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Accurate Cosmology with Galaxy and Quasar Surveys Boris Leistedt

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Accurate Cosmology with Galaxy and Quasar Surveys Boris Leistedt Accurate Cosmology with Galaxy and Quasar Surveys Boris Leistedt Submitted for the degree of Doctor of Philosophy Department of Physics and Astronomy University College London September 2014 I, Boris Leistedt, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. 1 Abstract Observations of the cosmic microwave background have led to a golden age of cosmology, where precise measurements can be confronted with predictions from cosmological models. Ongoing and future surveys of the distribution of galaxies will continue this revolution: they will enable us to test the laws of gravity, uncover the properties of dark energy and dark matter, and reinforce the connection to high-energy physics. However, current galaxy survey analyses are already limited by our ability to identify and treat observational systematics, and this problem will be even more pronounced in future experiments. Therefore, it is essential to develop novel methods to deal with these complications when testing cosmological models and searching for new physics. This is the focus of this thesis. Firstly, I will present measurements of primordial non-Gaussianity obtained from the clustering of quasars from the Sloan Digital Sky Survey. Primordial non-Gaussianity is a powerful probe of inflation, the leading theory of the initial conditions of the universe, but its effects on the distribution of quasars are mimicked by observational systematics. I will describe a framework to deal with these systematics and robustly measure primordial non-Gaussianity from the clustering of quasars. Secondly, I will present a new set of wavelet transforms on the sphere and the ball. These approaches are highly promising for analysing cosmological and geophysical data and dealing with their systematics in novel ways. Finally, I will examine the recent claims that extra massive neutrinos can resolve the tensions between cosmic microwave background, galaxy survey and supernova observations. I will demon- strate that this conclusion is premature since it is driven by the least robust data sets. Given the growing number of cosmological observables and their varied levels of robustness, combining data sets and dealing with such tensions will become critical in the near future. 2 Acknowledgements First and foremost, I would like to express my deepest gratitude and appreciation to my advisor, Hiranya Peiris. During the past three years, you have been an attentive, supportive, and inspiring mentor, and I am extremely grateful for the infinite amount of time and energy you have invested in me. My time in UCL has been a life changing experience, and I could never hope for a better supervisor. I would also like to thank the exceptional individuals I have had the chance to collaborate with: Jason McEwen, Daniel Mortlock, Andrew Pontzen, Aur´elien Benoit-L´evy, Licia Verde, Nina Roth, and Franz Elsner (in order of appearance). I have learned so much from you, both personally and scientifically, and you made me discover how fun, fascinating, and humanly enriching research could be. Thank you to Ofer Lahav and Filipe Adballa for the useful discussions and advice during the course of this PhD. I am also grateful to Alan Heavens and Benjamin Joachimi, who kindly accepted to examine this thesis and provide many useful comments and suggestions. My experience in UCL would not have been complete without the UCL astro-p(i)gs. For all the love, laughs and tears, I thank all the students and post-docs of the Astrophysics Group. Special thoughts go to the inhabitants of G16, this parallel universe where I worked during the three years of my PhD. Thanks to you I have enjoyed every single day in the office. I am indebted to my parents and my brothers for their unconditional backing over the years. Thank you for encouraging me and providing me everything I needed to follow my dreams. And finally, thank you Olivier, for standing by my side from the very first day, and making my life so colourful. Without your love and support, this document would simply be blank. 3 Contents 1 Introduction 15 1.1 The Universe....................................... 15 1.1.1 Composition and structure............................ 15 1.1.2 Brief history.................................... 19 1.2 The early Universe.................................... 20 1.2.1 The cosmic microwave background....................... 20 1.2.2 Inflation and primordial non-Gaussianity.................... 22 1.3 The evolved Universe................................... 25 1.3.1 Matter perturbations and structure formation................. 26 1.3.2 Galaxy surveys.................................. 27 1.3.3 Scale-dependent halo and galaxy bias..................... 29 1.3.4 Quasars...................................... 31 1.3.5 Cosmological neutrinos............................. 32 1.4 Wavelets in cosmology.................................. 34 1.5 Thesis outline....................................... 35 2 Estimating the large-scale angular power spectrum in the presence of systematics: a case study of Sloan Digital Sky Survey quasars 37 2.1 Abstract.......................................... 37 2.2 Introduction........................................ 38 2.3 Theory and methods................................... 40 2.3.1 Background.................................... 40 4 2.3.2 Partial sky coverage and quadratic estimators................. 41 2.3.3 Likelihood analysis and band-powers...................... 46 2.3.4 Galaxy surveys, shot noise and systematics................... 50 2.3.5 Illustration: recovering the power spectrum of the CMASS sample...... 51 2.4 Application to SDSS photometric quasars........................ 54 2.4.1 Data and subsamples............................... 54 2.4.2 Theory predictions................................ 56 2.4.3 Redshift distributions estimates......................... 58 2.4.4 Masks and systematics.............................. 62 2.4.5 Power spectrum results............................. 64 2.5 Discussion......................................... 68 2.6 Aknowledgements.................................... 72 2.7 Appendices........................................ 72 2.7.1 Pixelisation, band-limit and smoothing issues................. 72 2.7.2 Karhunen-Lo`eve compression demystified................... 74 2.7.3 χ2 for band-power estimates.......................... 76 3 Exploiting the full potential of photometric quasar surveys: optimal power spectra through blind mitigation of systematics 78 3.1 Abstract.......................................... 78 3.2 Introduction........................................ 79 3.3 Theory and methods................................... 81 3.3.1 Power spectrum estimation........................... 81 3.3.2 Extended mode projection............................ 83 3.3.3 Fast cross-power spectra and null-tests..................... 87 3.4 Application to SDSS photometric quasars........................ 88 3.4.1 Sample selection and redshift distributions................... 89 3.4.2 Masks and systematic uncertainties....................... 92 3.4.3 Estimation settings and blind mitigation of systematics............ 95 3.4.4 Power spectrum measurements......................... 97 3.5 Conclusion........................................ 101 3.6 Acknowledgements.................................... 103 5 4 Constraints on primordial non-Gaussianity from 800,000 photometric quasars 105 4.1 Abstract.......................................... 105 4.2 Introduction........................................ 106 4.3 PNG with photometric quasars............................. 107 4.4 XDQSOz power spectrum measurements........................ 108 4.5 Halo bias from PNG................................... 110 4.6 Monte Carlo Markov Chain (MCMC) analysis..................... 111 4.7 Results........................................... 112 4.8 Future prospects..................................... 115 4.9 Conclusion........................................ 115 4.10 Acknowledgments.................................... 116 5 S2LET: A code to perform fast wavelet analysis on the sphere 117 5.1 Abstract.......................................... 117 5.2 Introduction........................................ 118 5.3 Wavelets on the sphere.................................. 119 5.3.1 Harmonic analysis on the sphere........................ 120 5.3.2 Scale-discretised wavelets on the sphere.................... 121 5.4 The S2LET code...................................... 125 5.4.1 Multiresolution algorithm............................ 125 5.4.2 Implementation.................................. 127 5.4.3 Numerical validation............................... 128 5.4.4 Future extensions................................. 131 5.5 Examples......................................... 132 5.5.1 Wavelet transform from the command line................... 132 5.5.2 Wavelet transform in Matlab and IDL ...................... 133 5.5.3 Wavelet denoising in C .............................. 133 5.6 Summary......................................... 136 5.7 Acknowledgements.................................... 136 6 Exact Wavelets on the Ball 139 6.1 Abstract.......................................... 139 6.2 Introduction........................................ 140 6.3 Harmonic Analysis on the Ball.............................. 141 6 6.3.1 The spherical Laguerre transform........................ 142 6.3.2 Relation to the spherical Bessel transform................... 144 6.3.3 The
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