Astrophysical Tests of Modified Gravity

University of Cambridge Department of Applied Mathematics and Theoretical Physics Astrophysical Tests of Modified Gravity Jeremy Aaron Sakstein This thesis is submitted to the University of Cambridge for the degree of Doctor of Philosophy Downing College Cambridge, United Kingdom March 2014 Ph.D. Dissertation, March 2014 Jeremy Aaron Sakstein Department of Applied Mathematics and Theoretical Physics & Downing College University of Cambridge, United Kingdom This thesis is dedicated to my mother, Laura Sakstein, who unequivocally supported and aided me throughout my entire academic career, which ultimately led to the completion of this thesis. Abstract Einstein’s theory of general relativity has been the accepted theory of gravity for nearly a century but how well have we really tested it? The laws of gravity have been probed in our solar system to extremely high precision using several different tests and general relativity has passed each one with flying colours. Despite this, there are still some mysteries it cannot account for, one of which being the recently discovered acceleration of the universe and this has prompted a theoretical study of modified theories of gravity that can self-accelerate on large scales. Indeed, the next decade will be an exciting era where several satellites will probe the structure of gravity on cosmological scales and put these theoretical predictions to the test. Despite this, one must still worry about the behaviour of gravity on smaller scales and the vast majority of these theories are rendered cosmologically uninteresting when confronted with solar system tests of gravity. This has motivated the study of theories that differ from general relativity on large scales but include screening mechanisms which act to hide any modifications in our own solar system. This then presents the problem of being able to distinguish these theories from general relativity. In the last few years, astrophysical scales have emerged as a new and novel way of probing these theories. These scales encompass the mildly non-linear regime between galactic and cosmological scales where the astrophysical objects have not yet joined the Hubble flow. For this reason, the screening mechanism is active but not overly efficient and novel effects may be present. Furthermore, these tests do not require a large iii iv Abstract sample of galaxies and hence do not require dedicated surveys; instead they can piggyback on other experiments. This thesis explores a class of theories of screened modified gravity which are scalar- tensor theories where the field is conformally coupled to matter via the metric and includes chameleon and symmetron models as well as those that screen using the environment-dependent Damour-Polyakov effect. The thesis is split into two parts. The first is aimed at searching for new and novel astrophysical probes and using them to place new constraints on the model parameters. In particular, we derive the equations governing hydrodynamics in the presence of an external gravitational field that includes the modifications of general relativity. Using this, we derive the equations governing the equilibrium structure of stars and show that unscreened stars are brighter and hotter than their screened counterparts owing to the larger nuclear burning rate in the core needed to combat the additional inward force. These theories have the property that the laws of gravity are different in unscreened galaxies from our own. This means that the inferred distance to an unscreened galaxy using a stellar effect that depends on the law gravity will not agree with a measurement using a different method that is insensitive gravitational physics. We exploit this property by comparing the distances inferred using pulsating Cepheid variable stars, tip of the red giant branch stars and water masers to place new constraints on the model parameters that are three orders of magnitude stronger than those previously reported. Finally, we perturb the equations of modified gravity hydrodynamics to first order and derive the equations governing the oscillations of stars about their equilibrium structure. By solving these equations we show that unscreened stars are more stable to small perturbations than screened stars. Furthermore, we find that the oscillation period is far shorter than was previously estimated and this means that the current constraints can potentially be improved using previous data-sets. We discuss these new results in light of current and future astrophysical tests of modified gravity. The final part of this thesis is dedicated to the search for supersymmetric completions of modified theories of gravity. There have been recent investigations into the quantum stability v of these models and there is evidence that they may suffer from quantum instabilities. Super- symmetric theories enjoy powerful non-renormalisation theories that may help to avoid these issues. For this reason, we construct a framework for embedding these models into global supersymmetry and investigate the new features this introduces. We show how supersymmetry is broken at a scale set by the ambient density and that, with the exception of no-scale models, supergravity corrections already constrain the model parameters to levels where it is not possible to probe the theories with astrophysics or laboratory experiments. Next, we construct a class of supersymmetric chameleon models and investigate their cosmology. In particular, we find that they are indistinguishable from the ΛCDM model at the background level but that they may show deviations in the cold dark matter power spectrum that can be probed using upcoming experiments. Finally, we introduce a novel mechanism where a cosmological constant in the form of a Fayet-Illiopoulos term can appear at late times and investigate the constraints this imposes on the model parameter space. vi Abstract Declaration This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text. In particular, the work presented in chapter3 is based on reference [1], which was authored in collaboration with Anne-Christine Davis, Eugene A. Lim and Douglas J. Shaw and my own work published in reference [2]. The work detailed in chapter4 is published in reference [3] and was done in collaboration with Bhuvnesh Jain and Vinu Vikram. Only results that I made a significant contribution to obtain are detailed. The original research in chapter5 is the result of my own work and is published in reference [2]. The work presented in chapters6 and7 was a collaboration between myself, Anne-Christine Davis and Philippe Brax and is published in ref- erences [4] and [5]. Only work derived by myself or to which I made a significant contribution is presented. This thesis conforms with the regulations set forth by the degree committee of the Faculty of Mathematics. No part of this thesis has been submitted for any other qualification, either to the University of Cambridge or any other institution. vii viii Declaration Acknowledgements First and foremost I would like to thank my supervisor, Anne-Christine Davis, for working so hard to aid me throughout the entirety of my time in Cambridge and beyond. I was fortunate enough to spend the final year of my Ph.D. as a visiting fellow at the Perimeter Institute for Theoretical Physics. I am incredibly grateful to everyone there and especially to Niayesh Afshordi, who took a great interest in my well-being. I enjoyed several productive visits to the University of Pennsylvania and I would like to thank Bhuvnesh Jain for his hospitality whilst there and his continued interest in my work and progress. It was a pleasure to have him as a collaborator. I was fortunate enough to share an office for two years with Raquel H. Ribeiro, my “big sister” who taught me a lot about what it is to be a scientist, a teacher and an academic and continued to be a source of knowledge and wisdom even after she left Cambridge. She always had time for me and I have benefited greatly from it. I would also like to thank Eugene A. Lim, with whom I spent many happy hours chatting about physics. I learned a lot from him, and not just about Lane-Emden models. I had the pleasure of working on several projects with Philippe Brax, who was a great source of knowledge on all things supersymmetry and I would like to thank him for many conversations that certainly improved my knowledge of several different areas of physics. Many of the results obtained in this thesis were obtained using a modified version of the stellar structure code MESA and I would like to thank its author, Bill Paxton, and the rest of the MESA community for answering my many questions. I ran MESA ix x Acknowledgements on the COSMOS supercomputer and I am grateful to Andrey Kaliazin for his assistance with this. I had the pleasure of several enlightening and interesting discussions with Neil Barnaby, Daniel Baumann, Avery Broderick, Carstan van de Bruck, Clare Burrage, Philip Chang, Lam Hui, Justin Khoury, Kazuya Koyama, Baojiu Li, Claudia Maraston, Levon Pogosian, Fabian Schmidt, Douglas J. Shaw, Alessandra Silvestri, Mark Trodden, Jake VanderPlas, Vinu Vikram, Hans Arnold Winther and Dennis Zaritsky. I would like to give a special mention to my friend Adam Solomon, with whom I had many fun times with and who was always ready with a pint of old Rosie and his shisha pipe if things weren’t going so well. Many of my endeavours would certainly have been more complicated if it were not for Amanda Stagg, who often went out of her way to aid me where possible with the more administrative aspects of Cambridge life. Finally, I would also like to thank the other friends I made at DAMTP,who made my time there infinitely more enjoyable: Valentin Assassi, Chris Blair, Mike Blake, Tai-Jun Chen, Tom Hammant, Rahul Jha, Joe Keir, Emanuel Malek, Jessie Muir, Laurence Perreault-Levasseur, Sophie Renner, Alisdair Routh, Marcel Schmittfull, Andrew Singleton, David Twigg and Kenny Wong.

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