Springer Theses

Recognizing Outstanding Ph.D. Research Aims and Scope

The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

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• They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder. • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. • The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field.

More information about this series at http://www.springer.com/series/8790 Sunny Vagnozzi

Weigh Them All! Cosmological Searches for the Neutrino Mass Scale and Mass Ordering

Doctoral Thesis accepted by Stockholm University, Stockholm, Sweden

123 Author Supervisor Dr. Sunny Vagnozzi Prof. Katherine Freese Kavli Institute for Cosmology Department of Physics University of Cambridge University of Texas Cambridge, UK Austin, USA

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-030-53501-8 ISBN 978-3-030-53502-5 (eBook) https://doi.org/10.1007/978-3-030-53502-5

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Neutrinos, they are very small They have no charge and have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids down a drafty hall Or photons through a sheet of glass. They snub the most exquisite gas, Ignore the most substantial wall, Cold-shoulder steel and sounding brass, Insult the stallion in his stall, And, scorning barriers of class, Infiltrate you and me! Like tall And painless guillotines, they fall Down through our heads into the grass. At night, they enter at Nepal And pierce the lover and his lass From underneath the bed—you call It wonderful; I call it crass. —Cosmic Gall, John Updike (1960) Neutrinos...win the minimalist contest: zero charge, zero radius, and very possibly zero mass —The God Particle: If the Universe is the Answer, What is the Question? Leon M. Lederman and Dick Teresi (1993), p. xiii Neutrinos have mass? I didn’t even know they were Catholic! —Robert Langdon to Vittoria Vetra in Angels and Demons, Dan Brown (2000), p. 476 A Cristina, il mio Universo Supervisor’s Foreword

Modern cosmology, the study of the Universe as a whole, has seen remarkable advances since its inception one hundred years ago with the brilliant insights of Albert Einstein. Many age-old questions about the Cosmos have been answered. The Hot Big Bang model, the idea that the Universe started out hot and dense and subsequently cooled off and expanded, has been shown to be basically correct, albeit incomplete. The shape of the Universe has been found to have no spatial curvature; the total amount of mass and energy content of the Universe is known; the age of the Universe is roughly 14 billion years. We are in the era of “precision cosmology” in that basic properties of the Universe are now known to great accuracy. However, as always, new knowledge leads to new questions. The most bizarre perhaps is the breakdown of the Universe into its chief components. All the material of our daily experience—our bodies, the air we breathe, the houses we live in, the Earth, the Sun, the planets—all constitute only 5% of the total content of the Universe. The rest is 25% dark matter and 70% dark energy, mysterious compo- nents observed to exist but of an as yet unknown nature. Scientists believe that most of the mass in the Universe is made of unknown particles yet to be discovered. Of the known particles, neutrinos are the most elusive and surprising. Discovered as missing energy in the decays of neutrons to protons in 1956, their properties have only recently come to be elucidated by experiments of the past several decades. The 2015 Nobel Prize in Physics was awarded for the discovery that neutrinos have mass. In the Standard Model of Particle Physics, there are three species of neutrinos (electron, muon, and tau neutrinos), and all were expected to be massless, like the photons that are the particles of light. Instead, neutrinos have been found to oscillate from one type to another en route from the Sun to our detectors on Earth as well as in traveling through Earth’s atmosphere. The only way these oscillations can happen is if the neutrinos have small but nonzero masses. The particles predicted to exist in the Standard Model—quarks, leptons, gauge bosons, and the Higgs boson—have now all been found with the anticipated properties, but with one exception: the unexpected neutrino mass.

ix x Supervisor’s Foreword

Sunny Vagnozzi’s world-leading research has led to powerful advances in learning about these neutrinos, which are so important since their mass is the only direct indication for physics Beyond the Standard Model. His extraordinary thesis describes the story of his studies that seek to elucidate the properties of these particles using cosmological datasets as a probe. The thesis provides an excellent summary of the status of modern cosmology, with special focus on the inference of the neutrino masses from the rich set of data that has been obtained through large cosmological surveys in recent years. Using a combination of datasets from observations of the Cosmic Microwave Background (CMB), the leftover light from the Big Bang, together with studies of the large-scale structure of the Universe—the galaxies, the clusters, and even larger structures— observed in large redshift surveys, he discovered important information about the neutrino mass and hierarchy (or mass ordering). He showed that neutrinos must be ten billion times lighter than the protons that are the predominant constituents of ordinary matter. He showed that these limits favour the normal ordering over the inverted one, and devised ways to robustly quantify this preference. He showed that these bounds hold up for most viable models of dark energy, and proposed a recipe for avoiding the limitations posed by “bias” in the interpretation of galaxy clus- tering data. Sunny Vagnozzi’s results are now highly cited by physicists throughout the world. Indeed the bounds on the neutrino masses are quoted in the “Particle Data Group’s Review of Particle Properties”, the “Bible” that particle physicists turn to for the latest information on particle properties. Further, the text of the thesis serves as an excellent reference for anyone working on the subject. It will most certainly help many new students interested in diving into the subject. As the research discussed in this work is significant, and the overview of the field of cosmology beautifully explained, Dr. Vagnozzi’s thesis clearly deserves to be published in the Springer Theses series. I have been extremely fortunate to be the Ph.D. supervisor of Sunny Vagnozzi, whose work has been absolutely outstanding. His Ph.D. work led to more than 25 publications, all of the highest quality. He delved into data, asked the right ques- tions, made predictions for upcoming cosmological experiments and telescopes, and wrote a beautiful thesis. It has been a pleasure to work with a student of such extraordinary caliber and I have no doubt he will have an outstanding career.

Austin, TX, USA Prof. Katherine Freese April 2020 Abstract

The elusive neutrinos are among the most intriguing constituents of the particle zoo. The observation of neutrino flavour oscillations, indicating that neutrinos are massive, provides the only direct evidence for physics beyond the Standard Model. Neutrinos imprint peculiar signatures in the Cosmic Microwave Background (CMB) and in the distribution of Large-Scale Structures (LSSs) in the Universe, making cosmology a very promising arena for probing neutrino properties. A detection of neutrino masses is avowedly among the key goals of several upcoming CMB and LSS surveys. For such a promise to be robustly realized, a number of issues need to be addressed, particularly on the LSS side. In this thesis, I describe a number of recent important developments in neutrino cosmology on three fronts. Firstly, focusing on LSS data, I will show that current cosmological probes (and particularly galaxy power spectrum data) contain a wealth of information on the sum of the neutrino masses. I will report on the analysis leading to the currently best upper limit on the sum of the neutrino masses of 0:12 eV. I show how cosmological data exhibits a weak preference for the normal neutrino mass ordering because of parameter space volume effects, and propose a simple method to quantify this preference. Secondly, I will discuss how galaxy bias represents a severe limitation towards fully capitalizing on the neutrino information hidden in LSS data. I propose a method for calibrating the scale-dependent galaxy bias using CMB lensing-galaxy cross-correlations. Another crucial issue in this direction is represented by how the bias is defined in the first place. In the presence of massive neutrinos, the usual definition of bias becomes inadequate, as it leads to a scale-dependence on large scales which has never been accounted for. I show that failure to define the bias appropriately will be a problem for future LSS surveys, leading to incorrectly estimated cosmological parameters. In doing so, I propose a simple recipe to account for the effect of massive neutrinos on galaxy bias. Finally, I take on a different angle and discuss implications of correlations between neutrino parameters and other cosmological parameters. I show how, in non-phantom dynamical dark energy models (which include quintessence), the upper limit on the sum of the neutrino masses becomes tighter than the KCDM

xi xii Abstract limit. Therefore, such models exhibit an even stronger preference for the normal ordering, and their viability could be jeopardized should near-future laboratory experiments determine that the mass ordering is inverted. I then discuss correlations between neutrino and inflationary parameters. I find that our determination of inflationary parameters is relatively stable against reasonable assumptions about the neutrino sector, and thus that neutrino unknowns do not represent an important nuisance for our understanding of inflation and the initial conditions of the Universe. The findings reported in this thesis answer a number of important open questions whose addressing is necessary to ensure a robust detection of neutrino masses (and possibly of the neutrino mass ordering) from future cosmological data, opening the door towards physics beyond the Standard Model. Preface

This thesis, which covers the results reported in five related papers [1–5], deals with recent developments in the quest towards using cosmological observations to determine properties of the elusive particles known as neutrinos, with a particular focus on their mass and mass ordering. The fact that neutrinos are massive repre- sents the only direct evidence for physics beyond the Standard Model, while the three neutrinos remain to date the only particles of the Standard Model of unknown mass. Disclosing the neutrino mass scale would unlock the door for physics beyond the Standard Model, likely operating at energy scales we can only ever dream of reaching on Earth. Cosmological observations, particularly observations of the large-scale structure of the Universe, have long been known to have the potential to measure the sum of the neutrino masses. In a very simplified picture, reaching this tremendous achievement would consist of at least two steps. The first step would be to make sure we address a number of difficulties associated with the use of large-scale structure data, or at least keep them under control. The second step would be to actually convince the cosmology and non-cosmology communities that we have genuinely detected neutrino masses, and not something else which can mimic their effect. The papers related to this thesis work towards achieving both the first [1–3] and, at least in part, the second goal [4, 5]. The main aim of this thesis is to put the related papers into the broader context for non-experts. The physics required to fully understand the five related papers [1–5] span a very broad range of topics within the field of cosmology, ranging from the complex statistical mechanics (equilibrium and non-equilibrium) underlying the Cosmic Microwave Background and more generally the early Universe, to galaxy bias (a topic of research still very much under development and definitely not as well understood as we would like), dark energy, cosmic inflation, as well as non-cosmology topics such as neutrino oscillation experiments. With the above in mind, it is certainly not feasible to provide a pedagogical introduction to all these topics, and in most cases the related papers contain introductory sections (written mostly by myself) which are quite self-contained. Therefore, the first part of my thesis will intentionally only provide an introductory

xiii xiv Preface review to the topics discussed in the papers, going deeper into the technical details only whenever strictly necessary. Rather, my aim is to focus on providing the context within which the work was done. On the other hand, I aim to make up for this deficiency in depth by providing (or at least attempting to provide) a very broad coverage in my bibliography, wherein the reader will find excellent references for a more in-depth and pedagogical/technical coverage of the topics discussed. The same holds for my results: Chaps. 6 through 10 of the thesis itself will only summarize my results, and the interested and expert reader is invited to read the related papers alongside the thesis to get a deeper understanding of the results and their implications.

Cambridge, UK Sunny Vagnozzi

References

1. Vagnozzi S, Giusarma E, Mena O, Freese K, Gerbino M, Ho S et al (2017) Unveiling ” secrets with cosmological data: neutrino masses and mass hierarchy. Phys Rev D96 123503, [1701.08172] 2. Giusarma E, Vagnozzi S, Ho S, Ferraro S, Freese K, Kamen-Rubio R et al (2018) Scale-dependent galaxy bias, CMB lensing-galaxy cross-correlation, and neutrino masses. Phys Rev D98 123526, [1802.08694] 3. Vagnozzi S, Brinckmann T, Archidiacono M, Freese K, Gerbino M, Lesgourgues J et al (2018) Bias due to neutrinos must not uncorrect’d go, JCAP 1809 001, [1807.04672] 4. Vagnozzi S, Dhawan S, Gerbino M, Freese K, Goobar A, Mena O (2018), Constraints on the sum of the neutrino masses in dynamical dark energy models with wðzÞ À1 are tighter than those obtained in KCDM, Phys Rev D98 083501, [1801.08553]. 5. Gerbino M, Freese K, Vagnozzi S, Lattanzi M, Mena O, Giusarma E et al (2017) Impact of neutrino properties on the estimation of inflationary parameters from current and future observations, Phys Rev D95 043512, [1610.08830] Publications Related to This Thesis

The following papers are related to this thesis, and are discussed, in the order listed below, in Chaps. 6–10, respectively. I Sunny Vagnozzi, Elena Giusarma, Olga Mena, Katherine Freese, Martina Gerbino, Shirley Ho & Massimiliano Lattanzi, Unveiling ” secrets with cosmological data: neutrino masses and mass hierarchy, Phys. Rev. D 96 (2017) 123503 [arXiv:1701.08172] II Elena Giusarma, Sunny Vagnozzi, Shirley Ho, Simone Ferraro, Katherine Freese, Rocky Kamen-Rubio & Kam-Biu Luk, Scale-dependent galaxy bias, CMB lensing-galaxy cross-correlation, and neutrino masses, Phys. Rev. D 98 (2018) 123526 [arXiv:1802.08694] III Sunny Vagnozzi, Thejs Brinckmann, Maria Archidiacono, Katherine Freese, Martina Gerbino, Julien Lesgourgues & Tim Sprenger, Bias due to neutrinos must not uncorrect’dgo, JCAP 1809 (2018) 001 [arXiv:1807.04672] IV Sunny Vagnozzi, Suhail Dhawan, Martina Gerbino, Katherine Freese, Ariel Goobar & Olga Mena, Constraints on the sum of the neutrino masses in dynamical dark energy models with wðzÞ À1 are tighter than those obtained in KCDM, Phys. Rev. D 98 (2018) 083501 [arXiv:1801.08553] V Martina Gerbino, Katherine Freese, Sunny Vagnozzi, Massimiliano Lattanzi, Olga Mena, Elena Giusarma & Shirley Ho, Impact of neutrino properties on the estimation of inflationary parameters from current and future observations, Phys. Rev. D 95 (2017) 043512 [arXiv:1610.08830]

xv Acknowledgements

My first and foremost thank you goes to my advisor Katie Freese. Working with you has been challenging but also great fun. Thank you for all the energy, expe- rience, and passion you put into training me as a scientist, for always leaving me enormous independence in pursuing my research interests and ideas, and for always pushing me to do my best. Next, I cannot express how much I am grateful to my de facto co-advisors Shirley Ho and Olga Mena. Thank you for all the time and passion you put in mentoring me, even though I was not officially your student. I am also extremely grateful to my official co-advisors Lars Bergström and Joakim Edsjö for always having their doors open whenever I needed help or advice, and particularly for valuable help both on the scientific and practical sides when preparing for my Ph.D. defense. Thanks are also due to Alessandra Silvestri for having agreed to be my opponent at my Ph.D. defense (and apologies for forcing you to read this beast!). People often ask me how I managed to write so many papers during my Ph.D. The honest answer is that I was extremely lucky and privileged to have awesome collaborators. I want to express my huge thanks to two collaborators who stick out particularly among the crowd: Martina Gerbino and Elena Giusarma have been my de facto day-to-day mentors, and I could not have asked for better postdocs to mentor me. Thank you for teaching me how science is done in practice, for your infinite patience, and for bringing a bit of italianity (or should I say laziality?) in my everyday work routine. I thank all my other collaborators and co-authors, whose input has been invalu- able in my research and from whom I have learned a great deal. In rigorously alphabetical order (by last name): Maria Archidiacono, Cosimo Bambi, Thejs Brinckmann, Nadia Bolis, Alessandro Casalino, Guido Cognola, Pablo Fernández de Salas, Suhail Dhawan, Eleonora Di Valentino, Jibitesh Dutta, Mads Frandsen, Simone Ferraro, Ariel Goobar, Steffen Hagstotz, Steen Hannestad, Robert Foot, Rocky Kamen-Rubio, Wompher Khyllep, Will Kinney, Massi Lattanzi, Julien Lesgourgues, Kam-Biu Luk, David Mota, Ratbay Myrzakulov, Rafael Nunes,

xvii xviii Acknowledgements

Supriya Pan, Max Rinaldi, Manos Saridakis, Subir Sarkar, Thomas Schwetz, Lorenzo Sebastiani, Ian Shoemaker, Tim Sprenger, Nicola Tamanini, Luca Visinelli, Weiqiang Yang, Sergio Zerbini, Thomas Zurbuchen, and all my collaborators in the Simons Observatory collaboration (especially, again, Martina Gerbino). My stay at the OKC has been amazing, thanks to a large number of people, who have made science an extremely enjoyable adventure. Special thanks to Sebastian Baum, Andrea Chiappo, Adri Duivenvoorden, Pablo Fernández de Salas, Martina Gerbino, Ariel Goobar, Jón Gudmundsson, Steffen Hagstotz, Fawad Hassan, Edvard Mörtsell, Francesco Torsello, Janina Renk, Doug Spolyar, Luca Visinelli, and Axel Widmark for their friendship, company over lunch or a drink, for the good times spent sharing our office (especially Adri and Janina and, for a much shorter time, Sebastian and Francesco), och för att alltid ha haft en öppen dörr för att diskutera fysik och öva min svenska (Ariel och Edvard). Jag ärväldigt tacksam mot Vetenskapsrådet för att ha gjort det möjligt för mig att arbeta i en så prestigefylld institution som OKC. And, of course, I apologize if I inadvertently left someone out! Ringrazio anche tutti i miei amici e colleghi “trentini”: Lorenzo Andreoli, Dante Bonolis, Andrea Endrizzi, Lorenzo Festa, Davide Gualdi, Vittorio Ghirardini, Alan Hubert, Paolo Mori, Matteo Puel, Ilenia Salvadori, e Daniela Scardi. L’Università di Trento è sempre stata e sarà sempre per me la mia prima “casa accademica”. Per questo ringrazio Max Rinaldi, Lorenzo Sebastiani, e Sergio Zerbini per avermi sempre fatto sentire bentornato lì, nonché per le molte interessanti discussioni, collaborazioni, e inviti a visitare nel corso di questi anni. Tak også til Amel Duraković for altid at være en konstant kilde til ekstremt interessante diskussioner og ideer til projekter (såvel som mærkelige dansk-svenske samtaler). And thanks to my Aussie friends Callum Jones, Brian Le, and Alex Millar, and to Vitali Halenka, for your friendship and our many interesting conversations over the years. There is, of course, life outside of physics. My father, mother, and brother have been a constant source of unconditional support and encouragement. Thank you so much for all the troubles you had to endure, for always having an open door, and for your being a continuous source of wisdom. This would not have been possible without you. Grazie anche a Claudio e Mariella, Leda e Massimo, ai miei amici d’infanzia Cecilia, Daniele, Davide, Riccardo, Francesco I., e Francesco T., e ai miei futuri suoceri Elisabetta e Mauro, per tutti i bei momenti passati insieme ogni volta che torno in Italia. La mia passione per il violino, e il mio amore incon- dizionato per la Juve (nonostante in occasione delle due finali di Champions perse mi abbia fatto dannare) e il Latina (una menzione speciale al gruppo MLM) mi hanno aiutato a rimanere sano in tutti questi anni, anche nelle occasioni in cui lo stress da lavoro diventava schiacciante. Einfine, last but absolutely not least, grazie con tutto il cuore alla mia futura moglie Cristina. Grazie per il tuo infinito amore, compagnia, e incrollabile supporto in ogni momento della giornata. Grazie di ogni momento passato insieme, dal primo Acknowledgements xix istante la mattina all’ultimo la sera, e di tutti i momenti che verranno. Grazie di essere stata al mio fianco per tutte le interminabili sere mentre scrivevo questa tesi, e mentre lavoravo per scrivere gli articoli qui inclusi. È a te che dedico questo lavoro.

Stockholm, Sweden Sunny Vagnozzi May 2020 Thesis Plan

This thesis is divided into two parts: the first part provides an introduction to the field of cosmology, with a focus on neutrino cosmology, in order to put my work in context. The second part discusses the related papers [1–5]. In the first part, Chap. 1 provides a layman introduction to the current status of cosmology and the importance of neutrinos, setting the scene for the rest of the thesis: ideally, it should be understandable to the general public. Chapter 2 provides a brief introduction to the Standard Model of particle physics, and a more detailed introduction to the Standard Model of cosmology (the KCDM model). Chapter 3 provides an overview of a number of concepts in modern cosmology useful for understanding the subsequent chapters, in particular, the thermal history of the Universe. Chapter 4 presents a review of modern cosmological observations, inevitably biased towards the observations this thesis will focus on: Cosmic Microwave Background (CMB) and Large-Scale Structure (LSS). The same chapter is devoted to an account of how massive neutrinos impact CMB and LSS observations, and therefore, of how one can use the latter to constrain neutrino properties. Chapter 5 then introduces some basic data analysis and statistics tools widely used in cosmology and, in particular, in deriving the results presented in the related papers [1–5]. The second part discusses the five related papers [1–5]. Chapter 6 summarizes the results of [1], which discusses cosmological limits on neutrino masses and the neutrino mass ordering using state-of-the-art datasets, highlighting important issues which need to be addressed if progress is to be made. A better understanding of galaxy bias, and its scale-dependence, is highlighted as a particularly pressing concern. This problem is partially addressed in Chap. 7 which summarizes the results of [2], where we propose a new method to calibrate the scale-dependent galaxy bias, based on cross-correlations between CMB lensing and galaxy maps. A related issue is addressed in Chap. 8 which summarizes the results of [3], where we highlight the importance of defining the galaxy bias in the presence of massive neutrinos in a meaningful way, a subtlety which had not been appreciated so far. The final two papers deal with the issue of degeneracies, i.e. the fact that different cosmological parameters (among which neutrino masses) can have comparable

xxi xxii Thesis Plan effects on cosmological observations, and hence it is sometimes difficult to disen- tangle the individual effects. As a result, our upper limits on neutrino masses usually degrade when relaxing our assumptions on the underlying cosmological model, and hence our ignorance on other parameters affects what we learn about neutrinos and vice-versa. In Chap. 9 which summarizes the results of [4], we argue that this is not always the case, highlighting an important example where we relax the assumption that dark energy should consist of a simple cosmological constant. Finally, in Chap. 10 which summarizes the results of [5], we tackle the reverse problem, namely whether our ignorance of neutrino properties can affect what we learn about the rest of the Universe. We focused on what we learn about cosmic inflation, which supposedly occurred in the very early instants of the Universe and set the initial conditions for the hot Big Bang theory. Finally, Chap. 11 provides a conclusive summary and outlook on future directions. Contents

1 Introduction ...... 1 1.1 Cosmology, the Dark Universe, and Neutrinos ...... 1 1.2 Outline of the Thesis...... 3 References ...... 4 2 Standard Models and What Lies Beyond ...... 5 2.1 The Standard Model of Particle Physics ...... 6 2.2 The Standard Model of Cosmology ...... 7 2.2.1 A Brief History of Cosmology ...... 7 2.2.2 Basics of Physical Cosmology ...... 9 2.2.3 A Sneak Peek at the Concordance KCDM Model ..... 11 References ...... 12 3 Overview of Physical Cosmology...... 37 3.1 Elementary Notions of Cosmology...... 37 3.2 The Hot Big Bang Theory ...... 42 3.2.1 Brief Thermal History of the Universe ...... 46 3.2.2 Inflation...... 49 3.3 The Concordance KCDM Model ...... 52 References ...... 54 4 Massive Neutrinos and How to Search for Them with Cosmological Observations ...... 65 4.1 Neutrinos and the Quest for Their Mass ...... 65 4.1.1 Neutrino Oscillations ...... 66 4.1.2 The History of Cosmic Neutrinos ...... 69 4.2 Cosmological Observations ...... 74 4.2.1 Cosmic Microwave Background ...... 74 4.2.2 Large-Scale Structure ...... 86

xxiii xxiv Contents

4.3 Neutrino Signatures in Cosmological Observations ...... 94 4.3.1 Signatures of Neutrinos in the CMB Anisotropies ..... 94 4.3.2 Signatures of Neutrinos in the Matter Power Spectrum ...... 102 References ...... 105 5 A Brief Interlude: Statistical Methods in Cosmology ...... 123 5.1 Bayesian Versus Frequentist Statistics ...... 124 5.2 Elementary Notions of Bayesian Statistics ...... 125 5.2.1 Bayes’ Theorem ...... 125 5.2.2 Marginalization, Credible Regions, and Model Comparison ...... 128 5.3 Bayesian Statistics in Practice: MCMC Methods ...... 131 References ...... 134 6 Early 2017 Limits on Neutrino Masses and Mass Ordering ...... 137 6.1 Executive Summary ...... 144 References ...... 145 7 Scale-Dependent Galaxy Bias and CMB Lensing-Galaxy Cross-Correlations ...... 151 7.1 Executive Summary ...... 155 References ...... 156 8 Scale-Dependent Galaxy Bias Induced by Massive Neutrinos ..... 159 8.1 Executive Summary ...... 163 References ...... 163 9 Massive Neutrinos Meet (Non-Phantom) Dark Energy ...... 167 9.1 Executive Summary ...... 172 References ...... 173 10 Massive Neutrinos Meet Inflation ...... 179 10.1 Executive Summary ...... 185 References ...... 186 11 Summary and Outlook ...... 189 References ...... 192 Abbreviations

BAO Baryon Acoustic Oscillations BBN Big Bang Nucleosynthesis BE Bose-Einstein BOSS Baryon Oscillation Spectroscopic Survey BSM Beyond the Standard Model C.L. Confidence level CDM Cold Dark Matter CKM Cabibbo-Kobayashi-Maskawa CMB Cosmic Microwave Background CNB Cosmic Neutrino Background COBE Cosmic Background Explorer CPL Chevallier-Polarski-Linder DDE Dynamical Dark Energy DE Dark Energy DES Dark Energy Survey DESI Dark Energy Spectroscopic Instrument DM Dark Matter DR Data Release DUNE Deep Underground Neutrino Experiment eBOSS Extended Baryon Oscillation Spectroscopic Survey EISW Early integrated Sachs-Wolfe EoS Equation of State EW Electro-weak FD Fermi-Dirac FIRAS Far Infrared Absolute Spectrophotometer FKP Feldman-Kaiser-Peacock FLRW Friedmann-Lemaître-Robertson-Walker GR General Relativity GW Gravitational Wave HFI High Frequency Instrument IO Inverted neutrino mass ordering

xxv xxvi Abbreviations

ISW Integrated Sachs-Wolfe KamLAND Kamioka Liquid Scintillator Antineutrino Detector LFI Low Frequency Instrument LISW Late integrated Sachs-Wolfe LSS Large-scale structure LSST Large Synoptic Space Telescope MCMC Markov Chain Monte Carlo MGS Main Galaxy Sample MSW Mikheyev-Smirnov-Wolfenstein NISDB Neutrino-Induced Scale-Dependent Bias NO Normal neutrino mass ordering NO”A Neutrinos at the main injector off-axis ”e appearance NPDDE Non-phantom dynamical dark energy PCA Principal component analysis PMNS Pontecorvo-Maki-Nakagawa-Sakata QCD Quantum chromodynamics RSD Redshift-space distortions SDSS Sloan Digital Sky Survey SM Standard Model of Particle Physics SNe1a Type 1a Supernovae SNO Sudbury Neutrino Observatory SPHEREx Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer T2K Tokai to Kamioka UV Ultraviolet WFIRST Wide Field Infrared Survey Telescope WMAP Wilkinson Microwave Anisotropy Probe KCDM Kcold dark matter (standard model of cosmology) 2dfGRS 2-degree field galaxy redshift survey 6dFGS 6-degree field galaxy survey Notation

Certain symbols have more than one meaning, which depends on the context. These symbols are marked by “(context)” a Scale factor/scale-independent bias factor (context) alm Coefficients of the decomposition of H in spherical harmonics anr Scale factor at znr a0 Scale factor today (usually normalized to 1) AL Phenomenological parameter governing the amplitude of CMB lensing As Amplitude of primordial scalar power spectrum b Galaxy bias bauto Galaxy bias in auto-correlation bcb Galaxy bias defined with respect to the cold dark matter + baryons field bcross Galaxy bias in cross-correlation Bij Bayes factor of model i with respect to model j bm Galaxy bias defined with respect to the total matter field c Scale-dependent bias factor in cross-correlation cs Speed of sound BB C‘ CMB B-mode polarization anisotropy angular power spectrum EE C‘ CMB E-mode polarization anisotropy angular power spectrum TE C‘ CMB temperature-E-mode polarization anisotropy angular cross-power spectrum TT C‘ CMB temperature anisotropy angular power spectrum jg C‘ CMB lensing convergence-galaxy angular cross-power spectrum // C‘ CMB lensing potential power spectrum c” Neutrino speed C Collision operator d Scale-dependent bias factor in auto-correlation d Data i dR Right-handed down quark singlet

xxvii xxviii Notation dV Volume distance drT =dX Thomson scattering differential cross section D‘ ‘ð‘ þ 1ÞC‘ i eR Right-handed electron singlet EðdÞ Bayesian evidence/marginal likelihood EðzÞ Normalized expansion rate EðzÞHðzÞ=H0 f Distribution function f cb Growth rate of the cold dark matter + baryons power spectrum f m Growth rate of the matter power spectrum f ” Fraction of the matter density parameter in neutrinos f ”  X”=Xm gi Internal degrees of freedom of species i gH Effective number of relativistic degrees of freedom s gH Effective number of entropy degrees of freedom GF Fermi constant Gl” Einstein tensor h Reduced Hubble constant H Hubble parameter at a given redshift/neutral Hydrogen (context) H0 Hubble constant k FLRW metric curvature/wavenumber (context) keq Wavenumber of perturbation entering the horizon at zeq kfs Neutrino free-streaming wavenumber kn Wavenumber of the n-th CMB acoustic peak knr Wavenumber of perturbation entering the horizon at znr ksd Wavenumber at which scale-dependent bias becomes important i LL Left-handed lepton doublet L Liouville operator LðdjhÞ Likelihood LSM Standard Model Lagrangian ‘ Multipole ‘n Multipole of the n-th CMB acoustic peak mi Mass of species i mlight Mass of lightest neutrino eigenstate eff ms Effective sterile neutrino mass M” Sum of the three active neutrino masses ne Number density of free electrons ni Number density of species i nrun Running of the scalar spectral index dns=d ln k nrunrun Running of the running of the scalar spectral index dnrun=d ln k ns Tilt of primordial scalar power spectrum (scalar spectral index) Neff Effective number of relativistic degrees of freedom NH Number of e-folds of cosmic inflation p Momentum/probability (context) pðhjdÞ Posterior distribution PcbðkÞ Cold dark matter + baryons power spectrum Notation xxix

Pi Pressure of species i PðkÞ Matter power spectrum PgðkÞ Galaxy power spectrum PHF”(k) Non-linear power spectrum from Halofit calibrated to massive neutrinos PmgðkÞ Matter-galaxy cross-power spectrum PprimðkÞ Primordial power spectrum of matter fluctuations PRðkÞ Primordial power spectrum of R PR Dimensionless primordial power spectrum of R Pshot Shot noise PðhÞ Prior distribution i QL Left-handed quark doublet qðhHjhÞ Proposal distribution for Metropolis-Hastings algorithm R Baryon-to-photon momentum density ratio r Tensor-to-scalar ratio evaluated at the pivot scale k ¼ 0:05 MpcÀ1 rd Damping scale rfs Neutrino free-streaming horizon rs Comoving sound horizon si Entropy density of species i t Time T Temperature of the Universe (photon temperature) TCMB CMB temperature today TðkÞ Transfer function Tl” Stress-energy tensor T” Effective neutrino temperature T”;dec Neutrino decoupling temperature i uR Right-handed up quark singlet Uij PMNS matrix w Dark energy equation of state w0 Dark energy EoS today (CPL parametrization) wa Minus derivative of dark energy EoS with respect to scale factor (CPL parametrization) W j Kernel for CMB lensing Ylm Spherical harmonics Yp Primordial Helium fraction z Redshift zdec Redshift of decoupling zdrag Redshift of baryon drag zeff Effective redshift zeq Redshift of matter-radiation equality znr Redshift of neutrino non-relativistic transition zre Redshift of reionization zK Redshift of matter-K equality a 4=3 a ½1 þ 7=8ð4=11Þ Neff Šð1 þ 0:2271 Neff Þ xxx Notation

C Reaction rate d Dirac Delta di Overdensity of species i D 2 m21 Solar mass-squared splitting jD 2 j m31 Atmospheric mass-squared splitting g Baryon-to-photon ratio h Parameter vector hd Angular size of the damping scale hn Angular size of the n-th CMB acoustic peak hs Angular size of the first CMB acoustic peak H CMB temperature anisotropies/Heaviside step function (context) j CMB lensing convergence ‚ Wavelength ‚fs Neutrino free-streaming scale K Cosmological constant ”i Neutrino mass eigenstates (i ¼ 1; 2; 3) ”a Neutrino flavour eigenstates (a ¼ e; l; ¿) nðrÞ Galaxy 2-point correlation function qcrit Critical energy density of the Universe today qi Energy density of species i rT Thomson scattering cross section r8 Amplitude of matter fluctuations averaged on a sphere of radius 8 hÀ1Mpc ¿ Optical depth to reionization / Inflation/gravitational potential/lensing potential/quintessence field (context) U Higgs doublet v Comoving distance to a given redshift vh Comoving particle horizon at a given redshift vH Comoving distance to zdec W Gravitational potential xb Physical density parameter of baryons xc Physical density parameter of cold dark matter xk Physical density parameter associated to curvature xm Physical density parameter of matter xr Physical density parameter of radiation x° Physical density parameter of photons x” Physical density parameter of neutrinos xK Physical density parameter of K Xb Density parameter of baryons Xc Density parameter of cold dark matter Xk Density parameter associated to curvature Xm Density parameter of matter Xr Density parameter of radiation Notation xxxi

X° Density parameter of photons X” Density parameter of neutrinos XK Density parameter of K