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Theoretical and Phenomenological Viability of Scalar Field Theories University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2017 Theoretical And Phenomenological Viability Of Scalar Field Theories Benjamin Elder University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Other Physics Commons Recommended Citation Elder, Benjamin, "Theoretical And Phenomenological Viability Of Scalar Field Theories" (2017). Publicly Accessible Penn Dissertations. 3004. https://repository.upenn.edu/edissertations/3004 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/3004 For more information, please contact [email protected]. Theoretical And Phenomenological Viability Of Scalar Field Theories Abstract The objective of this Thesis is to explore several related questions with regards to criteria for viability in scalar field theories. Roughly the first half is vde oted to theoretical criteria, while the second half focuses on phenomenological ones. We begin with an overview of theories that violate the null energy condition, highlighting the pathologies that inevitably appear. We then present a theory that violates the null energy condition while remaining free of the problems that plagued previous attempts. Next we explore a global condition for classical stability in scalar field theories, namely, the requirement that the total energy of the space-time be positive. This property is guaranteed if the theory admits a positive energy theorem. After reviewing existing proofs of positive energy for canonical scalar fields, we then extend those proofs to theories with derivative interactions, proving a positive energy theorem for a wide class of P(X) theories. The second half of this Thesis considers experimental constraints on scalar field theories. eW focus on what may be learned from atom interferometry experiments, which have been a powerful probe of fundamental physics for over two decades but only recently gained the ability to constrain screened scalar field theories. eW present a general analytic and numerical framework for precise predictions of scalar field theories in atom interferometry experiments, and use those techniques to derive new limits on chameleon and symmetron field theories. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Physics & Astronomy First Advisor Justin Khoury Subject Categories Other Physics This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/3004 THEORETICAL AND PHENOMENOLOGICAL VIABILITY OF SCALAR FIELD THEORIES Benjamin Elder A DISSERTATION in Physics and Astronomy Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2017 Supervisor of Dissertation Justin Khoury, Professor of Physics and Astronomy Graduate Group Chairperson Joshua Klein, Professor of Physics and Astronomy Dissertation Committee: Mark Trodden, Fay R. and Eugene L. Langberg Professor of Physics and Astronomy Joshua Klein, Professor of Physics and Astronomy Adam Lidz, Associate Professor of Physics and Astronomy Tom Lubensky, Christopher H. Browne Distinguished Professor of Physics and Astronomy THEORETICAL AND PHENOMENOLOGICAL VIABILITY OF SCALAR FIELD THEORIES c COPYRIGHT 2017 Benjamin Curtis Elder This work is licensed under the Creative Commons Attribution NonCommercial-ShareAlike 3.0 License To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ Acknowledgements Nobody writes a thesis alone, and I am no exception. I am infinitely grateful to my advisor, Justin Khoury, for all of his generous support, encouragement, and knowledge over the past four years. Working with him has been truly inspiring. I admit that there were many times I wished I could stay a graduate student for a decade just so I could stay and keep working on projects with him. I would also like to thank Mark Trodden, who has patiently explained many ideas and concepts to me. There were numerous occasions where I chanced upon him while lost in thought, and he was always happy to hear what I was thinking about and to help un-muddle my thoughts. Thanks are also due to Josh Klein for always having exciting new ideas to discuss, as well as for serving on my thesis committee. On that note, I'd also like to thank Adam Lidz, Tom Lubensky, and Mark Trodden (again) for being on my committee. Warm thanks are also due to all of my collaborators, without whom I would not have been able to do the work presented in this Thesis. I'm also extremely grateful to Austin Joyce for all of his long and elucidating dis- cussions, as well as his encouragement. Arriving at Penn to work on ideas I didn't understand was a daunting prospect and Austin patiently explained a great many things to me, especially in those first few months. I'm similarly grateful to Lasha Berezhiani, Yi-Zen Chu, Garrett Goon, Adam Solomon, Mariana Carrillo Gonzalez, and Rehan Deen. Special thanks are due to Jeremy Sakstein for saving my life by introducing me to BibTeX. I've also been very glad to share an office with Ashley, Mariana, and Yuedong. I'd be remiss not to mention all the care and support I've gotten from my parents, who have always encouraged me to pursue my ambitions, and from Charlotte, who has iii been a steady companion throughout this journey. Bonus points are also due to her for bringing along Nubi and Tink, who quickly became my favorite furry co-authors. iv ABSTRACT THEORETICAL AND PHENOMENOLOGICAL VIABILITY OF SCALAR FIELD THEORIES Benjamin Elder Justin Khoury The objective of this Thesis is to explore several related questions with regards to criteria for viability in scalar field theories. Roughly the first half is devoted to theoretical criteria, while the second half focuses on phenomenological ones. We be- gin with an overview of theories that violate the null energy condition, highlighting the pathologies that inevitably appear. We then present a theory that violates the null energy condition while remaining free of the problems that plagued previous attempts. Next we explore a global condition for classical stability in scalar field theories, namely, the requirement that the total energy of the space-time be positive. This property is guaranteed if the theory admits a positive energy theorem. After reviewing existing proofs of positive energy for canonical scalar fields, we then ex- tend those proofs to theories with derivative interactions, proving a positive energy theorem for a wide class of P (X) theories. The second half of this Thesis considers experimental constraints on scalar field theories. We focus on what may be learned from atom interferometry experiments, which have been a powerful probe of funda- mental physics for over two decades but only recently gained the ability to constrain screened scalar field theories. We present a general analytic and numerical framework for precise predictions of scalar field theories in atom interferometry experiments, and use those techniques to derive new limits on chameleon and symmetron field theories. v Contents 1 Introduction 1 1.1 Scalar fields: kinetic classification . .8 1.2 Effective field theory pathologies . 17 1.3 Atom Interferometry . 21 2 Violating the Null Energy Condition 26 2.1 Attempts to violate the NEC . 33 2.2 A no-go argument for interpolating solutions . 43 2.3 Construction of the theory . 45 2.4 Radiative stability . 51 2.5 NEC violation and neglecting gravity . 52 2.6 Cosmological Evolution . 56 2.7 Stability of perturbations . 57 2.8 Conclusions . 61 3 A Positive Energy Theorem for P (X) Theories 64 3.1 Two-Field Description . 69 3.2 Direct derivation . 72 3.3 Special Cases . 75 3.4 Conclusions . 78 4 Constraints on Chameleon Field Theories 81 4.1 Chameleons: A Brief Review . 87 4.2 Existing Constraints and Motivations for this Work . 93 4.3 Numerical Method . 97 vi 4.4 Successive Steps Towards Realistic Set-Up . 100 4.5 Simulation of the Experiment . 106 4.6 Forecasts for ongoing and upcoming experiments . 108 4.7 Conclusions . 112 5 Constraints on Symmetron Field Theories 113 5.1 Symmetrons: A Brief Review . 115 5.2 Numerical analysis . 118 5.3 Conclusion . 121 6 Conclusions 123 A Screening Factors 125 A.1 The field from a single object . 125 A.2 Motion of an extended object . 128 References 131 vii List of Tables 2.1 Checklist of properties of various theories which possess null energy condition-violating solutions. See Section 1.2 for a discussion of the patholo- gies in this Table. .............................. 42 4.1 Densities of the materials in the experiment. 97 viii List of Figures 1.1 Schematic of the effective potential felt by a chameleon field (solid line), given by the sum of the bare potential of runaway form, V (φ) (dashed line), and a density-dependent piece, from coupling to matter (dotted line). As the 2 density ρ increases, so does the effective mass of the chameleon mφ = Veff ;φφ, which depends on the second derivative of the effective potential about the minimum. ................................. 12 1.2 Schematic of the effective potential felt by a symmetron field. At low den- sities, the quadratic term in the effective potential is negative and the field rolls to a local minimum at a nonzero value of φ (green line). At high den- sities the sign of the quadratic term flips and the minimum of the effective potential is at φ = 0. ............................ 13 1.3 Acceleration of an unscreened test particle towards a massive body in P (X) and Galileon theories, divided by the Newtonian gravitational force. We have arbitrarily chosen Λ = MPl, and both forces have been normalizedp such that Fφ=FN ! 1 at large radii. For P (X), this correspondsp to M = 2MPl, while for the cubic galileon the choice is M = MPl= 3. In both cases the scalar force is strongly suppressed relative to gravity for r < r∗, and P (X) screening is actually more efficient due to the greater degree of non-linearity in its equation of motion.
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