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Origin & Evolution of the Universe

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Origin & Evolution of the Universe Origin & evolution of the Universe Darsh Kodwani St Hugh's College University of Oxford arXiv:2006.12126v3 [astro-ph.CO] 24 Jun 2020 A thesis submitted for the degree of Doctor of Philosophy Michaelmas 2019 The best teacher in life is experience. Experience comes with time. Time is in the future; which is where I will spend the rest of my life... Acknowledgements Firstly I would like to thank my main supervisors at both Oxford and Toronto, Pedro Ferreira, David Alonso and Ue-Li Pen. In particular, David is almost single handedly responsible for developing my computa- tional skills, and having the patience to help me with many of the silly mistakes I made along the way, for which I will always be indebted to him. It has been a real pleasure to work with them throughout my DPhil and it wouldn't have been possible without their constant support and encour- agement to pursue my ideas. I have also had the pleasure of collaborating with many other amazing scientists throughout my studies, in particu- lar: Daan Meerburg and Xin Wang have both taken the time to help me in various projects and immensely augmented my research abilities. Research in physics is driven by constantly using creative ideas to solve challenging problems. I have had the pleasure of working with many of the most creative people in physics; none more than I-Sheng Yang whom I have worked with on several projects. I-Sheng's ability to solve prob- lems from many different areas of physics and constantly challenging the basic assumptions is something that has always amazed me and this is the approach I have tried to take during my research as well. His initial sup- port and guidance in helping me formulating new problems have had the most direct impact on me having a successful research career so far and I will always be grateful for that. In Oxford, Harry Desmond has played a similar role. His ability to understand the fundamentals of a problem and suggest new approaches to solve them has always been something I have admired. Moreover, he has also been a close friend and mentor for me, not to mentioning the constant schooling of new vocabulary that he has given me! In addition to working on research projects, I have always maintained a friendship with all my collaborators which has made my DPhil an extremely enjoyable endeavour. Thank you all! Maintaining a good work-life balance and a calm mental state is crucial to being creative and solving challenging problems that inevitably come up during research. A lot of credit for me being able to do this has to go the friends I have made along the way. Firstly, my office mates in Toronto; Derek and Dana with whom I shared many coffee breaks and stories about our struggles with research, were always a source of comfort and support for me. Also Daniel, my academic twin in Toronto and also coauthor, Leonardo, Tharshi (for making me most welcome in Toronto at first), Vincent, Sonia (for putting up with my lame physics jokes), Gunjan, Simon, Alex (for teaching me smash bros!), Phil (with whom I am also writing a never ending paper) have all been a source of fun and support throughout my time in Toronto and I am sure will continue to be so in the future. In Oxford, my incoming class of fellow students have always been a source of comfort and support and being around them is something that I have always enjoyed. In particular, Dina (my academic twin), Christiane, Alvaro, Theresa (and our many \therapy" sessions in uni parks), Sam, Eva, Shahab, Andrea, Sergio, Emilio, Max (also soon to be co-author), Ryo, Richard (another soon to be co-author), Zahra, Stefan have made my time in Oxford extremely enjoyable and I am sure we will have many enjoyable times in the future as well. Finally, without the unwavering confidence, support and faith of my par- ents none of this would be possible. They have always encouraged me to pursue my interests and not worry about anything else. It is this freedom that has lead to my pursuit of understanding the origin and evolution of the universe. I am also indebted to my family in India for their affection and support throughout. In particular my nephews and niece's, Maitri, Pari, Parth, Dhriti, who have always brightened up even the darkest days. Figure1 shows the people most responsible for keeping me going through the journey of understanding the origin and evolution of the universe. Figure 1: Dhriti, Parth, Maitri, Pari and Me 4 Abstract The aim of this thesis is to question some of the basic assumptions that go into building the ΛCDM model of our universe. The assumptions we focus on are the initial conditions of the universe, the fundamental forces in the universe on large scales and the approximations made in analysing cosmological data. For each of the assumptions we outline the theoretical understanding behind them, the current methods used to study them and how they can be improved and finally we also perform numerical analysis to quantify the novel solutions/methods we propose to extend the previous assumptions. The work on the initial conditions of the universe focuses on understand- ing what the most general, gauge invariant, perturbations are present in the beginning of the universe and how they impact observables such as the CMB anisotropies. We show that the most general set of initial conditions allows for a decaying adiabatic solution which can have a non- zero contribution to the perturbations in the early universe. The decaying mode sourced during an inflationary phase would be highly suppressed and should have no observational effect, thus, if these modes are detected they could potentially rule out most models of inflation and would require a new framework to understand the early universe such as a bouncing/cyclic universe. After studying the initial conditions of the universe, we focus on under- standing the nature of gravity on the largest scales. It is assumed that gravity is the only force that acts on large scales in the universe and we propose a novel test of this by cross-correlating two different types of galaxies that should be sensitive to fifth-force's in the universe. By focusing on a general class of scalar-tensor theories that have a property of screening, where the effect of the fifth force depends on the local en- ergy density, we show that future surveys will have the power to constrain screened fifth-forces using the method we propose. Finally, to test theoretical models with observations a complete under- standing of the statistical methods used to compare data with theory is required. The goal of a statistical analysis in cosmology is usually to infer cosmological parameters that describe our theoretical model from observa- tional data. We focus on one particular aspect of cosmological parameter estimation which is the covariance matrix used during an inference pro- cedure. The usual assumption in modelling the covariance matrix is that it can be computed at a fiducial point in parameter space, however, this is not self-consistent. We check this claim explicitly by calculating the effect of including the parameter dependence in the covariance matrix on the constraining power of cosmological parameters. 6 Contents 1 Introduction1 1.1 A brief history of the Universe . .1 1.2 ΛCDM model . .4 1.2.1 Background . .4 1.2.2 Perturbations . .9 1.3 Probes of cosmology . 11 1.3.1 Cosmic microwave background . 11 1.3.1.1 Temperature anisotropies . 12 1.3.1.2 Polarisation anisotropies . 17 1.3.2 Galaxy clustering . 18 1.3.3 Galaxy lensing . 23 1.4 Statistical methods for cosmology . 25 1.4.1 The two schools . 25 1.4.2 Bayesian analysis . 25 1.4.3 Likelihoods in cosmology . 26 1.4.4 Inference . 27 1.4.4.1 MCMC . 28 1.4.4.2 Fisher analysis . 28 1.5 Overview of thesis . 29 2 Initial conditions of the universe: A sign of the sine mode 31 2.1 Introduction and historical context . 31 2.2 Theory of the decaying mode . 34 2.2.1 Review of radiation domination . 34 2.2.2 CMB anisotropies . 35 2.3 Analysis . 41 2.4 Summary and future outlook . 46 3 Initial conditions of the universe: Decaying tensor modes 48 3.1 Introduction . 48 3.2 Decaying tensor modes . 49 3.2.1 Primordial perturbations . 49 3.2.2 Review of CMB anisotropies . 51 3.3 Analysis . 54 3.3.1 C` results . 54 i 3.3.2 Fisher results . 58 3.4 Discussion & future outlook . 61 4 Screened fifth forces in parity breaking correlation functions 62 4.1 Introduction . 62 4.2 Screened fifth forces . 65 4.3 Correlation Functions under Screened Fifth Forces . 66 4.4 Correlation function parameter space . 71 4.4.1 Global parameters . 71 4.4.2 Local parameters . 73 4.5 Results . 75 4.6 Summary and future work . 79 5 The effect on cosmological parameter estimation of a parameter de- pendent covariance matrix 82 5.1 Introduction . 82 5.2 Approximating the likelihood . 84 5.2.1 Likelihoods and covariances: the case of a 2-dimensional Gaus- sian field . 84 5.2.2 Likelihoods and covariances: the general case . 87 5.2.3 Large-scale structure likelihoods . 89 5.2.4 Analytic example: the power spectrum amplitude . 92 5.3 Forecasts . 93 5.3.1 Survey specifications . 94 5.3.2 Results . 95 5.4 Summary . 97 6 Concluding remarks 100 6.1 Summary of thesis .
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