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Constraints on Cosmology and Quantum Gravity from Quantum Mechanics and Quantum Field Theory

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Constraints on Cosmology and Quantum Gravity from Quantum Mechanics and Quantum Field Theory Thesis by Jason Pollack In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2017 Defended May 19, 2017 ii c 2017 Jason Pollack ORCID: 0000-0003-4754-4905 All rights reserved iii Acknowledgments Many individuals and groups of people helped shape my time at Caltech: • The Friday night dinner/drinks/D&D group: Dustin Anderson, Kevin Barkett, Tony Bartolotta, Jonathan Blackman, Daniel Brooks, and Jeremy Brouillet. • The Sunday night TV-watching group: Joe Lozier, Dan Pershey, and Paul Plucinsky. • My parents, for their continuing support of my pursuit of academia, despite the transformation over the last five years of even the titles of my papers into incomprehensibility. • My fellow Ph 20/21/22 TAs: Casey Handmer, Jenia Mozgunov, and Masha Okounkova; and • The Ph 20/21/22 instructors, Alan Weinstein and Tom Prince, who were always willing to let us do our own thing and practically run the course, making it both great fun and great experience to TA. • Senior grad students: Tristan Mckinney, Ingmar Saberi, Chia Hsien Shen, and especially Kim Boddy. • Junior grad students: Charles Cao, Aidan Chatwin-Davies, and Ashmeet Singh. • Grad students in my year: Enrico Herrmann, Nick Hunter-Jones, Murat Kologlu, Grant Remmen, and especially my officemate, Tony Bartolotta. • Postdocs: Stefan Leichenauer in my first years at Caltech and Ning Bao more recently, mentors, inspirations, and dispensers of invaluable advice on how to survive grad school and take the next steps forward into academia. • Cliff Cheung and Mark Wise, for sharing some of their vast knowledge of quan- tum field theory with me over the years, and for always having their doors open for me to wander in and ask a question when I was stuck. iv • The Cosmological Quantum Mechanics reading group, the impetus for the ideas for a number of the papers presented herein, and also responsible for the on- going development of what seems to be a unique and fruitful set of ideas on how to think about the emergence of spacetime and structure from the Hilbert space. I’m glad to have been a part of it from the beginning, and I wouldn’t be surprised if fifty years from now we’re all writing up our recollections of its its first steps. • Everyone who participated in our many wide-ranging lunch conversations, some of them even about physics, at the tables outside of Chandler and the bookstore over the last five years. We never succeeded in solving the cosmological constant problem once and for all, but it was still worth trying. • Everyone involved with the Caltech GSC, who let me progress from wandering into a meeting lured by free food in 2013 to chairing Caltech’s grad student government in 2015-6, and discover in the process that I both enjoyed and was good at a whole set of skills and subjects I’d never contemplated before: – The wonderful faculty, deans, administrators, and staff I had the oppor- tunity to work with and even to select, and who encouraged me rather than saying I was crazy when I just showed up and started doing things. In the grad office and Caltech adminstration: Felicia Hunt, Kate McAn- ulty, Doug Rees, Tom Rosenbaum, Joe Shepherd, and Cindy Weinstein. In Physics and PMA: Olga Batygin, Cliff Cheung, Fiona Harrison, Lynne Hillenbrand, Sofie Leon, and Gil Refael. I was privileged to be a part of the committees that picked Doug, Kate, and Sofie for their positions, and so I get to claim a (very) small part of the credit for all of the positive change they’ve created, and will continue to create, at Caltech! – GSC Steering buddies: Sunita Darbe, Henry Ngo, Andrew Robbins, Emily Blythe, Natalie Higgins, Gina Duggan. – Finally, especially, Alicia Lanz and Allison Strom. I’m so, so, grateful for your friendship over these last two years, and for all the great conversations and shenanigans it entailed. I wish it had started earlier, and I look forward to it continuing for a long, long time! • All of my collaborators, especially: v – Paul Steinhardt and David Spergel, who helped me bridge the gap from Princeton to Caltech and were endlessly patient and encouraging coau- thors on a paper that took much longer to come to fruition than it should have (entirely my fault!) but which I’m very glad I persisted with; – Stefan Leichenauer, for guiding me through my first paper and pushing me out of my comfort zone to explore new fields; – Kim Boddy, for permitting me to jump on board with her collaboration with Sean, enduring endless stupid arguments about grammar, serving as an inspiration that there really was life after Caltech, and sticking with the collaboration even once she’d moved to Hawai’i; – Ning Bao, for coming in to the Cosmo QM group and catalyzing an incred- ible amount of new research, for always pushing to take the half-formed idea we’d come up with at lunch or in group meeting and turn it into a paper, for endless irrelevant and irreverent comments to keep me on my toes, and for that whole year you’d sneak into my office and stand up the Superman flash drive on my desk; – Grant Remmen, for being just as obsessed with grammar and punctuation as I am (much to Ning’s chagrin), for being the resident GR expert while still knowing how to translate crazy differential geometry and incredibly confusing terminology into something I could get physical intuition for, and for inadvertently getting me involved with the GSC; – Aidan Chatwin-Davies, for putting up with me barging into his office at random times with bizarre questions, for reporting on Sean’s whereabouts, for suggestions for paper titles I’m sad we never used, for giving me inside info on Vancouver and UBC, not to mention Japan, for all the gaming hilarity, and for having way too many ways for us to get in touch with each other (I count 9); – Tony Bartolotta, for similarly letting me snipe his collaboration, being willing to put in the time to buckle down and work through the calcu- lations when the rest of us made excuses, constantly letting me bounce ideas and questions off of him, from notation to formatting to rants about QFT in curved space—and, no less importantly, for letting me dragoon him into DMing, for the endless chats about the craziness of American politics, and for putting up with me teasing him endlessly about that time vi he glued himself to the printer and that time he baked his laptop in the oven; • And, of course, my advisor, Sean Carroll. From the time I wandered into his office before the beginning of my first year and was immediately ushered into a collaboration with him and Stefan, through what must have been dozens of hours of meetings with him and Kim where we hashed out just what the late- time structure of de Sitter space and its derivatives looked like, to his unabating support of my career as I applied for postdocs, I couldn’t have asked for a more supportive and collaborative academic partner and mentor. That’s not even to mention the many speaker dinners, or Cosmo QM, or his patient toleration of my decision to become GSC chair. As I continue on with my career to UBC and wherever comes after that, Sean will be the model I’ll always try to emulate for how to collaborate, how to advise, and how to do physics. vii Abstract Typical cosmological states have structure, obey to very good approximation the laws of classical physics on large scales, and are far from equilibrium. Typical quantum- mechanical states have none of these properties. If the universe is described by a state in a Hilbert space, the state and its Hilbert space must therefore obey a number of constraints to describe realistic cosmological spacetimes. In particular, they must admit a quantum-to-classical transition via decoherence that allows for the emergence of classical spacetimes, and such spacetimes must obey gravitational constraints, in particular on the entanglement entropy of subsystems within them. The papers collected in this thesis are concerned with these constraints. We investigate two holographic correspondences inspired by AdS/CFT, the AdS-MERA correspondence, which suggests that anti-de Sitter space may be given a discretized description as a tensor network, and the ER=EPR duality, which identified entangled qubits with wormholes connecting them. In the former case, we use holographic entropy bounds to severely constrain the properties of any such tensor network; in the latter case we prove a new general-relativistic area theorem which states that an area corresponding to the entanglement entropy in wormhole geometries is exactly conserved. We use information-theoretic constraints to show that under mild assumptions about the black hole interior an observer falling beyond the horizon is unable to verify the claimed cloning of information in the firewall paradox before reaching the singularity. Finally, we analyze the decoherence structures of late-time de Sitter space and early- time slow-roll eternal inflation. We show that in the former case a universe with an infinite-dimensional Hilbert space and a positive cosmological constant inevitably reaches a maximum-entropy state from which no further branching or decoherence is possible, forbidding the existence of dynamical quantum fluctuations at late time. In the latter case, gravitational-strength interaction among inflaton modes leads to decoherence of sufficiently super-Hubble modes, which we argue backreacts to cause different histories of cosmological evolution on different branches and hence creates the conditions necessary for eternal inflation.
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