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

Axions are a class of hypothetical fundamental particles introduced formerly as a solution to the Strong CP problem of Quantum Chromodynamics (QCD), but also have been obtained in several low-energy compactification models of String Theory.Various astronomical and experimental constraints imply that the axion is ’invisible’.in the sense that its interactions with Standard Model (SM) particles are significantlyweak, which is why the axion is regarded as a viable candidate for Dark Matter.In this thesis, we discuss our new results on the topics that have been developedduring the three PhD years, in particular on Axion Cosmology and Axion Electrodynamics,research areas of strong interest nowadays, where the production of axion particleswith their topological defects, along with the interaction between SM particles and theaxions themselves are respectively studied and have been object of published papersand conference and workshop presentations. In particular, with a light on methods and results in non-equilibrium Quantum Field Theory and Quantum Field Theory incurved spacetimes.Those topics are addressed in the present PhD thesis. We first review the basics of Quantum Field Theory in curved spacetimes and some elements of Cosmology. Wewill introduce the Strong CP problem in the Standard Model of particle physics,which heavily justifies the introduction of a new particle, the QCD axion. Thisincludes the Peccei-Quinn solution for the Strong CP problem in QCD, the firstPeccei-Quinn-Wilczek-Weinberg (PQWW) axion model, and the invisible QCD axionmodels. Furthermore, we analyze the two main classes of UV completions to QCDaxion theory: the "field theory" completion models and the extradimensional ones,1both related to the so-called "quality problem" for the axions and the last one justifying the possible existence of further axions, known as axion-like particles (ALPs).All these introductory parts are relevant to understanding the current state andproblems in the literature on axions and on Quantum Field Theory in curved spacetimes;they are also significant to understanding and putting in the correct perspectivethe relevance of our original results, new theoretical results, and new experimental methods.We first investigate a practically interesting aspect of Axion physics, which isAxion Electrodynamics. Axion Electrodynamics is the study of the modifications toElectrodynamics due to the presence of an interacting classical axion field.It is deeply connected to applications for axion detection, since many of the most important experimental devices for detecting the axion utilize a strong magnetic field,and we expect a more significant classical behavior for the DM axion field, althoughsome recent claims of stochasticity from surviving axion miniclusters. However, it isalso related to the theoretical aspects we deal with in the involved Axion Cosmologycase, particularly energy-momentum conservation and the interplay between the condensate and particle kinetic regimes.Furthermore, we study some aspects that are less investigated in the literature, such as the effects of the axion field on electromagnetic Casimir forces. This leads to modifications of dispersion relations and zero-point energies that could be detectedby Casimir force experimental setups or by astronomical observations. We found thestudy of the Casimir force for a spatially dependent axion field to be of remarkableinterest, as it is deeply connected to cosmological thermal friction. We will considerin particular the following aspects due to the axion-photon interactions:• Basic aspects and modifications to Maxwell equations• Energy-momentum conservation in Axion Electrodynamics• Cavity haloscope models• Green’s functions in Axion Electrodynamics• Casimir physics in Axion Electrodynamics• Thermal friction on the effective axion domain wall• Optical properties of the axion mediumWe then investigate the non-equilibrium quantum field theory dynamics of a self-interacting axion field interacting with a generic Standard Model sector or a DarkSector, considering the path integral approach and the 2PI effective theory.We demonstrate that the nPI approach enables us to extend previous approachesand overcome their limitations in the approximations, in particular in the dynamical regimes where non-linear effects are relevant.We use the considerations above to start with dealing with two main cosmologicalscenarios:1. Preinflationary scenario for high-mass photophilic ALPs: We discuss the cosmologicalconstraints on the parameter space (ma, gaγγ ), in particular in the region of thehigh-mass axions with ma > 10 keV, from the contribution to ∆Nef f due to theirreducible axion freeze-in production.2. Postinflationary scenario for the QCD axion and high-mass photophilic ALPs:We discuss the Domain Wall problem for such models and analyse the dynamicsof the networks of these axion topological defects, from the current analyticalmodels based on the Velocity-One scale framework and its extensions of it3through a non-equilibrium QFT method. This last method involves adopting an extension of moduli space quantization.In both cases, we analyze the friction effects for the photophilic ALPs due tothe interaction with the SM primordial plasma by taking care of plasma effects, which we claim to be mostly coming from the presence of electrons and muons, and show the validity of our model and the connection with former approachesand constraints, along with preliminary results.

Axions are a class of hypothetical fundamental particles introduced formerly as a solution to the Strong CP problem of Quantum Chromodynamics (QCD), but also have been obtained in several low-energy compactification models of String Theory.Various astronomical and experimental constraints imply that the axion is ’invisible’.in the sense that its interactions with Standard Model (SM) particles are significantlyweak, which is why the axion is regarded as a viable candidate for Dark Matter.In this thesis, we discuss our new results on the topics that have been developedduring the three PhD years, in particular on Axion Cosmology and Axion Electrodynamics,research areas of strong interest nowadays, where the production of axion particleswith their topological defects, along with the interaction between SM particles and theaxions themselves are respectively studied and have been object of published papersand conference and workshop presentations. In particular, with a light on methods and results in non-equilibrium Quantum Field Theory and Quantum Field Theory in curved spacetimes.Those topics are addressed in the present PhD thesis. We first review the basics of Quantum Field Theory in curved spacetimes and some elements of Cosmology. We will introduce the Strong CP problem in the Standard Model of particle physics, which heavily justifies the introduction of a new particle, the QCD axion. This includes the Peccei-Quinn solution for the Strong CP problem in QCD, the first Peccei-Quinn-Wilczek-Weinberg (PQWW) axion model, and the invisible QCD axionmodels. Furthermore, we analyze the two main classes of UV completions to QCDaxion theory: the "field theory" completion models and the extradimensional ones,1both related to the so-called "quality problem" for the axions, and the last one justifying the possible existence of further axions, known as axion-like particles (ALPs).All these introductory parts are relevant to understanding the current state and problems in the literature on axions and on Quantum Field Theory in curved spacetimes; they are also significant to understanding and putting in the correct perspective the relevance of our original results, new theoretical results, and new experimental methods.We first investigate a practically interesting aspect of Axion physics, which is Axion Electrodynamics. Axion Electrodynamics is the study of the modifications toElectrodynamics due to the presence of an interacting classical axion field.It is deeply connected to applications for axion detection, since many of the most important experimental devices for detecting the axion utilize a strong magnetic field, and we expect a more significant classical behavior for the DM axion field, althoughsome recent claims of stochasticity from surviving axion miniclusters. However, it isalso related to the theoretical aspects we deal with in the involved Axion Cosmologycase, particularly energy-momentum conservation and the interplay between the condensateand particle kinetic regimes.Furthermore, we study some aspects that are less investigated in the literature,such as the effects of the axion field on electromagnetic Casimir forces. This leads to modifications of dispersion relations and zero-point energies that could be detectedby Casimir force experimental setups or by astronomical observations. We found thestudy of the Casimir force for a spatially dependent axion field to be of remarkable interest, as it is deeply connected to cosmological thermal friction. We will considerin particular the following aspects due to the axion-photon interactions:• Basic aspects and modifications to Maxwell equations• Energy-momentum conservation in Axion Electrodynamics• Cavity haloscope models• Green’s functions in Axion Electrodynamics• Casimir physics in Axion Electrodynamics• Thermal friction on the effective axion domain wall• Optical properties of the axion mediumWe then investigate the non-equilibrium quantum field theory dynamics of a self-interacting axion field interacting with a generic Standard Model sector or a DarkSector, considering the path integral approach and the 2PI effective theory.We demonstrate that the nPI approach enables us to extend previous approachesand overcome their limitations in the approximations, in particular in the dynamicalregimes where non-linear effects are relevant.We use the considerations above to start with dealing with two main cosmologicalscenarios:1. Preinflationary scenario for high-mass photophilic ALPs: We discuss the cosmologicalconstraints on the parameter space (ma, gaγγ ), in particular in the region of thehigh-mass axions with ma > 10 keV, from the contribution to ∆Neff due to theirreducible axion freeze-in production.2. Postinflationary scenario for the QCD axion and high-mass photophilic ALPs: We discuss the Domain Wall problem for such models and analyse the dynamicsof the networks of these axion topological defects, from the current analyticalmodels based on the Velocity-One scale framework and its extensions of it3through a non-equilibrium QFT method. This last method comes with adopting an extension of moduli space quantization.In both cases, we analyze the friction effects for the photophilic ALPs due tothe interaction with the SM primordial plasma by taking care of plasma effects, which we claim to be mostly coming from the presence of electrons and muons, and show the validity of our model and the connection with former approachesand constraints, along with preliminary results.