University of Sydney Doctoral Thesis Cosmological Implications of Quantum Anomalies Author: Supervisor: Neil D. Barrie Dr. Archil Kobakhidze A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the University of Sydney High Energy Physics Group School of Physics November 2017 Declaration of Authorship I, Neil David Barrie, declare that this thesis titled, `Cosmological Implications of Quantum Anomalies' and the work presented in it are my own. I confirm that: This work was done wholly or mainly while in candidature for a research degree at this University. Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated. Where I have consulted the published work of others, this is always clearly attributed. Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. I have acknowledged all main sources of help. Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself. Signed: Neil Barrie Date: 25/07/2017 i UNIVERSITY OF SYDNEY Abstract Faculty of Science School of Physics Doctor of Philosophy Cosmological Implications of Quantum Anomalies by Neil D. Barrie The aim of this thesis is to investigate the possible implications of quantum anomalies in the early universe. We first consider a new class of natural inflation models based on scale invariance, imposed by the dilaton. In the classical limit, the general scalar potential necessarily contains a flat direction; this is lifted by quantum corrections. The effective potential is found to be linear in the inflaton field, yielding inflationary predictions consistent with observation. A new mechanism for cogenesis during inflation is presented, in which a new anomalous U(1)X gauge group in introduced. Anomaly terms source and X violating processes during inflation, CP producing a non-zero CS number density that is distributed into baryonic and dark matter. The two U(1)X extensions considered in this general framework, gauged B and B L each containing − an additional dark matter candidate, successfully reproduce the observed parameters. We propose a reheating Baryogenesis scenario that utilises the Ratchet Mechanism. The model contains two scalars that interact via a derivative coupling; an inflaton consistent with the Starobinsky model, and a complex scalar baryon with a symmetric potential. The inflaton- scalar baryon system is found to act analogously to a forced pendulum, with driven motion near the end of reheating generating an ηB consistent with observation. Finally, we argue that a lepton asymmetric CνB develops gravitational instabilities related to the mixed gravity-lepton number anomaly. In the presence of this background, an effective CS term is induced which we investigate through two possible effects. Namely, birefringent propagation of gravitational waves, and the inducement of negative energy graviton modes in the high frequency regime. These lead to constraints on the allowed size of the lepton asymmetry. These models demonstrate that a concerted approach in cosmology and particle physics is the way forward in exploring the mysteries of our universe. Acknowledgements First and foremost, I would like to thank my supervisor Archil Kobakhidze for introducing me to world of particle physics, and for giving me the tools to explore the field. I have thoroughly enjoyed my PhD studies, and have grown considerably as a researcher under your guidance. I look forward to continuing our work together into the future. I would also like to thank my Associate Supervisor Michael Schmidt for our many fruitful discussions over the course of my studies. Thank you to all my collaborators for the opportunity to work with you, and for all the many insightful exchanges we have shared. I hope we shall continue to work together in the years to come. Special thanks to Kazuharu Bamba, Akio Sugamoto, Tatsu Takeuchi, and Kimiko Yamashita, for letting me join in their research pursuits. Also, a big thank you to Matthew Talia and Lei Wu for the many useful discussions over the course of our collaborations. To the residents of Room 342, thank you for the many informative and humorous discussions. These last few years would not have been as enjoyable or as filled with laughter without you. Particular thanks go to my long time office mates - Adrian Manning, Carl Suster, Matthew Talia, Jason Yue. I would also like to acknowledge Shennong for his amazing discovery 5000 years ago, which has made the last few years highly enjoyable and almost stress free. To Sonia, thank you for always being so supportive, positive and understanding. You have helped me more than you know during the stressful, final half of my degree. Finally, thank you to my family and friends for their ongoing support and help over the last few years, without which none of this could have been possible. iv Contents Declaration of Authorshipi Abstract iii Acknowledgements iv Contents v 1 Introduction 1 1.1 The Standard Model of Particle Physics.......................3 1.1.1 Formulation and Structure of the Standard Model.............4 1.1.2 Symmetries in the Standard Model......................7 1.1.3 Radiative Corrections and Quantum Anomaly Cancellation........9 1.2 The Standard Model of Cosmology and the Evolution of the Universe...... 12 1.2.1 The Friedmann-Robertson-Walker Metric.................. 13 1.2.2 The History of the Universe.......................... 14 1.3 Mysteries to be Solved................................. 16 1.3.1 The Inflationary Mechanism.......................... 16 1.3.2 The Origin of the Matter-Antimatter Asymmetry.............. 20 1.3.3 Dark Matter.................................. 23 1.3.4 Neutrino Properties and the Cosmic Neutrino Background......... 25 1.3.5 Gravitational Waves.............................. 26 1.3.6 Hierarchy Problem in the Standard Model.................. 26 1.4 Cosmological Implications of Quantum Anomalies................. 27 2 Scale Invariant Inflation 28 2.1 The Inflationary Epoch................................ 29 2.2 Modelling the Inflationary Epoch........................... 29 2.3 Scale Invariance, Weyl Transformations, and Non-minimal Couplings....... 33 2.4 Natural Inflation with Hidden Scale Invariance................... 34 2.4.1 Description of the Model........................... 35 2.5 Quantum Corrected Potential in Curved Spacetime................. 37 2.6 Observational Signatures and Model Predictions.................. 38 2.7 Conclusions and Future Prospects.......................... 40 3 An Asymmetric Universe from Inflation 41 v Contents vi 3.1 The Matter-Antimatter Asymmetry......................... 42 3.1.1 The Sakharov Conditions........................... 42 3.1.2 Asymmetric Dark Matter........................... 44 3.2 Topological Vacuum States and the Chern-Simons Number............ 44 3.2.1 Instanton and Sphaleron Transistions.................... 45 3.3 A Model of Inflationary Cogenesis.......................... 47 3.3.1 Models with an Anomalous U(1)X ...................... 48 3.4 Dynamics of an Anomalous Gauge Field During Inflation............. 51 3.5 Simultaneous Generation of Luminous and Dark Matter During Inflation.... 55 3.6 Replicating the Observed ρDM/ρB and ηB ...................... 57 3.7 Conclusions and Future Prospects.......................... 63 4 Baryogenesis During Reheating via the Ratchet Mechanism 64 4.1 The Reheating Epoch and Starobinsky Inflation................... 65 4.1.1 Starobinsky Inflation.............................. 66 4.2 Baryogenesis during Reheating via the Ratchet Mechanism............ 68 4.2.1 The Ratchet Mechanism............................ 68 4.2.2 Description of the Model........................... 68 4.3 Analytical Evaluation................................. 71 4.3.1 Approximate Analytical Solution....................... 74 4.3.2 Phase Locked States.............................. 76 4.4 The Generated Asymmetry Parameter........................ 78 4.4.1 Conversion to Standard Model Particles................... 78 4.5 Conclusions and Future Prospects.......................... 79 5 Gravitational Waves and the Cosmic Neutrino Background 82 5.1 The Cosmic Neutrino Background.......................... 83 5.2 Gravitational Waves and the Graviton Propagator................. 85 5.2.1 Linearised Gravitational Waves........................ 85 5.3 Graviton Polarisation Tensor in a Lepton Asymmetric CνB............ 86 5.4 Chern-Simons Modified Gravity and Observational Implications.......... 90 5.4.1 Birefringent Propagation through an Asymmetric CνB........... 90 5.5 Induced Ghost-like Modes and Vacuum Decay.................... 92 5.5.1 Photon Energy Spectrum from Induced Vacuum Decay.......... 93 5.6 Conclusions and Future Prospects.......................... 96 6 Concluding Remarks and Outlook 98 A Baryon and Lepton Number Anomalies in the Standard Model 101 A.1 Baryon Number Anomalies.............................. 101 A.2 Lepton Number Anomalies.............................. 102 A.3 Mixed Gauged Baryon and Lepton Number Anomalies............... 103 B Further Details of Chapter3 Calculations 104 B.1 F+ Coefficients, Eq. (3.20)............................... 104 B.2 F− Coefficients, Eq. (3.21)............................... 105 Contents vii C Further Details of Chapter5 Calculations 106 C.1 Dimensional Regularisation Integrals