Neutrino cosmology and large scale structure Christiane Stefanie Lorenz Pembroke College and Sub-Department of Astrophysics University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity 2019 Neutrino cosmology and large scale structure Christiane Stefanie Lorenz Pembroke College and Sub-Department of Astrophysics University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity 2019 The topic of this thesis is neutrino cosmology and large scale structure. First, we introduce the concepts needed for the presentation in the following chapters. We describe the role that neutrinos play in particle physics and cosmology, and the current status of the field. We also explain the cosmological observations that are commonly used to measure properties of neutrino particles. Next, we present studies of the model-dependence of cosmological neutrino mass constraints. In particular, we focus on two phenomenological parameterisations of time-varying dark energy (early dark energy and barotropic dark energy) that can exhibit degeneracies with the cosmic neutrino background over extended periods of cosmic time. We show how the combination of multiple probes across cosmic time can help to distinguish between the two components. Moreover, we discuss how neutrino mass constraints can change when neutrino masses are generated late in the Universe, and how current tensions between low- and high-redshift cosmological data might be affected from this. Then we discuss whether lensing magnification and other relativistic effects that affect the galaxy distribution contain additional information about dark energy and neutrino parameters, and how much parameter constraints can be biased when these effects are neglected. We conclude by describing current fields of active research in cosmology, and how the work presented in this thesis contributes to them. Declaration I declare that no part of this thesis has been accepted, or is currently being submitted, for any degree or diploma or certificate or any other qualification in this University or elsewhere. Except where explicit reference is made to the work of others, the work contained in this thesis is my own. Chapter 2 and parts of Chapter 1 are based on work I led that was published in Physical Review D: \Distinguishing between Neutrinos and time-varying Dark Energy through Cosmic Time [1]". I led all aspects of this work, except the implementation and running of the Fisher forecasting code which was done by Dr. David Alonso and Dr. Erminia Calabrese. Minor edits reflect comments and suggestions from the co-authors and the referee. Chapter 3 is based on work I led that was published in Physical Review D: \Time-varying neutrino mass from a supercooled phase transition: current cosmological constraints and impact on the Ωm-σ8 plane"[2]. I led most aspects of this work, apart from the theoretical part, which was led by Dr. Lena Funcke. This chapter has summarized findings from Refs. [3,4] more briefly compared to the paper [2]. Minor edits reflect comments and suggestions from the co-authors and the referee. Chapter 4 is based on work I led that was published in Physical Review D: \Impact of relativistic effects in cosmological parameter estimation"[5]. Minor edits reflect comments and suggestions from the co-authors and the referee. Christiane Stefanie Lorenz October 2019 Acknowledgements Firstly, I would like to thank my supervisors Pedro Ferreira, Erminia Calabrese and David Alonso. I have learnt very much from each of them, and I am very grateful to them for their support during the last three years. In addition, I would like to thank the people who made my transfer to astrophysics department possible, especially Erminia Calabrese, Pedro Ferreira, Jo Dunkley, Helen Johnson, Ashling Morris, Garret Cotter and my college advisor Alfons Weber. I also would like to thank the members of the cosmology group in Oxford, in particular Shahab Joudaki and Elisa Chisari, and my collaborators, Lena Funcke and Steen Hannestad. I am also grateful to the Clarendon Fund, Oxford University Press and Pembroke College for financial support that allowed me to pursue my course in Oxford. I would like to thank all the people who have supported me during the past months: most importantly my family, my friends Kilian, Lena, Andreas, Jonas, Hannah, Isa, Lena, Alice, Mariel, Harriet, Gus, Thibaud, Nina, Viki and Sonja. Especially I would like to thank Matthias who is always at my side to share both the happy and the difficult moments with me and who gives me optimism and vitality. Contents List of Figures ix List of Tables xi List of Abbreviations xiv 1 Introduction 1 1.1 The Standard Model of Cosmology............................1 1.1.1 An overview of thermal history..........................2 1.1.2 Einstein and Friedmann equations........................3 1.1.3 Distances......................................4 1.1.4 Energy densities..................................5 1.1.5 Cosmological perturbations............................6 1.2 Cosmological observations.................................7 1.2.1 The cosmic microwave background........................7 1.2.2 Supernovae..................................... 10 1.2.3 Baryonic acoustic oscillations........................... 10 1.2.4 Galaxy surveys................................... 11 1.2.5 Sunyaev-Zeldovich cluster counts......................... 13 1.2.6 Cosmic microwave background lensing...................... 14 1.3 Neutrinos.......................................... 15 1.3.1 Neutrino oscillations................................ 15 1.3.2 Neutrino mass mechanisms............................ 17 1.3.3 The evolution of cosmic neutrinos........................ 19 1.3.4 Neutrinos and BBN................................ 23 1.3.5 Current constraints of neutrino parameters................... 23 1.3.6 Open questions about neutrinos.......................... 24 1.3.6.1 How many neutrino types are there?.................. 24 1.3.6.2 Are neutrinos Majorana or Dirac particles?.............. 25 1.3.7 What are the absolute neutrino masses?..................... 25 1.4 Statistical methods in cosmology............................. 26 v 1.4.1 Fisher forecasts................................... 26 1.4.2 Monte Carlo Markov chains............................ 26 1.5 Overview of this thesis................................... 27 2 Neutrinos and time-varying dark energy 29 2.1 Introduction......................................... 29 2.2 Theoretical degeneracies.................................. 30 2.2.1 Time-varying dark energy............................. 32 2.2.1.1 Barotropic dark energy......................... 32 2.2.1.2 Early dark energy............................ 33 2.2.2 Observations at different cosmic times...................... 34 2.3 Constraints from current data............................... 35 2.3.0.1 Single-probe degeneracies........................ 36 2.3.0.2 Multi-probe analysis........................... 38 2.4 Future predictions..................................... 39 2.5 Conclusion......................................... 44 3 Time-varying neutrino masses 45 3.1 Introduction......................................... 45 3.2 Time-varying neutrino mass model............................ 47 3.2.1 Theoretical Foundations.............................. 47 3.2.2 Cosmological Observables............................. 51 3.3 Analysis methodology................................... 55 3.4 Results............................................ 56 3.4.1 Cosmological Mass Limits............................. 56 3.4.2 The Ωm-σ8 plane................................. 58 3.5 Summary and concluding remarks............................ 61 4 The impact of relativistic effects in Large Scale Structure 65 4.1 Observables and Large Scale Effects........................... 66 4.2 Methodology........................................ 68 4.2.1 The space of parameters.............................. 68 4.2.2 Fisher matrix forecasting formalism....................... 70 4.2.3 Upcoming surveys................................. 72 4.2.3.1 CMB Stage 4............................... 72 4.2.3.2 Large Synoptic Survey Telescope.................... 73 4.3 Results............................................ 75 4.3.1 Impact on dark energy and neutrino mass.................... 76 4.3.2 Impact on scalar-tensor theories......................... 77 vi 4.3.3 Impact on primordial non-Gaussianity...................... 78 4.3.4 Impact of magnification uncertainties...................... 80 4.4 Discussion.......................................... 81 5 Conclusions 87 5.1 Open questions in modern cosmology........................... 87 5.2 Summary of findings of this thesis and further remarks................. 89 A Complete expressions for the corrections to the number counts of galaxies 93 Bibliography 95 vii List of Figures 1.1 Cosmic microwave background temperature anisotropies power spectrum.......9 1.2 Evolution of neutrinos through cosmic time....................... 18 1.3 Impact of changes in Neff on the CMB temperature anisotropy power spectrum... 21 1.4 Impact of changes in Σmν on the matter power spectrum P (k)............ 22 2.1 Evolution of neutrinos and dark energy through cosmic time.............. 31 2.2 Single-probe analysis for barotropic dark energy model................. 36 2.3 Single-probe analysis for early dark energy model.................... 37 2.4 Multi-probe analysis for barotropic dark energy..................... 39 2.5 Multi-probe analysis for early dark energy........................ 40