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ETD-5608-032-LIN-9413.13.Pdf (3.426Mb) TESTING THE DARK SECTOR VERSUS MODIFIED GRAVITY MODELS IN COSMOLOGY by Weikang Lin APPROVED BY SUPERVISORY COMMITTEE: Dr. Mustapha Ishak-Boushaki, Chair Dr. Robert Glosser Dr. Michael Kesden Dr. Lindsay J. King Dr. Kaloyan Penev Copyright c 2018 Weikang Lin All rights reserved TESTING THE DARK SECTOR VERSUS MODIFIED GRAVITY MODELS IN COSMOLOGY by WEIKANG LIN DISSERTATION Presented to the Faculty of The University of Texas at Dallas in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY IN PHYSICS THE UNIVERSITY OF TEXAS AT DALLAS August 2018 ACKNOWLEDGMENTS I want to say thanks to many people. I am hoping I would not leave out anyone. First I would like to thank my advisor Dr. Mustapha Ishak for the past six years of support and advise for my graduate study. I am thankful that Dr. Ishak encouraged me to explore various sci- entific ideas. Dr. Ishak has provided significant help during my search for postdoctoral positions. I would also like to thank my dissertation committee including Dr. Mustapha Ishak, Dr. Robert Glosser, Dr. Michael Kesden, Dr. Lindsay King and Dr. Kaloyan Penev. I thank Dr. Glosser and Dr. Penev for providing advise about my career decision. I want to sincerely express my grati- tude to Dr. Michael Kesden and Dr. Lindsay King, for their help during my search of postdoctoral position. They both have pointed out to me many postdoctoral opportunities, especially the post- doctoral position at NCSU pointed out by Dr. Kesden. I owe a special thanks to Dr. Xingang Chen, who is not only one of my previous dissertation committee members but also my friend. I will always remember the times we played tennis and other games along with others (whom I shall soon express my gratitude to). I can’t say enough thanks to Dr. Wolfgang Rindler, who has been always encouraging, inspiring and supporting me. Dr. Xingang Chen and Dr. Wolfgang Rindler have also offered much support for my postdoctoral position searches. I also want to thank Dr. Mohammad Akbar for the wonderful lecture of quantum field theory, pleasure discussions on general relativity, and all the suggestions for the search of postdoctoral positions. I want to thank my family for their understandings and support, all my friends at UTD including Yuna, Chi-Te, Ji, Xinyu, Brandyn, Dimithree, Kuo-Yao, Kelly, Lyndon, Yang, Liang, Patrick, Taylor at Commerce, and so many others. At last, and most importantly, I want to thank the most significant one in my life, Michelle Hsu. She is always with me during all my hard times. She is the most beautiful and genuine girl I have ever met. June 2018 iv TESTING THE DARK SECTOR VERSUS MODIFIED GRAVITY MODELS IN COSMOLOGY Weikang Lin, PhD The University of Texas at Dallas, 2018 Supervising Professor: Dr. Mustapha Ishak-Boushaki, Chair This dissertation studies cosmological and astrophysical tests of gravity theories and the dark sec- tors. We focus on three tests. All of them are promising for future observations. The first test is about tensor-mode parameterization. While scalar-mode parameterization has been extensively studied, tensor-mode parameterization requires further investigations. This dissertation extends some previous work in the literature, and studies some physically motivated parameteri- zation schemes, the current observational constraints, the future constraint forecast as well as the impacts on inflation consistency relation. The second test is based on consistency tests. The idea is to compare constraints from different observations and check the consistency of a model. This dissertation introduces a novel measure, called the index of inconsistency (IOI). It is a simple and effective measure. We proposed a proce- dure based on IOI to test (in)consistencies of multiple observations. The difference between this consistency test and the first one is that we do not assume all data are correct. In fact, our procedure allows us to find observation outliers or the breakdown of the model. The third test is about a phenomenological difference between modified gravity and dark matter. We studied properties of the faintest galaxy system in our local group, called the ultra-faint dwarf galaxies. We found a loss of correlation between their luminosity and stellar velocity dispersion. This does not favor the modified gravity hypothesis. v TABLE OF CONTENTS ACKNOWLEDGMENTS . iv ABSTRACT . v LIST OF FIGURES . xi LIST OF TABLES . xiii CHAPTER 1 INTRODUCTION AND THE PURPOSE OF THIS DISSERTATION . 1 1.1 Outline of this dissertation . .1 1.2 A brief summary of the first part - Modified gravity and tensor mode perturbations .4 1.3 A brief summary of the second part - index of inconsistency . .5 1.4 A brief summary of the third part - ultra-faint dwarf galaxies as a test of modified gravity and dark matter hypotheses . .7 CHAPTER 2 BACKGROUNDS IN COSMOLOGY AND THE COSMIC ACCELERATION PROBLEM . 9 2.1 The standard theory and the standard model - homogeneous evolution . .9 2.1.1 The FLRW metric . 10 2.1.2 The cosmological constant, Λ ........................ 12 2.1.3 Observables at the background-level cosmology . 15 2.2 The standard cosmological model 2 - perturbations beyond the homogeneous uni- verse.......................................... 19 2.2.1 Physical objects at the perturbation level . 20 2.2.2 Properties of primordial perturbations . 26 2.2.3 The parameters of the standard cosmological model . 29 2.3 A few words on the standard cosmological model . 32 2.4 Dynamical dark energy . 33 2.5 Modified Gravity . 35 2.5.1 What does "modified gravity" mean? . 35 2.5.2 Classification based on the Lovelock’s theorem . 37 2.5.3 Classification based on the three equivalence principles . 38 2.5.4 The difference between dark energy and modified gravity . 40 2.5.5 Testing modified gravity theories . 43 vi 2.6 Other approaches for the problem of cosmic acceleration . 44 2.7 The inflation hypothesis . 45 CHAPTER 3 TESTING MODIFIED GRAVITY THEORIES USING TENSOR PERTUR- BATIONS . 48 3.1 Introduction . 48 3.2 Tensor Modes in Modified Gravity and their Parametrization . 49 3.3 Effects of Tensor mode Modified Gravity Parameters . 55 3.3.1 Analyzing the effects of modified friction and nonstandard speed . 56 3.3.2 Effects of large-scale deviation . 57 3.3.3 Effects of small-scale deviation . 60 3.4 Constraints on Tensor Mode Modified Gravity Parameters . 61 3.4.1 Updating the constraints on friction and constant speed . 63 3.4.2 Constraints on large-scale deviation . 64 3.5 Forecast of constraints on Tensor mode modified gravity parameters . 65 3.5.1 Formalism of CMB forecast and foreground residuals estimation . 66 3.5.2 Performance forecast of constraints on tensor-mode MG parameters . 70 3.6 Summary of this chapter . 74 CHAPTER 4 PRIMORDIAL GRAVITATIONAL WAVESDURING INFLATION, AND THE STANDARD VERSUS MG INFLATION CONSISTENCY RELATION . 76 4.1 Tensor-mode perturbations during inflation with constant friction and speed . 76 4.2 Testing the standard consistency relation vs the MG consistency relation . 80 CHAPTER 5 INDEX OF INCONSISTENCY (IOI), INTRODUCTION AND PROPERTIES 83 5.1 Why do we need a measure of inconsistency? . 83 5.2 Experimental inconsistencies . 85 5.3 Notations . 88 5.4 The reasoning that leads to the definition of IOI . 89 5.5 Definition of IOI . 91 5.6 Inconsistency measures and Gaussianity . 95 5.7 Factors affecting IOI and inconsistency measures . 97 5.8 Parameter marginalization and IOI . 99 vii 5.9 Two single-parameter measures . 101 5.10 IOI eigenmodes of inconsistency . 103 5.11 IOI in nested models . 104 5.12 Nuisance and unshared parameters . 106 5.13 Summary of this chapter . 107 CHAPTER 6 COMPARISON WITH OTHER MEASURES OF INCONSISTENCY IN THE LITERATURE . 109 6.1 The robustness - A Bayes evidence ratio . 109 6.2 The Tension - Another Bayes evidence ratio . 116 6.3 The discordance .................................... 118 6.4 The distribution of the difference vector and the measure C ............. 120 6.5 The surprise ...................................... 123 6.6 The calibrated evidence ratio . 126 6.7 Level of concordance . 127 6.8 Relation between IOI and the Surprise ........................ 127 6.9 Quantifying inconsistency between geometry and growth . 129 6.9.1 Data sets . 130 6.9.2 Results from application to data: A moderate to strong inconsistency . 133 6.9.3 two measures in wCDM . 136 6.10 Summary of this chapter . 137 CHAPTER 7 APPLICATION OF THE INDEX OF INCONSISTENCY . 139 7.1 Introduction . 140 7.2 Methodology, algorithm to find dataset outlier or breakdown of the model . 142 7.3 Hubble constant from five methods . 146 7.4 Internal (in)consistency between Planck temperature and polarization data sets . 151 7.5 Consistency between Large-scale-structure data sets . 153 7.6 Planck vs Large-scale-structure data sets . 154 7.7 Forecasting the level of tension between Planck and LSST cosmic shear . 159 7.8 Summary of this chapter . 161 viii CHAPTER 8 DARK MATTER AND MODIFIED GRAVITY CONFRONT UFDS . 163 8.1 Introduction . 163 8.2 Possible difference between the dark matter and modified gravity scenarios in UFDs 165 8.3 Results - loss of correlation for UFD . 168 8.4 Summary of this chapter . 174 CHAPTER 9 A SUMMARY AND CONCLUDING REMARKS . 176 APPENDIX A METRIC SIGNATURE, SIGN CONVENTION AND UNITS . 180 APPENDIX B DISTANCES IN COSMOLOGY . 181 B.1 The radial co-moving distance and the transverse co-moving distance: . 181 B.2 The luminosity distance: . 184 B.3 The angular diameter distance: . 185 B.4 The co-moving volume: . 186 APPENDIX C ADDITIONAL REMARKS ON THE COSMOLOGICAL CONSTANT . 187 C.1 Geometrical interpretation of the cosmological constant . 187 C.2 Cosmological Constant in QFT . 188 APPENDIX D MG TENSOR PERTURBATIONS DURING INFLATION - DETAILS .
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