DOCSLIB.ORG

Theoretical and Phenomenological Viability of Scalar Field Theories

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

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.
Recommended publications
  • Book of Abstracts

    Book of Abstracts

    The 19th Particles and Nuclei International Conference (PANIC11) Scientific Program Laboratory for Nuclear Science Massachusetts Institute of Technology July 24-29, 2011 Table of Contents Contents Sunday, 24 July 1 Pedagogical Lectures for Students - Kresge Auditorium (09:00-15:45)................. 1 Welcome Reception - Kresge Oval Tent (16:00-19:00) . ................... 1 Monday, 25 July 2 Opening Remarks - Kresge Auditorium (08:30-08:55) . ................... 2 Plenary1 - KresgeAuditorium (08:30-10:05) . ................. 2 Plenary1 - KresgeAuditorium (10:45-12:00) . ................. 2 Parallel 1A - Parity Violating Scattering - W20-307 (MezzanineLounge)(13:30-15:30) . 3 Parallel 1B - Nuclear Effects & Hadronization - W20-306 (20 Chimneys)(13:30-15:30) . 4 Parallel 1C - Recent Baryon Results I - W20-201 (West Lounge) (13:30-15:30). 6 Parallel 1D - Kaonic Atoms and Hypernuclear Physics - 4-149 (13:30-15:30) . 8 Parallel 1E - Neutrino Oscillations I - 4-163 (13:30-15:30) ....................... 10 Parallel 1F - Dark Forces and Dark Matter - 4-153 (13:30-15:30) ................... 12 Parallel 1G - P- and T-violating weak decays - Kresge - RehearsalA(13:30-15:30) . 14 Parallel 1H - Electroweak Cross Sections at the TeV Scale - Kresge - Rehearsal B (13:30-15:30) . 16 Parallel 1I - CKM & CP Violation - Kresge - Little Theatre (13:30-15:30) .............. 17 Parallel 1J - Collider Searches Beyond the Standard Model - Kresge Auditorium (13:30-15:30) . 18 Parallel 1K - Hydrodynamics - W20-407 (13:30-15:30) . ................... 19 Parallel 1L - Heavy Ion Collisions I - W20-491 (13:30-15:30) ...................... 20 Parallel 2A - Generalized Parton Distributions - W20-307 (Mezzanine Lounge) (16:00-17:40). 21 Parallel 2B - Parton Distribution Functions and Fits - W20-306 (20 Chimneys) (16:00-17:40) .
  • Chapter 2 Introduction to Electrostatics

    Chapter 2 Introduction to Electrostatics

    Chapter 2 Introduction to electrostatics 2.1 Coulomb and Gauss’ Laws We will restrict our discussion to the case of static electric and magnetic fields in a homogeneous, isotropic medium. In this case the electric field satisfies the two equations, Eq. 1.59a with a time independent charge density and Eq. 1.77 with a time independent magnetic flux density, D (r)= ρ (r) , (1.59a) ∇ · 0 E (r)=0. (1.77) ∇ × Because we are working with static fields in a homogeneous, isotropic medium the constituent equation is D (r)=εE (r) . (1.78) Note : D is sometimes written : (1.78b) D = ²oE + P .... SI units D = E +4πP in Gaussian units in these cases ε = [1+4πP/E] Gaussian The solution of Eq. 1.59 is 1 ρ0 (r0)(r r0) 3 D (r)= − d r0 + D0 (r) , SI units (1.79) 4π r r 3 ZZZ | − 0| with D0 (r)=0 ∇ · If we are seeking the contribution of the charge density, ρ0 (r) , to the electric displacement vector then D0 (r)=0. The given charge density generates the electric field 1 ρ0 (r0)(r r0) 3 E (r)= − d r0 SI units (1.80) 4πε r r 3 ZZZ | − 0| 18 Section 2.2 The electric or scalar potential 2.2 TheelectricorscalarpotentialFaraday’s law with static fields, Eq. 1.77, is automatically satisfied by any electric field E(r) which is given by E (r)= φ (r) (1.81) −∇ The function φ (r) is the scalar potential for the electric field. It is also possible to obtain the difference in the values of the scalar potential at two points by integrating the tangent component of the electric field along any path connecting the two points E (r) d` = φ (r) d` (1.82) − path · path ∇ · ra rb ra rb Z → Z → ∂φ(r) ∂φ(r) ∂φ(r) = dx + dy + dz path ∂x ∂y ∂z ra rb Z → · ¸ = dφ (r)=φ (rb) φ (ra) path − ra rb Z → The result obtained in Eq.
  • The Penrose and Hawking Singularity Theorems Revisited

    The Penrose and Hawking Singularity Theorems Revisited

    Classical singularity thms. Interlude: Low regularity in GR Low regularity singularity thms. Proofs Outlook The Penrose and Hawking Singularity Theorems revisited Roland Steinbauer Faculty of Mathematics, University of Vienna Prague, October 2016 The Penrose and Hawking Singularity Theorems revisited 1 / 27 Classical singularity thms. Interlude: Low regularity in GR Low regularity singularity thms. Proofs Outlook Overview Long-term project on Lorentzian geometry and general relativity with metrics of low regularity jointly with `theoretical branch' (Vienna & U.K.): Melanie Graf, James Grant, G¨untherH¨ormann,Mike Kunzinger, Clemens S¨amann,James Vickers `exact solutions branch' (Vienna & Prague): Jiˇr´ıPodolsk´y,Clemens S¨amann,Robert Svarcˇ The Penrose and Hawking Singularity Theorems revisited 2 / 27 Classical singularity thms. Interlude: Low regularity in GR Low regularity singularity thms. Proofs Outlook Contents 1 The classical singularity theorems 2 Interlude: Low regularity in GR 3 The low regularity singularity theorems 4 Key issues of the proofs 5 Outlook The Penrose and Hawking Singularity Theorems revisited 3 / 27 Classical singularity thms. Interlude: Low regularity in GR Low regularity singularity thms. Proofs Outlook Table of Contents 1 The classical singularity theorems 2 Interlude: Low regularity in GR 3 The low regularity singularity theorems 4 Key issues of the proofs 5 Outlook The Penrose and Hawking Singularity Theorems revisited 4 / 27 Theorem (Pattern singularity theorem [Senovilla, 98]) In a spacetime the following are incompatible (i) Energy condition (iii) Initial or boundary condition (ii) Causality condition (iv) Causal geodesic completeness (iii) initial condition ; causal geodesics start focussing (i) energy condition ; focussing goes on ; focal point (ii) causality condition ; no focal points way out: one causal geodesic has to be incomplete, i.e., : (iv) Classical singularity thms.
  • Tests of Chameleon Gravity

    Tests of Chameleon Gravity

    Tests of Chameleon Gravity Clare Burrage,a;∗ and Jeremy Saksteinb;y aSchool of Physics and Astronomy University of Nottingham, Nottingham, NG7 2RD, UK bCenter for Particle Cosmology, Department of Physics and Astronomy University of Pennsylvania, Philadelphia, PA 19104, USA Abstract Theories of modified gravity where light scalars with non-trivial self-interactions and non-minimal couplings to matter|chameleon and symmetron theories|dynamically sup- press deviations from general relativity in the solar system. On other scales, the environ- mental nature of the screening means that such scalars may be relevant. The highly- nonlinear nature of screening mechanisms means that they evade classical fifth-force searches, and there has been an intense effort towards designing new and novel tests to probe them, both in the laboratory and using astrophysical objects, and by reinter- preting existing datasets. The results of these searches are often presented using different parametrizations, which can make it difficult to compare constraints coming from dif- ferent probes. The purpose of this review is to summarize the present state-of-the-art searches for screened scalars coupled to matter, and to translate the current bounds into a single parametrization to survey the state of the models. Presently, commonly studied chameleon models are well-constrained but less commonly studied models have large re- gions of parameter space that are still viable. Symmetron models are constrained well by astrophysical and laboratory tests, but there is a desert separating the two scales where the model is unconstrained. The coupling of chameleons to photons is tightly constrained but the symmetron coupling has yet to be explored.
  • Classical and Semi-Classical Energy Conditions Arxiv:1702.05915V3 [Gr-Qc] 29 Mar 2017

    Classical and Semi-Classical Energy Conditions Arxiv:1702.05915V3 [Gr-Qc] 29 Mar 2017

    Classical and semi-classical energy conditions1 Prado Martin-Morunoa and Matt Visserb aDepartamento de F´ısica Te´orica I, Ciudad Universitaria, Universidad Complutense de Madrid, E-28040 Madrid, Spain bSchool of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand E-mail: [email protected]; [email protected] Abstract: The standard energy conditions of classical general relativity are (mostly) linear in the stress-energy tensor, and have clear physical interpretations in terms of geodesic focussing, but suffer the significant drawback that they are often violated by semi-classical quantum effects. In contrast, it is possible to develop non-standard energy conditions that are intrinsically non-linear in the stress-energy tensor, and which exhibit much better well-controlled behaviour when semi-classical quantum effects are introduced, at the cost of a less direct applicability to geodesic focussing. In this chapter we will first review the standard energy conditions and their various limitations. (Including the connection to the Hawking{Ellis type I, II, III, and IV classification of stress-energy tensors). We shall then turn to the averaged, nonlinear, and semi-classical energy conditions, and see how much can be done once semi-classical quantum effects are included. arXiv:1702.05915v3 [gr-qc] 29 Mar 2017 1Draft chapter, on which the related chapter of the book Wormholes, Warp Drives and Energy Conditions (to be published by Springer) will be based. Contents 1 Introduction1 2 Standard energy conditions2 2.1 The Hawking{Ellis type I | type IV classification4 2.2 Alternative canonical form8 2.3 Limitations of the standard energy conditions9 3 Averaged energy conditions 11 4 Nonlinear energy conditions 12 5 Semi-classical energy conditions 14 6 Discussion 16 1 Introduction The energy conditions, be they classical, semiclassical, or \fully quantum" are at heart purely phenomenological approaches to deciding what form of stress-energy is to be considered \physically reasonable".
  • Light Rays, Singularities, and All That

    Light Rays, Singularities, and All That

    Light Rays, Singularities, and All That Edward Witten School of Natural Sciences, Institute for Advanced Study Einstein Drive, Princeton, NJ 08540 USA Abstract This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics at the Institute for Advanced Study, and also at the 2020 New Zealand Mathematical Research Institute summer school in Nelson, New Zealand. Contents 1 Introduction 3 2 Causal Paths 4 3 Globally Hyperbolic Spacetimes 11 3.1 Definition . 11 3.2 Some Properties of Globally Hyperbolic Spacetimes . 15 3.3 More On Compactness . 18 3.4 Cauchy Horizons . 21 3.5 Causality Conditions . 23 3.6 Maximal Extensions . 24 4 Geodesics and Focal Points 25 4.1 The Riemannian Case . 25 4.2 Lorentz Signature Analog . 28 4.3 Raychaudhuri’s Equation . 31 4.4 Hawking’s Big Bang Singularity Theorem . 35 5 Null Geodesics and Penrose’s Theorem 37 5.1 Promptness . 37 5.2 Promptness And Focal Points . 40 5.3 More On The Boundary Of The Future . 46 1 5.4 The Null Raychaudhuri Equation . 47 5.5 Trapped Surfaces . 52 5.6 Penrose’s Theorem . 54 6 Black Holes 58 6.1 Cosmic Censorship . 58 6.2 The Black Hole Region . 60 6.3 The Horizon And Its Generators . 63 7 Some Additional Topics 66 7.1 Topological Censorship . 67 7.2 The Averaged Null Energy Condition .
  • 2 Classical Field Theory

    2 Classical Field Theory

    2 Classical Field Theory In what follows we will consider rather general field theories. The only guiding principles that we will use in constructing these theories are (a) symmetries and (b) a generalized Least Action Principle. 2.1 Relativistic Invariance Before we saw three examples of relativistic wave equations. They are Maxwell’s equations for classical electromagnetism, the Klein-Gordon and Dirac equations. Maxwell’s equations govern the dynamics of a vector field, the vector potentials Aµ(x) = (A0, A~), whereas the Klein-Gordon equation describes excitations of a scalar field φ(x) and the Dirac equation governs the behavior of the four- component spinor field ψα(x)(α =0, 1, 2, 3). Each one of these fields transforms in a very definite way under the group of Lorentz transformations, the Lorentz group. The Lorentz group is defined as a group of linear transformations Λ of Minkowski space-time onto itself Λ : such that M M→M ′µ µ ν x =Λν x (1) The space-time components of Λ are the Lorentz boosts which relate inertial reference frames moving at relative velocity ~v. Thus, Lorentz boosts along the x1-axis have the familiar form x0 + vx1/c x0′ = 1 v2/c2 − x1 + vx0/c x1′ = p 1 v2/c2 − 2′ 2 x = xp x3′ = x3 (2) where x0 = ct, x1 = x, x2 = y and x3 = z (note: these are components, not powers!). If we use the notation γ = (1 v2/c2)−1/2 cosh α, we can write the Lorentz boost as a matrix: − ≡ x0′ cosh α sinh α 0 0 x0 x1′ sinh α cosh α 0 0 x1 = (3) x2′ 0 0 10 x2 x3′ 0 0 01 x3 The space components of Λ are conventional three-dimensional rotations R.
  • Electromagnetic Fields and Energy

    Electromagnetic Fields and Energy

    MIT OpenCourseWare http://ocw.mit.edu Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207. Please use the following citation format: Haus, Hermann A., and James R. Melcher, Electromagnetic Fields and Energy. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed [Date]). License: Creative Commons Attribution-NonCommercial-Share Alike. Also available from Prentice-Hall: Englewood Cliffs, NJ, 1989. ISBN: 9780132490207. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms 8 MAGNETOQUASISTATIC FIELDS: SUPERPOSITION INTEGRAL AND BOUNDARY VALUE POINTS OF VIEW 8.0 INTRODUCTION MQS Fields: Superposition Integral and Boundary Value Views We now follow the study of electroquasistatics with that of magnetoquasistat­ ics. In terms of the flow of ideas summarized in Fig. 1.0.1, we have completed the EQS column to the left. Starting from the top of the MQS column on the right, recall from Chap. 3 that the laws of primary interest are Amp`ere’s law (with the displacement current density neglected) and the magnetic flux continuity law (Table 3.6.1). � × H = J (1) � · µoH = 0 (2) These laws have associated with them continuity conditions at interfaces. If the in­ terface carries a surface current density K, then the continuity condition associated with (1) is (1.4.16) n × (Ha − Hb) = K (3) and the continuity condition associated with (2) is (1.7.6). a b n · (µoH − µoH ) = 0 (4) In the absence of magnetizable materials, these laws determine the magnetic field intensity H given its source, the current density J.
  • Arxiv:1603.06587V1 [Astro-Ph.CO] 21 Mar 2016 Nevertheless They Have Managed to Escape Detection (Thus Far) Through So-Called Screening Mech- Anisms

    Arxiv:1603.06587V1 [Astro-Ph.CO] 21 Mar 2016 Nevertheless They Have Managed to Escape Detection (Thus Far) Through So-Called Screening Mech- Anisms

    Chameleon Dark Energy and Atom Interferometry Benjamin Elder1, Justin Khoury1, Philipp Haslinger3, Matt Jaffe3, Holger M¨uller3;4, Paul Hamilton2 1Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 2Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 3Department of Physics, University of California, Berkeley, CA 94720 4Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 Abstract Atom interferometry experiments are searching for evidence of chameleon scalar fields with ever-increasing precision. As experiments become more precise, so too must theoretical predictions. Previous work has made numerous approximations to simplify the calculation, which in general requires solving a 3-dimensional nonlinear partial differential equation (PDE). In this paper, we introduce a new technique for calculating the chameleonic force, using a numerical relaxation scheme on a uniform grid. This technique is more general than previous work, which assumed spherical symmetry to reduce the PDE to a 1-dimensional ordinary differential equation (ODE). We examine the effects of approximations made in previous efforts on this subject, and calculate the chameleonic force in a set-up that closely mimics the recent experiment of Hamilton et al. Specifically, we simulate the vacuum chamber as a cylinder with dimensions matching those of the experiment, taking into account the backreaction of the source mass, its offset from the center, and the effects of the chamber walls. Remarkably, the acceleration on a test atomic particle is found to differ by only 20% from the approximate analytical treatment. These results allow us to place rigorous constraints on the parameter space of chameleon field theories, although ultimately the constraint we find is the same as the one we reported in Hamilton et al.
  • Chapter 2. Electrostatics

    Chapter 2. Electrostatics

    Chapter 2. Electrostatics Introduction to Electrodynamics, 3rd or 4rd Edition, David J. Griffiths 2.3 Electric Potential 2.3.1 Introduction to Potential We're going to reduce a vector problem (finding E from E 0 ) down to a much simpler scalar problem. E 0 the line integral of E from point a to point b is the same for all paths (independent of path) Because the line integral of E is independent of path, we can define a function called the Electric Potential: : O is some standard reference point The potential difference between two points a and b is The fundamental theorem for gradients states that The electric field is the gradient of scalar potential 2.3.2 Comments on Potential (i) The name. “Potential" and “Potential Energy" are completely different terms and should, by all rights, have different names. There is a connection between "potential" and "potential energy“: Ex: (ii) Advantage of the potential formulation. “If you know V, you can easily get E” by just taking the gradient: This is quite extraordinary: One can get a vector quantity E (three components) from a scalar V (one component)! How can one function possibly contain all the information that three independent functions carry? The answer is that the three components of E are not really independent. E 0 Therefore, E is a very special kind of vector: whose curl is always zero Comments on Potential (iii) The reference point O. The choice of reference point 0 was arbitrary “ambiguity in definition” Changing reference points amounts to adding a constant K to the potential: Adding a constant to V will not affect the potential difference: since the added constants cancel out.
  • The Gammev-CHASE Search for Couplings Between Light and Chameleon Dark Energy

    The Gammev-CHASE Search for Couplings Between Light and Chameleon Dark Energy

    How Dark Is Dark Energy? The GammeV-CHASE Search for Couplings between Light and Chameleon Dark Energy Jason Steffen, FNAL; Amol Upadhye, T-2; Over the past decade, evidence has continued to mount for an astonishing astrophysical phenomenon Alan Baumbaugh, Aaron S. Chou, Peter O. Mazur, known as the cosmic acceleration. The universe appears to be expanding increasingly rapidly; distant ob- Raymond Tomlin, FNAL; A. Weltman, Cape Town; jects are receding faster and faster. If the universe consisted entirely of ordinary matter, and if gravity were William Wester, FNAL well-described by Einstein’s General Relativity, then the expansion of the universe would slow down due to attractive gravitational forces. Thus, the cosmic acceleration demands a significant change to one of our two most fundamental theories. Either General Relativity breaks down on cosmological scales, or a new type of particle must be added to the Standard Model of particle physics, the quantum theory describing all known particles. Since particle physicists have known for some time that General Relativity cannot be incorporated directly into a quantum theory such as the Standard Model, the cosmic acceleration may give some insight into a more fundamental theory unifying gravity and quantum mechanics. he simplest theoretical modification that could explain the theories consistent with current observations are “chameleon” theories, acceleration is the “cosmological constant,” a constant vacuum which “hide” fifth forces and variations in fundamental constants by Tenergy density, which Einstein noted could be added to the equations of becoming massive in high-density regions of the universe. Since massive General Relativity. The contribution of Standard Model fields to the fields give rise to very short-range forces, chameleon dark energies are cosmological constant is approximately 120 orders of magnitude greater notoriously difficult to detect.
  • General Relativistic Energy Conditions: the Hubble Expansion in the Epoch of Galaxy Formation

    General Relativistic Energy Conditions: the Hubble Expansion in the Epoch of Galaxy Formation

    General Relativistic Energy Conditions: The Hubble expansion in the epoch of galaxy formation. Matt Visser† Physics Department Washington University Saint Louis Missouri 63130-4899 USA 26 May 1997; gr-qc/9705070 Abstract The energy conditions of Einstein gravity (classical general relativity) are designed to extract as much information as possible from classical general relativity without enforcing a particular equation of state for the stress-energy. This systematic avoidance of the need to specify a particular equation of state is particularly useful in a cosmological setting — since the equation of state for the cosmological fluid in a Friedmann–Robertson– Walker type universe is extremely uncertain. I shall show that the energy conditions provide simple and robust bounds on the behaviour of both the density and look-back time as a function of red-shift. I shall show that current observations suggest that the so-called strong energy condition (SEC) is violated sometime between the epoch of galaxy formation and the present. This implies that no possible combination of “normal” matter is capable of fitting the observational data. PACS: 98.80.-k; 98.80.Bp; 98.80.Hw; 04.90.+e † E-mail: [email protected] 1 1 Introduction The discussion presented in this paper is a model-independent analysis of the misnamed age-of-the-universe problem, this really being an age-of-the-oldest- stars problem. In this paper I trade off precision against robustness: I sacrifice the precision that comes from assuming a particular equation of state, for the robustness that arises from model independence. A briefer presentation of these ideas can be found in [1], while a related analysis is presented in [2].