment, thermal/non-thermal production, domain walls) and explores AED in condensed matter contexts (Weyl semimetals) to reveal novel electromagnetic phenomena and potential experimental probes. By addressing UV completions, the axion quality problem, and a broad constraint landscape (cosmological, astrophysical, and laboratory), the thesis highlights the viability and richness of axion physics as a bridge between fundamental theory and observable signals in cosmology and materials science.

Abstract

Axions are hypothetical pseudoscalar particles introduced initially as a solution to the Strong CP problem in Quantum Chromodynamics (QCD), and they also arise naturally in a broad class of low-energy compactifications of string theory. Astrophysical, cosmological, and laboratory constraints require axions to be extremely weakly coupled to Standard Model particles, making them viable dark matter candidates .This PhD thesis presents original results developed over three years of research, focusing on axion cosmology and axion electrodynamics. These topics address the production of axions and their associated topological defects in the early Universe, as well as the interactions of axions with Standard Model particles. The analysis combines methods from non-equilibrium quantum field theory and quantum field theory in curved spacetimes. After reviewing the foundations of quantum field theory in curved spacetimes and cosmology, the thesis introduces the Strong CP problem and the Peccei-Quinn mechanism, including the PQWW axion model and its invisible extensions. Ultraviolet completions of QCD axion theories are discussed in both field-theoretic and extra-dimensional frameworks. A significant part of the thesis is devoted to axion electrodynamics, where a classical axion background modifies Maxwell's equations and electromagnetic observables. The non-equilibrium dynamics of self-interacting axion fields coupled to the Standard Model or to a dark sector are also studied using the two-particle-irreducible effective action, and applied to pre- and post-inflationary cosmological scenarios, yielding new insights and preliminary constraints.

Figures (50)

• Figure 1: The Bronshtein's cube, showing the main current physics theories and how they are connected. They can be distinguished by which combination of the fundamental constants and the typical speed of the physical system of interest is contained more significantly. Our work is in the $(1,1,0)$ cube vertex. Image from Ref. unknown1.
• Figure 2: Matrix representation of a generic stress-energy tensor, which will be useful for the following of the thesis. Image inspired by a similar one from Elizabeth Winstanley.
• Figure 3: Brief history of the Universe by Particle Data groupolive2014review. .
• Figure 4: A schematic representation of the static Casimir effect between two parallel metallic plates at distance $d$. The effect provides a purely macroscopic manifestation of quantum mechanics, reflecting the nontrivial structure of the quantum vacuum and its fluctuations. We illustrate how vacuum modes are continuous in the exterior regions, while the inner ones are discrete due to boundary conditions. This mismatch leads to a discontinuity in the vacuum expectation value of the normal component of the stress tensor $T_{zz}$, resulting in a net pressure.
• Figure 5: Plot of the action density of the instanton configuration of Eq. (\ref{['instanto']}) in arbitrary units, with a slice at $x_2=x_3=0$. More details are shown in Ref. FavittaDWAnimation