DOCSLIB.ORG

Testing General Relativity in Cosmology

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Testing General Relativity in Cosmology Living Reviews in Relativity (2019) 22:1 https://doi.org/10.1007/s41114-018-0017-4 REVIEW ARTICLE Testing general relativity in cosmology Mustapha Ishak1 Received: 28 May 2018 / Accepted: 6 November 2018 © The Author(s) 2018 Abstract We review recent developments and results in testing general relativity (GR) at cosmo- logical scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy asso- ciated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, gravitational screening mechanisms, and computer codes developed for these tests. We then provide summaries of recent cosmological constraints on MG parameters and selected MG models. We supplement these cosmological constraints with a summary of implications from the recent binary neutron star merger event. Next, we summarize some results on MG parameter forecasts with and without astrophysical systematics that will dominate the uncertainties. The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field. It can also serve as a quick reference to recent results and constraints on testing gravity at cosmological scales. Keywords Tests of relativistic gravity · Theories of gravity · Modified gravity · Cosmological tests · Post-Friedmann limit · Gravitational waves Contents 1 Introduction ............................................... 2 General relativity (GR) ......................................... 2.1 Basic principles .......................................... 2.2 Einstein field equations (EFEs) and their exact solutions ..................... 3 The standard model of cosmology ................................... 3.1 The homogeneous cosmological background ........................... 3.1.1 FLRW metric and Friedmann’s equations ......................... B Mustapha Ishak [email protected] 1 Department of Physics, The University of Texas at Dallas, Richardson, TX 75080, USA 0123456789().: V,-vol 123 1 Page 2 of 204 M. Ishak 3.1.2 Cosmic mass-energy budget, dark energy and cosmic acceleration ............ 3.1.3 Cosmological distances .................................. 3.2 The inhomogeneous lumpy universe and the growth of large-scale structure .......... 3.2.1 Large-scale structure and cosmological perturbations .................. 3.2.2 Growth factor and growth rate of large-scale structure .................. 3.2.3 Correlation function and matter power spectrum ..................... 4 Cosmological probes of gravity theory ................................. 4.1 Probes of cosmic geometry and expansion ............................ 4.1.1 Standard candles: type Ia supernova ........................... 4.1.2 Standard rulers: angular distance to CMB last scattering surface and baryon acoustic oscillations ......................................... 4.1.3 Local measurements of the Hubble constant or measurements of H(z) .......... 4.2 Weak gravitational lensing .................................... 4.3 Galaxy surveys: clustering and redshift space distortions (RSD) ................. 4.4 Cosmic microwave background radiation ............................. 4.4.1 Integrated Sachs–Wolfe (ISW) effect ........................... 4.4.2 CMB lensing ........................................ 5 Formalisms and approaches to testing GR at cosmological scales ................... 5.1 Effective field theory (EFT) approach to dark energy and modified gravity ........... 5.2 Modified growth parameters ................................... 5.3 Evolution of MG parameters in time and scale .......................... 5.4 The growth index parameter γ .................................. 5.5 The EG -parameter test ...................................... 5.6 Parameterized post-Friedmann formalism ............................ 5.7 Remarks on transition to nonlinear scales ............................ 6 Constraints and results on MG parameters (i.e., deviations from GR) from current cosmological data sets ................................................. 6.1 Constraints on modified growth parameters ........................... 6.1.1 Constraints from Planck CMB, ISW, CMB lensing, and other data sets ......... 6.1.2 Constraints on MG parameters from mainly weak lensing data ............. 6.1.3 Constraints on MG parameters from various probes and analyses ............ 6.2 Constraints on f σ8 from galaxy surveys and RSD measurements ............... 6.3 Constraints on EG ........................................ 7 Types of modifications to GR at cosmological scales and corresponding MG models ........ 7.1 Cartan–Weyl–Lovelock theorem ................................. 7.2 Modified gravity versus dark energy ............................... 7.3 Modified gravity theories with extra fields ............................ 7.3.1 Theories with extra scalar field .............................. 7.3.2 Extra vector field(s) .................................... 7.3.3 Extra vector and scalar fields ............................... 7.3.4 Extra tensor fields ..................................... 7.4 Modified gravity theories with higher-order derivatives ..................... 7.4.1 Illustrative example 1: f (R) theories ........................... 7.4.2 Illustrative example 2: Hoˇrava–Lifshitz .......................... 7.4.3 Other higher order derivative theories ........................... 7.5 Modified gravity theories with higher-dimensions ........................ 7.5.1 Theories with compact dimensions versus braneworld models .............. 7.5.2 Illustrative example : Dvali–Gabadadze–Porrati gravity (DGP) ............. 7.6 Non-local modified gravity theories ............................... 7.6.1 Illustrative example: RR model .............................. 7.6.2 Other non-local gravity theories .............................. 8 Screening mechanisms ......................................... 8.1 Large-mass based screening .................................... 8.2 Weak-coupling based screening .................................. 8.3 Large kinetic terms based screening ............................... 9 Constraints on MG models from current cosmological data sets .................... 9.1 Constraints on Horndeski and beyond Horndeski models .................... 123 Testing general relativity in cosmology Page 3 of 204 1 9.2 Constraints on Brans–Dicke theory ................................ 9.3 Constraints on vector–tensor and generalized Einstein aether theories .............. 9.4 Constraints on massive gravity and bigravity ........................... 9.5 Constraints on f (R) models ................................... 9.6 Constraints on DGP models .................................... 9.7 Constraints on Galileon models .................................. 9.8 Constraints on TeVeS ....................................... 9.9 Constraints on non-local gravity models ............................. 10 Constraints on deviations from GR and MG models from neutron star merger event GW170817/GRB170817A 10.1 Implications for scalar–ensor theories .............................. 10.1.1 Implications for Horndeski models ............................ 10.1.2 Implications for Beyond Horndeski models ........................ 10.2 Implications for vector–tensor theories .............................. 10.3 Implications for massive gravity and bigravity theories ..................... 10.4 Implications for ghost condensates and Horˇava–Lifshitz Gravity ................ 10.5 Implications for higher dimension models ............................ 10.6 Implications for results on MG parameters and large-scale-structure from GW170817 and GRB170817A ........................................... 10.7 Implications for Vainshtein screening mechanism after GW170810 and GRB170817A ..... 10.8 Further notes or caveats on the implications of GW170817 and GRB170817A ......... 11 Computer codes and packages for testing gravity at cosmological scales ............... 11.1 Integrated Software in Testing General Relativity (ISiTGR) .................. 11.2 Modification of growth with CAMB (MGCAMB)andMGCosmoMC ................ 11.3 Horndeski in CLASS (hi_class) ............................... 11.4 Effective field theory with CAMB (EFTCAMB)and(EFTCosmoMC) ............... 11.5 Recent comparison of Einstein–Boltzmann solver codes for testing general relativity ...... 12 Systematic effects in cosmological probes and degeneracies with modifications to GR ........ 13 Future cosmological constraints on GR and MG parameter forecasts ................. 14 Concluding remarks and outlook .................................... References .................................................. 1 Introduction For over a century, Einstein’s general relativity (GR) has continued to be an impressive theory of gravity that fits observations from our solar system to the entire cosmological model of the universe. Guided by some key principles, Einstein came to the important realization of a very close relationship between the curvature of spacetime and gravity. Taking into account further requirements, such as coordinate invariance, conservation laws, and limits that must be consistent with Newtonian gravity, he proposed his grav- itational field equations (Einstein 1915). Astonishingly, the same simple
Load more

Recommended publications
  • Galaxies 2013, 1, 1-5; Doi:10.3390/Galaxies1010001
    Galaxies 2013, 1, 1-5; doi:10.3390/galaxies1010001 OPEN ACCESS galaxies ISSN 2075-4434 www.mdpi.com/journal/galaxies Editorial Galaxies: An International Multidisciplinary Open Access Journal Emilio Elizalde Consejo Superior de Investigaciones Científicas, Instituto de Ciencias del Espacio & Institut d’Estudis Espacials de Catalunya, Faculty of Sciences, Campus Universitat Autònoma de Barcelona, Torre C5-Parell-2a planta, Bellaterra (Barcelona) 08193, Spain; E-Mail: [email protected]; Tel.: +34-93-581-4355 Received: 23 October 2012 / Accepted: 1 November 2012 / Published: 8 November 2012 The knowledge of the universe as a whole, its origin, size and shape, its evolution and future, has always intrigued the human mind. Galileo wrote: “Nature’s great book is written in mathematical language.” This new journal will be devoted to both aspects of knowledge: the direct investigation of our universe and its deeper understanding, from fundamental laws of nature which are translated into mathematical equations, as Galileo and Newton—to name just two representatives of a plethora of past and present researchers—already showed us how to do. Those physical laws, when brought to their most extreme consequences—to their limits in their respective domains of applicability—are even able to give us a plausible idea of how the origin of our universe came about and also of how we can expect its future to evolve and, eventually, how its end will take place. These laws also condense the important interplay between mathematics and physics as just one first example of the interdisciplinarity that will be promoted in the Galaxies Journal. Although already predicted by the great philosopher Immanuel Kant and others before him, galaxies and the existence of an “Island Universe” were only discovered a mere century ago, a fact too often forgotten nowadays when we deal with multiverses and the like.
    [Show full text]
  • PRESS RELEASE Solved: the Mystery of the Expansion of the Universe
    PRESS RELEASE Geneva | March 10th, 2020 The earth, solar system, entire Milky Way and the few thousand ga- Solved: laxies closest to us move in a vast “bubble” that is 250 million light years in diameter, where the average density of matter is half as large the mystery as for the rest of the universe. This is the hypothesis put forward by a theoretical physicist from the University of Geneva (UNIGE) to solve of the expansion a conundrum that has been splitting the scientific community for a decade: at what speed is the universe expanding? Until now, at least of the universe two independent calculation methods have arrived at two values that are different by about 10% with a deviation that is statistically A UNIGE researcher has irreconcilable. This new approach, which is set out in the journal Phy- solved a scientific sics Letters B, erases this divergence without making use of any “new controversy about the speed physics”. of the expansion The universe has been expanding since the Big Bang occurred 13.8 bil- of the universe by lion years ago – a proposition first made by the Belgian canon and suggesting that it is not physicist Georges Lemaître (1894-1966), and first demonstrated by Edwin Hubble (1889-1953). The American astronomer discovered in totally homogeneous on a 1929 that every galaxy is pulling away from us, and that the most dis- large scale. tant galaxies are moving the most quickly. This suggests that there was a time in the past when all the galaxies were located at the same spot, a time that can only correspond to the Big Bang.
    [Show full text]
  • Some Aspects in Cosmological Perturbation Theory and F (R) Gravity
    Some Aspects in Cosmological Perturbation Theory and f (R) Gravity Dissertation zur Erlangung des Doktorgrades (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn von Leonardo Castañeda C aus Tabio,Cundinamarca,Kolumbien Bonn, 2016 Dieser Forschungsbericht wurde als Dissertation von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Bonn angenommen und ist auf dem Hochschulschriftenserver der ULB Bonn http://hss.ulb.uni-bonn.de/diss_online elektronisch publiziert. 1. Gutachter: Prof. Dr. Peter Schneider 2. Gutachter: Prof. Dr. Cristiano Porciani Tag der Promotion: 31.08.2016 Erscheinungsjahr: 2016 In memoriam: My father Ruperto and my sister Cecilia Abstract General Relativity, the currently accepted theory of gravity, has not been thoroughly tested on very large scales. Therefore, alternative or extended models provide a viable alternative to Einstein’s theory. In this thesis I present the results of my research projects together with the Grupo de Gravitación y Cosmología at Universidad Nacional de Colombia; such projects were motivated by my time at Bonn University. In the first part, we address the topics related with the metric f (R) gravity, including the study of the boundary term for the action in this theory. The Geodesic Deviation Equation (GDE) in metric f (R) gravity is also studied. Finally, the results are applied to the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime metric and some perspectives on use the of GDE as a cosmological tool are com- mented. The second part discusses a proposal of using second order cosmological perturbation theory to explore the evolution of cosmic magnetic fields. The main result is a dynamo-like cosmological equation for the evolution of the magnetic fields.
    [Show full text]
  • Penetration of Fast Projectiles Into Resistant Media: from Macroscopic
    Penetration of fast projectiles into resistant media: from macroscopic to subatomic projectiles Jos´e Gaite Applied Physics Dept., ETSIAE, Universidad Polit´ecnica de Madrid, E-28040 Madrid, Spain∗ (Dated: July 21, 2017) The penetration of a fast projectile into a resistant medium is a complex process that is suitable for simple modeling, in which basic physical principles can be profitably employed. This study connects two different domains: the fast motion of macroscopic bodies in resistant media and the interaction of charged subatomic particles with matter at high energies, which furnish the two limit cases of the problem of penetrating projectiles of different sizes. These limit cases actually have overlapping applications; for example, in space physics and technology. The intermediate or mesoscopic domain finds application in atom cluster implantation technology. Here it is shown that the penetration of fast nano-projectiles is ruled by a slightly modified Newton’s inertial quadratic force, namely, F ∼ v2−β , where β vanishes as the inverse of projectile diameter. Factors essential to penetration depth are ratio of projectile to medium density and projectile shape. Keywords: penetration dynamics; energy loss; collisions; supersonic motion. I. INTRODUCTION Between subatomic and macroscopic projectiles, there is a mesoscopic range of nano-projectiles, with important technological applications.23 The few studies of their re- The analytical study of the resistance to the motion of lation to macroscopic projectiles24,25 only treat particu- projectiles begins with Book Two of Newton’s Principia, lar aspects of the problem. Here we study the problem entitled The motion of bodies (in resisting mediums).1 of resistance to projectile penetration within a unified Other classics have studied this subject, which has obvi- conceptual framework that applies to the full ranges of ous applications, for example, military applications.
    [Show full text]
  • Open Sloan-Dissertation.Pdf
    The Pennsylvania State University The Graduate School LOOP QUANTUM COSMOLOGY AND THE EARLY UNIVERSE A Dissertation in Physics by David Sloan c 2010 David Sloan Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2010 The thesis of David Sloan was reviewed and approved∗ by the following: Abhay Ashtekar Eberly Professor of Physics Dissertation Advisor, Chair of Committee Martin Bojowald Professor of Physics Tyce De Young Professor of Physics Nigel Higson Professor of Mathematics Jayanth Banavar Professor of Physics Head of the Department of Physics ∗Signatures are on file in the Graduate School. Abstract In this dissertation we explore two issues relating to Loop Quantum Cosmology (LQC) and the early universe. The first is expressing the Belinkskii, Khalatnikov and Lifshitz (BKL) conjecture in a manner suitable for loop quantization. The BKL conjecture says that on approach to space-like singularities in general rela- tivity, time derivatives dominate over spatial derivatives so that the dynamics at any spatial point is well captured by a set of coupled ordinary differential equa- tions. A large body of numerical and analytical evidence has accumulated in favor of these ideas, mostly using a framework adapted to the partial differential equa- tions that result from analyzing Einstein's equations. By contrast we begin with a Hamiltonian framework so that we can provide a formulation of this conjecture in terms of variables that are tailored to non-perturbative quantization. We explore this system in some detail, establishing the role of `Mixmaster' dynamics and the nature of the resulting singularity. Our formulation serves as a first step in the analysis of the fate of generic space-like singularities in loop quantum gravity.
    [Show full text]
  • The Cosmological Constant Einstein’S Static Universe
    Some History TEXTBOOKS FOR FURTHER REFERENCE 1) Physical Foundations of Cosmology, Viatcheslav Mukhanov 2) Cosmology, Michael Rowan-Robinson 3) A short course in General Relativity, J. Foster and J.D. Nightingale DERIVATION OF FRIEDMANN EQUATIONS IN A NEWTONIAN COSMOLOGY THE COSMOLOGICAL PRINCIPAL Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers. This amounts to the strongly philosophical statement that the part of the Universe which we can see is a fair sample, and that the same physical laws apply throughout. => the Hubble expansion is a natural property of an expanding universe which obeys the cosmological principle Distribution of galaxies on the sky Distribution of 2.7 K microwave radiation on the sky vA = H0. rA vB = H0. rB v and r are position and velocity vectors VBA = VB – VA = H0.rB – H0.rA = H0 (rB - rA) The observer on galaxy A sees all other galaxies in the universe receding with velocities described by the same Hubble law as on Earth. In fact, the Hubble law is the unique expansion law compatible with homogeneity and isotropy. Co-moving coordinates: express the distance r as a product of the co-moving distance x and a term a(t) which is a function of time only: rBA = a(t) . x BA The original r coordinate system is known as physical coordinates. Deriving an equation for the universal expansion thus reduces to determining a function which describes a(t) Newton's Shell Theorem The force acting on A, B, C, D— which are particles located on the surface of a sphere of radius r—is the gravitational attraction from the matter internal to r only, acting as a point mass at O.
    [Show full text]
  • Formation of Structure in Dark Energy Cosmologies
    HELSINKI INSTITUTE OF PHYSICS INTERNAL REPORT SERIES HIP-2006-08 Formation of Structure in Dark Energy Cosmologies Tomi Sebastian Koivisto Helsinki Institute of Physics, and Division of Theoretical Physics, Department of Physical Sciences Faculty of Science University of Helsinki P.O. Box 64, FIN-00014 University of Helsinki Finland ACADEMIC DISSERTATION To be presented for public criticism, with the permission of the Faculty of Science of the University of Helsinki, in Auditorium CK112 at Exactum, Gustaf H¨allstr¨omin katu 2, on November 17, 2006, at 2 p.m.. Helsinki 2006 ISBN 952-10-2360-9 (printed version) ISSN 1455-0563 Helsinki 2006 Yliopistopaino ISBN 952-10-2961-7 (pdf version) http://ethesis.helsinki.fi Helsinki 2006 Helsingin yliopiston verkkojulkaisut Contents Abstract vii Acknowledgements viii List of publications ix 1 Introduction 1 1.1Darkenergy:observationsandtheories..................... 1 1.2Structureandcontentsofthethesis...................... 6 2Gravity 8 2.1Generalrelativisticdescriptionoftheuniverse................. 8 2.2Extensionsofgeneralrelativity......................... 10 2.2.1 Conformalframes............................ 13 2.3ThePalatinivariation.............................. 15 2.3.1 Noethervariationoftheaction..................... 17 2.3.2 Conformalandgeodesicstructure.................... 18 3 Cosmology 21 3.1Thecontentsoftheuniverse........................... 21 3.1.1 Darkmatter............................... 22 3.1.2 Thecosmologicalconstant........................ 23 3.2Alternativeexplanations............................
    [Show full text]
  • The Dark Energy of the Universe the Dark Energy of the Universe
    The Dark Energy of the Universe The Dark Energy of the Universe Jim Cline, McGill University Niels Bohr Institute, 13 Oct., 2015 image: bornscientist.com J.Cline, McGill U. – p. 1 Dark Energy in a nutshell In 1998, astronomers presented evidence that the primary energy density of the universe is not from particles or radiation, but of empty space—the vacuum. Einstein had predicted it 80 years earlier, but few people believed this prediction, not even Einstein himself. Many scientists were surprised, and the discovery was considered revolutionary. Since then, thousands of papers have been written on the subject, many speculating on the detailed properties of the dark energy. The fundamental origin of dark energy is the subject of intense controversy and debate amongst theorists. J.Cline, McGill U. – p. 2 Outline Part I History of the dark energy • Theory of cosmological expansion • The observational evidence for dark energy • Part II What could it be? • Upcoming observations • The theoretical crisis !!! • J.Cline, McGill U. – p. 3 Albert Einstein invents dark energy, 1917 Two years after introducing general relativity (1915), Einstein looks for cosmological solutions of his equations. No static solution exists, contrary to observed universe at that time He adds new term to his equations to allow for static universe, the cosmological constant λ: J.Cline, McGill U. – p. 4 Einstein’s static universe This universe is a three-sphere with radius R and uniform mass density of stars ρ (mass per volume). mechanical analogy potential energy R R By demanding special relationships between λ, ρ and R, λ = κρ/2 = 1/R2, a static solution can be found.
    [Show full text]
  • 3.1 the Robertson-Walker Metric
    M. Pettini: Introduction to Cosmology | Lecture 3 RELATIVISTIC COSMOLOGY 3.1 The Robertson-Walker Metric The appearance of objects at cosmological distances is affected by the curvature of spacetime through which light travels on its way to Earth. The most complete description of the geometrical properties of the Universe is provided by Einstein's general theory of relativity. In GR, the fundamental quantity is the metric which describes the geometry of spacetime. Let's look at the definition of a metric: in 3-D space we measure the distance along a curved path P between two points using the differential distance formula, or metric: (d`)2 = (dx)2 + (dy)2 + (dz)2 (3.1) and integrating along the path P (a line integral) to calculate the total distance: Z 2 q Z 2 q ∆` = (d`)2 = (dx)2 + (dy)2 + (dz)2 (3.2) 1 1 Similarly, to measure the interval along a curved wordline, W, connecting two events in spacetime with no mass present, we use the metric for flat spacetime: (ds)2 = (cdt)2 − (dx)2 − (dy)2 − (dz)2 (3.3) Integrating ds gives the total interval along the worldline W: Z B q Z B q ∆s = (ds)2 = (cdt)2 − (dx)2 − (dy)2 − (dz)2 (3.4) A A By definition, the distance measured between two events, A and B, in a reference frame for which they occur simultaneously (tA = tB) is the proper distance: q ∆L = −(∆s)2 (3.5) Our search for a metric that describes the spacetime of a matter-filled universe, is made easier by the cosmological principle.
    [Show full text]
  • Neutrino Cosmology and Large Scale Structure
    Neutrino cosmology and large scale structure Christiane Stefanie Lorenz Pembroke College and Sub-Department of Astrophysics University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity 2019 Neutrino cosmology and large scale structure Christiane Stefanie Lorenz Pembroke College and Sub-Department of Astrophysics University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity 2019 The topic of this thesis is neutrino cosmology and large scale structure. First, we introduce the concepts needed for the presentation in the following chapters. We describe the role that neutrinos play in particle physics and cosmology, and the current status of the field. We also explain the cosmological observations that are commonly used to measure properties of neutrino particles. Next, we present studies of the model-dependence of cosmological neutrino mass constraints. In particular, we focus on two phenomenological parameterisations of time-varying dark energy (early dark energy and barotropic dark energy) that can exhibit degeneracies with the cosmic neutrino background over extended periods of cosmic time. We show how the combination of multiple probes across cosmic time can help to distinguish between the two components. Moreover, we discuss how neutrino mass constraints can change when neutrino masses are generated late in the Universe, and how current tensions between low- and high-redshift cosmological data might be affected from this. Then we discuss whether lensing magnification and other relativistic effects that affect the galaxy distribution contain additional information about dark energy and neutrino parameters, and how much parameter constraints can be biased when these effects are neglected.
    [Show full text]
  • Analysis and Simulation of Hypervelocity Gouging Impacts
    Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-13-2006 Analysis and Simulation of Hypervelocity Gouging Impacts John D. Cinnamon Follow this and additional works at: https://scholar.afit.edu/etd Part of the Engineering Science and Materials Commons Recommended Citation Cinnamon, John D., "Analysis and Simulation of Hypervelocity Gouging Impacts" (2006). Theses and Dissertations. 3318. https://scholar.afit.edu/etd/3318 This Dissertation is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. Analysis and Simulation of Hypervelocity Gouging Impacts DISSERTATION John D. Cinnamon, Major, USAF AFIT/DS/ENY/06-01 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this work are those of the author and do not reflect the official policy or position of the Department of Defense or the United States Government. AFIT/DS/ENY/06-01 Analysis and Simulation of Hypervelocity Gouging Impacts DISSERTATION Presented to the Faculty Department of Aeronautics and Astronautics Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy John D. Cinnamon, B.S.E., M.S.E., P.E. Major, USAF June 2006 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT/DS/ENY/06-01 Abstract Hypervelocity impact is an area of extreme interest in the research community.
    [Show full text]
  • Challenges to Self-Acceleration in Modified Gravity from Gravitational
    Physics Letters B 765 (2017) 382–385 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Challenges to self-acceleration in modified gravity from gravitational waves and large-scale structure ∗ Lucas Lombriser , Nelson A. Lima Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK a r t i c l e i n f o a b s t r a c t Article history: With the advent of gravitational-wave astronomy marked by the aLIGO GW150914 and GW151226 Received 2 September 2016 observations, a measurement of the cosmological speed of gravity will likely soon be realised. We show Received in revised form 19 December 2016 that a confirmation of equality to the speed of light as indicated by indirect Galactic observations Accepted 19 December 2016 will have important consequences for a very large class of alternative explanations of the late-time Available online 27 December 2016 accelerated expansion of our Universe. It will break the dark degeneracy of self-accelerated Horndeski Editor: M. Trodden scalar–tensor theories in the large-scale structure that currently limits a rigorous discrimination between acceleration from modified gravity and from a cosmological constant or dark energy. Signatures of a self-acceleration must then manifest in the linear, unscreened cosmological structure. We describe the minimal modification required for self-acceleration with standard gravitational-wave speed and show that its maximum likelihood yields a 3σ poorer fit to cosmological observations compared to a cosmological constant. Hence, equality between the speeds challenges the concept of cosmic acceleration from a genuine scalar–tensor modification of gravity.
    [Show full text]