The Cosmology and Astrophysics of Axion-like Particles Andrew Powell St. Cross College University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity 2016 Abstract In this thesis I study astrophysical and cosmological effects of axion-like particles (ALPs). ALPs are pseudo-scalar particles, which are generally very weakly-interacting, a with a coupling M E · B to electromagnetism. They are predicted by many theories which extend the standard model (SM) of particle physics, most notably string theory. String theory compactifications also predict many scalar fields called moduli which describe the size and shape of the extra, compact dimensions. In string theory models generically the moduli fields are responsible for reheating the universe after inflation. Being gravitationally-coupled, they will also decay to any other particles or sectors of the theory, including any light ALPs, of which there are usually many. The ALPs produced by moduli decay will contribute to dark radia- tion, additional relativistic energy density. The amount of dark radiation is tightly constrained by observations, this bounds the branching fraction of moduli decays into ALPs, which constrains the string theory model itself. I calculate the amount of dark radiation produced in a model with one light modulus, solely responsible for reheating, called the Large Volume Scenario. I study a minimal version of this model with one ALP and a visible sector comprised of the minimal supersymmetric SM. The dom- inant visible sector decay mode is to two Higgses, I include radiative corrections to this decay and find that ALP dark radiation is over-produced in this minimal version of the model, effectively ruling it out. The production of ALPs from moduli decay at reheating seems to be a generic feature of string theory models. These ALPs would exist today as a homogeneous cosmic ALP background (CAB). The coupling of ALPs to electromagnetism allows ALPs to convert to photons and vice versa in a magnetic field, leading to potential ob- servable astrophysical signals of this CAB. Observations have shown an excess in soft X-ray emission from many galaxy clusters. I use detailed simulations of galaxy cluster magnetic fields to show that a CAB can explain these observations by conversion of ALPs into X-ray photons. I simulate ALP–photon conversion in four galaxy clusters and compare to soft X-ray observations. I show the excesses (or lack thereof) can be fit consistently across the clusters for a CAB with ALP–photon inverse coupling of M = 6 − 12 × 1012 GeV, if the CAB spectrum has energy ∼ 200 eV. I also study the possibility of using galaxy clusters to search for and constrain the ALP coupling to photons using cluster X-ray emission. Conversion of X-ray photons into ALPs will cause spectral distortions to the thermal X-ray spectrum emitted by galaxy clusters. I show that the non-observation of these distortions is able to produce the strongest constraints to date on the ALP–photon inverse coupling, 11 M & 7 × 10 GeV. Acknowledgements I would like to start by thanking my supervisor Joseph Conlon. I am grateful for his support, encouragement and help during my DPhil. I am also very grateful for the many interesting projects and topics he has in- troduced me to, and for the tips and advice for writing this thesis. I would also like to thank my examiners Pedro Ferreira and Mark Goodsell for tak- ing the time to read this thesis, and prodiving insightful and interesting questions and comments about the work. I would also like to thank my collaborators Stephen Angus, Marcus Berg, Francesca Day, Giovanni Grilli di Cortona, Ulrich Haisch, Edward Hardy, Nicholas Jennings, David Marsh, Markus Rummel, Sven Krippen- dorf, and Lukas Witkowski, who were a pleasure to work with. I would also like to thank the many other people, lecturers and fellow students who have helped me with my research, and have made the last four years fly by. An incomplete list includes Eirik Svanes, David Kraljic, James Scargill, James Scoville, Jim Talbert, Alexander Karlberg, Pedro Alvarez, Robert Lasenby, Subir Sarkar, and many others. I would especially like to thank Ed Hardy for taking the time to proof-read this thesis. Most of all I would like to thank my wife, Steph, whose love, support and encouragement has helped me no end throughout my DPhil, and during our seven wonderful years together. I also thank my family and all my other friends not mentioned above. Finally I am very grateful to the STFC and the ERC for providing me with the funding for my studies, and for allowing me to travel to many interesting conferences, schools, and workshops. Statement of Originality This thesis is based on original research and contains no material that has already been accepted, or is concurrently being submitted, for any degree or diploma or certificate or other qualification in this university or elsewhere. To the best of my knowledge and belief this thesis contains no material previously published or written by another person, except where due reference is made in the text. Andrew Powell 2016 Contents 1 Introduction and Motivation 1 1.1 Outline . .4 2 String Moduli and Cosmology 7 2.1 Dark Radiation . .8 2.2 String Moduli . 12 2.3 Moduli in Cosmology . 14 3 Axion-like Particles 18 3.1 The QCD Axion . 18 3.2 String Axions and Axion-like Particles . 21 3.3 Searching for ALPs . 23 3.3.1 ALP–photon Mixing . 24 3.3.2 Astrophysics . 26 3.3.3 Terrestrial Experiments . 29 4 ALP Dark Radiation Production in Large Volume Scenarios 32 4.1 Dark Radiation . 33 4.2 The Large Volume Scenario . 34 4.3 Tree Level Dark Radiation Prediction . 36 4.3.1 Decay Rates . 36 4.3.2 Dark Radiation Prediction . 38 4.4 Analytic Results . 39 4.4.1 Running of Volume Modulus Higgs Coupling . 40 4.5 Numerical Results . 42 4.5.1 Solution of RG Equations . 42 4.5.2 SM and MSUGRA Parameter Dependencies . 43 4.5.3 Predictions for the Effective Excess Number of Neutrinos . 45 4.6 Conclusions . 47 5 A Cosmic ALP Background and the Galaxy Cluster Soft X-ray Ex- cess 50 5.1 Introduction . 51 5.2 A Cosmic ALP Background . 53 5.3 The Cluster Soft X-ray Excess . 56 5.3.1 History of Soft Excess Observations . 56 5.3.2 Specific Clusters . 59 5.3.3 Astrophysical Models of the Soft Excess . 62 5.4 Cluster Magnetic Fields . 66 5.4.1 Magnetic Field Observations . 66 5.4.2 Magnetic Field Model . 69 5.4.3 Magnetic Field Generation . 77 5.5 ALP–photon Propagation . 77 iv 5.5.1 Homogeneous Solution . 78 5.5.2 Inhomogeneous Magnetic Fields . 80 5.6 Consistency Checks . 82 5.7 Coma . 83 5.7.1 Luminosity Calculation . 84 5.7.2 Results . 84 5.7.3 Summary of Coma Results . 100 5.8 A665, A2199 and A2255 . 101 5.8.1 Luminosity and Fractional Excess . 101 5.8.2 Results . 103 5.8.3 Comparison and Summary . 113 5.9 Conclusions . 117 6 Constraining ALPs using Galaxy Clusters 121 6.1 Current Bounds . 121 6.2 Photon-ALP Conversion in Galaxy Clusters . 122 6.3 Cluster Spectral Distortions from ALPs . 124 6.4 Further Properties of the Distorted Spectrum . 128 6.5 Conclusions . 130 7 Summary and Conclusions 133 References 139 v 1 Introduction and Motivation With the discovery of the Higgs boson, the Standard Model (SM) of particle physics is now complete. The SM is a theory of the electromagnetic, weak, and strong in- teractions and the three generations of quarks and leptons on which they act. The interactions are mediated by the bosons, the photon, gluon, and the W/Z. The Higgs mechanism solves the puzzle of how the W/Z bosons, the carriers of the weak inter- action, get their masses. It is also responsible for giving the leptons and quarks their masses. However we know that the SM does not describe every interaction between fun- damental particles. The theory does not include gravity, which is described at low energies by the General Theory of Relativity (GR). The SM is a quantum theory, however treating GR in this way leads to an ‘effective field theory’ valid only for 19 energies well below the Planck scale, Mpl = 1.22 × 10 GeV. At energies close to the Planck scale the theory breaks down. Thus it is thought that some new quantum gravity theory must complete GR close to this scale. We have other reasons for believing the SM is not the end of the story for particle physics. Astronomical and cosmological observations have shown that the majority of matter in the universe is not made up of particles from the SM. Instead, dark matter 1 accounts for more than 80% of the matter in the universe. Even more strangely, 68% of the energy density of the universe appears to reside as so-called dark energy. This is a fluid whose energy density stays constant with the expansion of the universe, thus the importance of which grows with time. It is a puzzle why this dark energy is only now starting to dominate the universe, as is the seemingly arbitrary value of the energy density, and the fact that its energy density is so much smaller than the natural particle physics scales. In addition, the SM alone cannot explain the particle anti-particle asymmetry ob- served in the universe. Neutrino masses, and why they are so much smaller than the other fundamental particles’ masses, are also unexplained. There is no explanation for why the Higgs mechanism breaks electroweak symmetry at scales much lower than the Planck scale, mweak Mpl.