Cosmology with CMB and Large Scale Structure Yin-Zhe Ma Institute of Astronomy and Kavli Institute for Cosmology, Trinity College University of Cambridge A thesis submitted for the degree of Doctor of Philosophy May 2011 2 I hereby declare that my thesis entitled ‘Cosmology with CMB and Large Scale Struc- ture’ is not substantially the same as any that I have submitted for a degree or diploma or other qualification at any other University. I further state that no part of my thesis has already been, or is concurrently being, submitted for any such degree, diploma or other qualification. Most of the original material in this thesis is based on papers that have either been published or submitted for publication as follows 1. Large-Angle Correlations in the Cosmic Microwave Background, G. Efstathiou, Y.Z. Ma, and D. Hanson, MNRAS 407 (2010) 2530; 2. Testing a direction-dependent power spectrum with Planck, Y.Z. Ma, G. Efstathiou, and A. Challinor, Phys. Rev. D 83 (2011) 083005; 3. Constraints on the standard and non-standard early Universe models from CMB B-mode polarization, Y.Z. Ma, W. Zhao and M. Brown, JCAP 10 (2010) 007; 4. Peculiar velocity field: constraining the tilt of the Universe, Y.Z. Ma, C. Gordon and H. Feldman, Phys. Rev. D 80 (2011) 103002; 5. Cosmic Mach Number as A Sensitive Test of Growth of Structure, Y.Z. Ma, J. P. Ostriker and G.B. Zhao, 1106.3327 [arXiv:astro-ph.CO], submitted to Phys. Rev. Lett; Although the original work listed here has been done in collaboration as described above, most of it has been done by the author. Various figures throughout the text are reproduced from the work of other authors, for illustration or discussion. Such figures are always credited in the associated caption. This thesis contains fewer than 60,000 words. Acknowledgements This thesis is about the stories that happened in the early and late time of the Universe, and it should be started by acknowledging the help, support and encouragement from all of my supervi- sors, family and friends which were invaluable to me. Beyond all of the acknowledgement, I would like to make my greatest thanks to my thesis supervisor, George Efstathiou. As a distinguished cosmologist and accomplished supervisor, he always mentors me to choose projects with the highest level of impact, and teaches me to tackle the problems in a distinctive way. His inspiring speeches and broad knowledge of astronomy also influence me a lot. I am looking forward to learning more from George in the years to come. I would also sincerely thank my second supervisor, Anthony Challinor for his help on many difficult problems that I could not solve by myself without his hints and inspiration. At the start of my PhD, I also enjoyed very much his lectures on large scale structure formation which got me quickly involved in real precision cosmology. I would also like to thank the cosmologists at IoA Cambridge with whom I had invaluable discussions: Michael Brown, Donald Lynden-Bell, Simeon Bird, Michael Bridges, Martin Haehnelt, Steven Gratton, Duncan Hanson, Lindsay King, Antony Lewis, Andrew Pontzen, Martin Rees, Richard Shaw. Among these people I would make special thanks to Duncan Hanson, who really helped me a lot with CMB programming at the start of my project; and Prof. Donald Lynden-Bell, for telling me of many interesting topics of astronomy and for inviting me to family gatherings. The Institute of Astronomy at Cambridge University is such an encouraging and thoughtful place where many outstanding scientists have been working. During discussions with Andrew Fabian, Gerry Gilmore, Paul Hewett, Robert Kennicutt and Carolin Crawford, I felt my knowledge of astronomy, was greatly broadened. I also enjoy the friendships with my peer graduate student, Becky Canning, Alex Calverley, Ryan Cooke, Stephanie Hunt, James Mead and James Owen. In addition, I thank the computing team for solving so many technical problems during my 3- year PhD (Hardip, Andrew and Sue). Furthermore, sincere thanks to the administrators of the Institute, Mrs. Margaret Harding, Susan Leatherbarrow, Sian Owen, Paula Younger, and Mr. Mark Hurn for their patient help and great strength of support for my travelling and for my scientific career in general. Margaret is always helpful in making travel arrangements for me to conferences and visits. Paula worked very hard for me to send references and arrange supervisor meetings even when she was several months pregnant. Mark always brings useful books to me when I need them. Before I came to Cambridge, I suffered a lot from bureaucracy imposed by various administrators, and I never encountered supporting staff who were as efficient and helpful as those at Institute of Astronomy. I can say that they are the best secretaries that I have ever met. College life and activities are also very much an important part of three year PhD at Cambridge. Trinity College Cambridge, is not only a prestigious and wealthy college, but also a wonderful place to meet many smart and eminent people in every different subject, and develop personal and professional networks. It is a place to learn about the world and I always feel that I was so lucky to be admitted. I would sincerely give thanks for the financial support from the College and the Cambridge Overseas Trust, and I could not have come to Cambridge for my degree without these funding schemes. In the college life, I am grateful to my English supervisor, Ms. Margaret de Vaux, for her efforts in improving my English reading, speaking and writing. I especially thank Lord Martin Rees, the Master of Trinity College and Astronomer Royal, for discussions on many exciting and important topics in astronomy as well as general science. As a world-famous cosmologist, Martin delivers articulate speeches on various occasions which have taught me how to make the science understandable and appreciated by the general public. At the end of my PhD, I got a “best-speaker” award at Trinity College Annual Science Symposium which I attribute to Martin’s inspiration and influence. His well-known formula, “ability impact” on how to search × for suitable projects, also impressed me a lot. I would like to thank my friends from Trinity with whom I have shared my three-year time with. In particular, I would like to thank my fantastic friends Johanna Tudeau, Juggs Ravalia, Lindsay Chura, Peng Zhao, Ena Hodzik, Sina Bonyadi, Sara Ahmadi, Rebekah Clements, Yang Xia, Xuxiao Zhang, Fangyuan Cheng, Hao Wu, Mao Zeng, Bo Zheng and Mingjie Dai et al.. I know they are less likely to read this thesis but they really deserve thanks. Collaborations are essential to a cosmologist and I have been lucky to work/discuss with many excellent researchers throughout the world during the PhD course. First I must thank Christopher Gordon, Hume Feldman and Douglas Scott for mentoring me closely on a number of occasions, offering new ideas, revising paper drafts, and supporting me in navigating postdoc jobs. I especially thank Douglas Scott and CITA office to support me as the CITA national fellow subsequent my degree. I must also thank Jeremiah Ostriker, Gongbo Zhao, Wen Zhao, Laurie Shaw, Houjun Mo, Xingang Chen, Baojiu Li, Xuelei Chen and Pengjie Zhang for the help and discussion they have given me on various occasions. I really gained much valuable knowledge of cosmology and astronomy from these collaborators. Last but not least, completing a PhD is not possible without the unwavering support from my family and closest people. I would like to thank my parents, Jian-Ming Ma and Yu-Qin Lu, as well as other family members, for their constant love and support. Abstract Cosmology has become a precision science due to a wealth of new precise data from various astronomical observations. It is therefore important, from a methodological point of view, to develop new statistical and numerical tools to study the Cosmic Microwave Background (CMB) radiation and Large Scale Structure (LSS), in order to test different models of the Universe. This is the main aim of this thesis. The standard inflationary Λ-dominated Cold Dark Matter (ΛCDM) model is based on the premise that the Universe is statistically isotropic and homogeneous. This premise needs to be rigorously tested observationally. We study the angular correlation function C(θ) of the CMB sky using the WMAP 5-year data, and find that the low-multipoles can be reconstructed from the data outside the sky cut. We apply a Bayesian analysis and find that S1/2 statistic (S1/2 = [C(θ)]2d cos θ, used by various investigators as a measure of correlations at large angular scales) Rcannot exclude the predictions of the ΛCDM model. We clarify some issues concerning estimation of correlations on large angular scales and their interpretation. To test for deviation from statistical isotropy, we develop a quadratic maximum likelihood estimator which we apply to simulated Planck maps. We show that the temperature maps from Planck mission should be able to constrain the amplitude of any spherical multipole of a scale- invariant quadrupole asymmetry at the 1% level (2σ). In addition, polarization maps are also precise enough to provide complimentary constraints. We also develop a method to search for the direction of asymmetry, if any, in Planck maps. B-mode polarisation of the CMB provides another important test of models of the early Uni- verse. Different classes of models, such as single-field inflation, loop quantum cosmology and cosmic strings give speculative but testable predictions. We find that the current ground-based experiments such as BICEP, already provided fairly tight constraints on these models. We inves- tigate how these constraints might be improved with future observations (e.g.