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Cosmology and the Local Group in ΛCDM and Modified Gravity

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Cosmology and the Local Group in ΛCDM and Modified Gravity Cosmology and the Local Group in LCDM and Modified Gravity Michael Alexander McLeod A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London. Department of Physics and Astronomy University College London October 14, 2018 2 I, Michael Alexander McLeod, 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 work. Abstract In the first part we shall consider the statistical analysis of large scale structure in galaxy surveys. We demonstrate a method for jointly constraining cosmology and photometric redshift distributions using cross correlations between photometric and spectroscopic redshift bins. This allows one to reduce the bias in the inferred cos- mological parameters which may be propagated from errors in the redshift distri- butions. We demonstrate this using parameters for a DES-like survey, using galaxy number count C(l)s and CMB-TT information. We continue in this vein to ap- ply these methods to the search for modified gravity using the Euclid survey. We forecast constraints on Horndeski theories using a-function parameterisation, us- ing combined probes of galaxy number counts cross correlated with weak lensing shear, and independently adding CMB-TT information. We see that, as expected, the constraints on the a-parameters are not significantly degenerate with the other cosmological parameters; this is promising as it means that their detection would be less prone to misconstruction. In the second part we consider the universe on considerably smaller scales, and concern ourselves with the local group (LG). We first explore the use of artificial neural networks for estimating the mass of the LG. Using the Timing Argument as a bench mark, we find that the ANN can make use of novel physical informa- tion (in our case, the eigenvalues and eigenvectors of the velocity shear tensor) to improve the scatter of the estimates considerably. We then proceed to explore the analytic Timing Argument mass further, exploring its dependency on dark energy and modified gravity models. Beginning with L, we proceed to perfect fluid models, quintessence fields, and scalar-tensor theories of gravity in the weak field limit. Abstract 4 Impact Statement The work presented in Part I of this thesis is primarily dedicated to analysing and improving the constraining power of galaxy surveys in cosmology. The methods described for photometric redshift calibration can be implemented into pipelines for large collaborations, which will bring us our most precise and accurate mea- sures of the universe. I hope that the work presented in the following pages can contribute to this deepening of our understanding of the universe. The work here also further explores a relatively recent approach to parameterised modified gravity, for the case of a major upcoming experiment (Euclid). The fact that we find our- selves able to constrain such a model, despite its additional complexities compared to the standard approach in modified gravity, shows that we can indeed use more in- tricate modelling in the near future. Our work also urges some caution, and I hope that our analysis of the stability of modified gravity models in the wake of grav- itational waves can stimulate discussion on the future of parameterised modified gravity. In Part II we look to the universe directly around us, and find it a vibrant playground for physics and numerical methods of a wide variety. The solutions for simple, two body interactions in modified gravity is little explored in the literature, and this work could help bring the interesting effects of these theories to a different audience. The Local Group is typically considered in the context of very standard physics, the assumption being that the scales are too small and the physics too New- tonian for other models to be worth the hassle. The work presented here can show that even on scales as small as our nearest galaxy, we should be considering the full breadth of physics available to us. We present highly competitive estimates for the mass of the Local Group, which is a fundamental measurement of our own home. By remaining close to home, I hope that this work can be inspiring both inside and outside academia. I believe that public engagement with science is crucial both to us as scientists, and to society at large. As astronomers, we are in a particularly advantageous position to engage with the public’s particularly fervent fascination with the space and the universe. I hope that the concrete example of our own galaxy and our closest partner (Andromeda) will be a gateway for the public into learning Abstract 5 about methods and ideas as complex and diverse as machine learning, galaxy flows, modified gravity, cosmological inference, and how we fit into the universe. Previously Published Work The work in chapter two is the basis of a paper published in MNRAS Volume 466, pp3358-3568, April 2017, entitled ‘A joint analysis for cosmology and photometric redshift calibration using cross-correlations’. The work in chapter four is the basis of a paper published in JCAP December 2017, entitled ’Estimating the mass of the Local Group using machine learning applied to numerical simulations’. Acknowledgements It is a challenge in itself to thank everyone who has made this PhD possible. I am, of course, indebted to my supervisors Dr. Filipe Abdalla and Prof. Ofer Lahav, who have guided me with their advice and expertise. They lead me to new questions I hadn’t previously considered, that allowed me to grow as a person and a scientist. Most importantly I wish to thank my parents, Joan McKenzie and David McLeod, for providing me extraordinary support throughout my entire education, and life in general. In particular I would like to thank my mother, Joan, for fostering my interest in the mathematical world from the earliest age, and thoroughly instill- ing in me the belief that education and intellectual exploration is a worthy cause for its own sake. In this way (and many others) she has probably influenced me more than any other person. Contents 1 Introduction 24 1.1 An Overview of Gravity and Cosmology . 26 1.1.1 The Chronology of the Universe . 27 1.1.2 There and Back Again: Newtonian Dynamics to General Relativity to the Weak Field Limit . 29 1.1.3 Background Cosmology and LCDM . 34 1.1.4 The Cosmological Parameters . 37 1.2 Beyond LCDM: Dark Energy and Modified Gravity . 41 1.2.1 Scalar Fields in Cosmology: The Minimally Coupled Scalar Field . 42 1.2.2 Scalar-Tensor Actions in the Jordan and Einstein Frames . 44 1.2.3 The Horndeski Class . 56 1.3 Structure and Dynamics in the Local Universe . 59 1.3.1 Motion of Matter in Static and Co-Moving Coordinates . 60 1.3.2 The Local Group . 62 1.3.3 The Cosmic Web & Cosmography . 63 1.4 Large Scale Structure . 64 1.4.1 Structure Formation Theory Basics . 65 1.4.2 Correlation Functions and the Power Spectrum . 66 1.4.3 Weak Gravitational Lensing . 71 1.5 Galaxy Surveys . 77 1.5.1 Redshift . 78 1.5.2 Observing Ellipticity . 81 Contents 8 1.5.3 Relevant Surveys: the Dark Energy Survey and Euclid . 82 1.6 Computing and Cosmology . 83 1.6.1 Numerical Sampling . 83 1.6.2 Machine Learning with Artificial Neural Networks . 86 I The Universe on Large Scales 94 2 Joint Analysis of Cosmological Parameters and Photometric Redshifts 95 2.1 Introduction . 95 2.2 The C(l) Calculation . 98 2.2.1 The C(l) formalism . 98 2.2.2 Window functions . 99 2.2.3 The significance of n(z) . 101 2.3 Modelling the Redshift Distributions . 103 2.3.1 Photmetric redshifts . 103 2.3.2 Spectroscopic redshifts . 104 2.4 The Likelihood Function and Sampling Methods . 105 2.4.1 The likelihood function for C(l)s . 105 2.4.2 Noise parameters and survey assumptions . 108 2.4.3 Computational details: UCLCl and PLINY codes . 109 2.4.4 The fiducial model . 109 2.5 Results . 111 2.5.1 Cosmological parameter bias from n(z) . 111 2.5.2 Autocorrelations with photometric redshift bins . 112 2.5.3 Cross correlating with spectroscopic redshifts . 116 2.6 Discussion . 117 2.6.1 On galaxy bias . 118 2.7 Further applications to non-Gaussian n(z) .............. 121 2.7.1 Details of n(z) Transformations . 121 2.7.2 Constraining higher moments . 124 2.7.3 Identifying anomalous features in n(z) ............ 126 Contents 9 3 Horndeski Gravity using Large Scale Structure and Weak Lensing 129 3.1 Introduction . 129 3.2 Scalar-Tensor Modified Gravity and Parameterisation . 132 3.2.1 The Horndeski action . 133 3.2.2 The a-functions and parameterisation . 134 3.2.3 Modified Growth and Lensing in Horndeski Gravity . 139 3.3 C(l)s and Window Functions . 142 3.3.1 Galaxy Number Counts . 143 3.3.2 Weak Lensing Shear . 143 3.4 The Likelihood Function . 144 3.5 Experimental Setup . 145 3.5.1 Photometric redshift distribution . 146 3.5.2 Spectroscopic redshift distribution . 147 3.5.3 CMB . 148 3.5.4 Noise functions . 149 3.5.5 Fiducial Model and Cosmological Parameters for Sampling 150 3.6 Sampling Results . 150 3.6.1 Redshift constraints and degeneracies . 154 3.6.2 Modified Gravity and cosmology with and without aT 6= 0 . 156 3.7 The role of aT and parameterisation . 157 3.7.1 Stability of the models in ai ∝ WDE ............. 158 3.8 Discussion . 159 II The Local Group 162 4 The Mass of the Local Group 163 4.1 Introduction .
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