Inhomogeneous cosmology in an anisotropic Universe Author: Hayley J. Macpherson Supervisors: Ass. Prof. Daniel Price Dr. Paul Lasky A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy in the Monash Centre for Astrophysics, School of Physics and Astronomy arXiv:1910.13380v1 [astro-ph.CO] 29 Oct 2019 October 30, 2019 iii Copyright notice c Hayley J. Macpherson (2019) This thesis must be used only under the normal conditions of “fair deal- ing” under the Copyright Act. It should not be copied or closely para- phrased in whole or in part without the written consent of the author. Proper written acknowledgement should be made for any assistance ob- tained from this thesis. I certify that I have made all reasonable efforts to secure copyright permissions for third-party content included in this thesis and have not knowingly added copyright content to my work without the owner’s permission. v Abstract With the era of precision cosmology upon us, and upcoming surveys ex- pected to further improve the precision of our observations below the per- cent level, ensuring the accuracy of our theoretical cosmological model is of the utmost importance. Current tensions between our observations and predictions from the standard cosmological model have sparked curiosity in extending the model to include new physics. Although, some sugges- tions include simply accounting for aspects of our Universe that are ignored in the standard model. One example acknowledges the fact that our Uni- verse contains significant density contrasts on small scales; in the form of galaxies, galaxy clusters, filaments, and voids. This small-scale structure is smoothed out in the standard model, by assuming large-scale homogene- ity of the matter distribution, which could have a measurable effect due to the nonlinearity of Einstein’s equations. This backreaction of small-scale structures on the large-scale dynamics has been suggested to explain the measured accelerating expansion rate of the Universe. Current standard cosmological simulations ignore the effects of General Relativity by assuming purely Newtonian dynamics. In this thesis, we take the first steps towards quantifying the backreaction of small-scale struc- tures by performing cosmological simulations that solve Einstein’s equa- tions directly. Simulations like these will allow us to quantify potentially important effects on our observations that could become measurable as the precision of these observations increases into the future. We begin by testing our computational setup to ensure our results are trustworthy. We then present simulations of a realistic matter distribution with initial conditions inspired by the early moments of our own Universe. Analysing the averaged, large-scale evolution of an inhomogeneous uni- verse in full General Relativity, we find negligible difference from small- scale structures. However, we do find significant effects present on small scales that could potentially influence future observations. While we sug- gest improvements to our computational framework to validate our results, we conclude that the backreaction of small-scale structures is unlikely to ex- plain the accelerating expansion of the Universe. Finally, we suggest future extensions to our analysis to improve the quantification of General-Relativistic effects on our cosmological observa- tions. vii Publications list 1. H. J. Macpherson, P. D. Lasky, and D. J. Price (Mar. 2017). “Inhomo- geneous cosmology with numerical relativity”. In: Phys. Rev. D 95.6, 064028, p. 064028. DOI: 10.1103/PhysRevD.95.064028. arXiv: 1611.05447 2. H. J. Macpherson, P. D. Lasky, and D. J. Price (Sept. 2018). “The Trou- ble with Hubble: Local versus Global Expansion Rates in Inhomo- geneous Cosmological Simulations with Numerical Relativity”. In: ApJ 865, L4, p. L4. DOI: 10.3847/2041- 8213/aadf8c. arXiv: 1807.01714 3. H. J. Macpherson, D. J. Price, and P. D. Lasky (Mar. 2019). “Einstein’s Universe: Cosmological structure formation in numerical relativity”. In: Phys. Rev. D 99.6, 063522, p. 063522. DOI: 10.1103/PhysRevD. 99.063522. arXiv: 1807.01711 ix Declaration of Authorship I, Hayley J. Macpherson, hereby declare that this thesis contains no ma- terial which has been accepted for the award of any other degree or diploma at any university or equivalent institution and that, to the best of my knowl- edge and belief, this thesis contains no material previously published or written by another person, except where due reference is made in the text of the thesis. This thesis includes three original papers published in peer reviewed journals in Chapters3,4, and5. The core theme of the thesis is cosmological simulations with numerical relativity. The ideas, development and writing up of all the papers in the thesis were the principal responsibility of myself, the student, working within the School of Physics and Astronomy under the supervision of Ass. Prof. Daniel Price and Dr. Paul Lasky. The inclusion of co-authors reflects the fact that the work came from ac- tive collaboration between researchers and acknowledges input into team- based research. I have renumbered sections of submitted or published pa- pers in order to generate a consistent presentation within the thesis. In the case of Chapters3,4, and5, my contribution to the work in each case is summarised in the table on the following page. Student signature: Date: October 30, 2019 I, Ass. Prof. Daniel Price, hereby certify that the above declaration cor- rectly reflects the nature and extent of the student’s and co-authors’ contri- butions to this work. In instances where I am not the responsible author I have consulted with the responsible author to agree on the respective con- tributions of the authors. Main Supervisor signature: Date: October 30, 2019 Co-author Nature and % of Co-authors, names, nature Thesis chapter Publication title Status student Monash student and % of contribution Y/N contribution Paul Lasky: 10% – Concept, 80% – Concept, coding, Inhomogeneous coding, analysis manuscript cosmology with Published (PRD, 3 of results, input. Daniel N numerical March 2017) manuscript Price: 10% – relativity authorship Concept, manuscript input. Daniel Price: 10% Einstein’s – Concept, Universe: 80% – Concept, coding, Cosmological coding, analysis manuscript Published (PRD, 4 structure of results, input. Paul N March 2019) formation in manuscript Lasky: 10% – numerical authorship Concept, relativity manuscript input. The Trouble with Hubble: Local Paul Lasky: 10% versus Global – Concept, 80% – Concept, Expansion Rates manuscript analysis of in Published (ApJL, input. Daniel 5 results, N Inhomogeneous September 2018) Price: 10% – manuscript Cosmological Concept, authorship x Simulations with manuscript Numerical input. Relativity xi Acknowledgements Firstly, I would like to thank my supervisors, Daniel Price and Paul Lasky. From the beginning of this project back in 2015, you have both chal- lenged me and helped me grow, while always being plenty of fun to work with. I wouldn’t be the scientist I am today if it weren’t for both of your help, encouragement, and breadth of knowledge. I’m inspired by both of your curiosity, without which this work would never have happened. I would like to apologise for being such an expensive student, please accept this thesis as official reimbursement. It’s been a grand journey becoming cosmologists together, we made it. I would also like to thank my collaborators, especially Marco Bruni, Chris Blake, and Julian Adamek, for many valuable discussions and vis- its that helped me get to where I am today. I have been extremely lucky to travel so much during my PhD, and attend many conferences in some amazing places around the world. To everyone I met — and explored, ate, drank, and hiked with — along the way; thank you. Over my 7 years at Monash I have made many lifelong friendships. A special thank you to Izzy for keeping me sane over those years, you will be my best friend for life. I would also like to thank all of my office mates, especially Dave, Conrad, and Zac for priceless banter over the past 4 years. The majority of the postgrad cohort in the School of Physics and Astronomy have contributed to my life at Monash in their own way, so to each of you; thank you. Perhaps my largest thanks goes to Jean Pettigrew, for doing basically everything for everyone, all the time. I know I am not alone in saying that you keep us students afloat. Of course, I would like to thank my parents for their never-ending love and support. Mum, your commitment and success have always inspired me to be the best version of myself I can be, and the care you show for those around you never ceases to amaze me. Hopefully this thesis will be useful in explaining my research to your friends. Dad, your endless encouragement and faith in me are a huge part of my achievements thus far. Thanks for the science chats, South Park and tacos, the good (and the bad) surfs, and of course for being “a cool nerd... the Ultimate Person” (Mark Macpherson, 2014). A special thanks to my Grandma, not only for feeding me and chatting MasterChef, but for your unconditional love and for researching any place I’m travelling to better than I ever do. I love you all, thank you. Lastly, but certainly not least, I would like to thank my girls; Abbey, Meag, and Jess, for always sticking by me and being my best friends and support system since high school, and definitely for the rest of our lives to come. Also, a big thanks to Kym for helping me through the past few months, I couldn’t have done it without you. This research was supported by an Australian Government Research Training Program (RTP) Scholarship. I also acknowledge the Astronomical Society of Australia for their funding support that helped contribute to this work. xiii Contents 1 Introduction and Background1 1.1 Einstein’s field equations .