A Note on the Holst Action, the Time Gauge, and the Barbero-Immirzi
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Immirzi Parameter Without Immirzi Ambiguity: Conformal Loop Quantization of Scalar-Tensor Gravity
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Aberdeen University Research Archive PHYSICAL REVIEW D 96, 084011 (2017) Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity † Olivier J. Veraguth* and Charles H.-T. Wang Department of Physics, University of Aberdeen, King’s College, Aberdeen AB24 3UE, United Kingdom (Received 25 May 2017; published 5 October 2017) Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field setting the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arbitrary group parameter that requires no further fixing as its present standard form does. Here, we find that this can be naturally realized via conformal frame transformations in scalar-tensor gravity. Such a theory generally incorporates a dynamical scalar gravitational field and reduces to general relativity when the scalar field becomes a pure gauge. In particular, we introduce a conformal Einstein frame in which loop quantization is implemented. We then discuss how different Immirzi parameters under this description may be related by conformal frame transformations and yet share the same quantization having, for example, the same area gaps, modulated by the scalar gravitational field. DOI: 10.1103/PhysRevD.96.084011 I. -
A Note on Conformally Compactified Connection Dynamics Tailored For
A note on conformally compactified connection dynamics tailored for anti-de Sitter space N. Bodendorfer∗ Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland October 9, 2018 Abstract A framework conceptually based on the conformal techniques employed to study the struc- ture of the gravitational field at infinity is set up in the context of loop quantum gravity to describe asymptotically anti-de Sitter quantum spacetimes. A conformal compactification of the spatial slice is performed, which, in terms of the rescaled metric, has now finite volume, and can thus be conveniently described by spin networks states. The conformal factor used is a physical scalar field, which has the necessary asymptotics for many asymptotically AdS black hole solutions. 1 Introduction The study of asymptotic conditions on spacetimes has received wide interest within general relativity. Most notably, the concept of asymptotic flatness can serve as a model for isolated systems and one can, e.g., study a system’s total energy or the amount of gravitational ra- diation emitted [1]. More recently, with the discovery of the AdS/CFT correspondence [2], asymptotically anti de Sitter spacetimes have become a focus of interest. In a certain low en- ergy limit of the correspondence, computations on the gravitational side correspond to solving the Einstein equations with anti-de Sitter asymptotics. Within loop quantum gravity (LQG), the issue of non-compact spatial slices or asymptotic conditions on spacetimes has received only little attention so far due to a number of technical reasons. However, also given the recent interest in holography from a loop quantum gravity point of view [3, 4, 5], this question is important to address. -
Open Taveras.Pdf
The Pennsylvania State University The Graduate School LOOP GRAVITY: AN APPLICATION AND AN EXTENSION A Dissertation in Physics by Victor Manuel Taveras c 2009 Victor Manuel Taveras Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2009 The thesis of Victor Manuel Taveras was reviewed and approved∗ by the following: Abhay Ashtekar Eberly Professor of Physics Dissertation Advisor, Chair of Committee Martin Bojowald Professor of Physics Sam Finn Professor of Physics Nigel Higson Professor of Mathematics Richard Robinett Professor of Physics Head of the Department of Physics ∗Signatures are on file in the Graduate School. Abstract In this thesis we address two issues in the area of loop quantum gravity. The first concerns the semiclassical limit in loop quantum cosmology via the use of so-called effective equations. In loop quantum cosmology the quantum dynamics is well understood. We can approximate the full quantum dynamics in the infi- nite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen semiclassical states. This submanifold is iso- morphic with the classical phase space and the projected dynamical flow provides effective equations incorporating the leading quantum corrections to the classical equations of motion. Numerical work has been done in the full theory using quan- tum states which are semiclassical at late times. These states follow the classical trajectory until the density is on the order of 1% of the Planck density then deviate strongly from the classical trajectory. The effective equations we obtain reproduce this behavior to surprising accuracy. The second issue concerns generalizations of the classical action which is the starting point for loop quantum gravity. -
Arxiv:1108.1178V2 [Gr-Qc]
Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model Aristide Baratin∗1 and Daniele Oriti†2 1Centre de Physique Th´eorique, CNRS UMR 7644, Ecole Polytechnique F-9112 Palaiseau Cedex, France 2Max-Planck-Institut f¨ur Gravitationsphysik Albert Einstein Institute Am M¨uhlenberg 2, 14476, Golm, Germany, EU A dual formulation of group field theories, obtained by a Fourier transform mapping functions on a group to functions on its Lie algebra, has been proposed recently. In the case of the Ooguri model for SO(4) BF theory, the variables of the dual field variables are thus so(4) bivectors, which have a direct interpretation as the discrete B variables. Here we study a modification of the model by means of a constraint operator implementing the simplicity of the bivectors, in such a way that projected fields describe metric tetrahedra. This involves a extension of the usual GFT framework, where boundary operators are labelled by projected spin network states. By construction, the Feynman amplitudes are simplicial path integrals for constrained BF theory. We show that the spin foam formulation of these amplitudes corresponds to a variant of the Barrett-Crane model for quantum gravity. We then re-examin the arguments against the Barrett-Crane model(s), in light of our construction. Introduction Group field theories (GFT) represent a second quantized framework for both spin networks and simplicial geometry [6, 7, 9], field theories on group manifolds (or Lie algebras) producing Feynman amplitudes which can be equivalently expressed as simplicial gravity path integrals [5] or spin foam models [10], in turn covariant formulations of spin networks dynamics [1]3. -
Tsallis, Rényi and Sharma-Mittal Holographic Dark Energy Models in Loop Quantum Cosmology
S S symmetry Article Tsallis, Rényi and Sharma-Mittal Holographic Dark Energy Models in Loop Quantum Cosmology Abdul Jawad 1 , Kazuharu Bamba 2,*, Muhammad Younas 1, Saba Qummer 1 and Shamaila Rani 1 1 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore-54000, Pakistan; [email protected] or [email protected] (A.J.); [email protected] (M.Y.); [email protected] (S.Q.); [email protected] (S.R.) 2 Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296, Japan * Correspondence: [email protected] Received: 7 October 2018; Accepted: 31 October 2018; Published: 13 Novemebr 2018 Abstract: The cosmic expansion phenomenon is being studied through the interaction of newly proposed dark energy models (Tsallis, Rényi and Sharma-Mittal holographic dark energy (HDE) models) with cold dark matter in the framework of loop quantum cosmology. We investigate different cosmic implications such as equation of state parameter, squared sound speed and cosmological plane 0 0 (wd-wd, wd and wd represent the equation of state (EoS) parameter and its evolution, respectively). It is found that EoS parameter exhibits quintom like behavior of the universe for all three models of HDE. The squared speed of sound represents the stable behavior of Rényi HDE and Sharma-Mittal 0 HDE at the latter epoch while unstable behavior for Tsallis HDE. Moreover, wd-wd plane lies in the thawing region for all three HDE models. Keywords: cosmoligical parameters; dark energy models; loop quantum cosmology 1. Introduction Observational data from type Ia supernovae (SNIa) [1–4], the large scale structure (LSS) [5–8] and the cosmic microwave background (CMB), anisotropies [9–11], tell us that the universe undergoes an accelerated expansion at the present time. -
An Introduction to Loop Quantum Gravity with Application to Cosmology
DEPARTMENT OF PHYSICS IMPERIAL COLLEGE LONDON MSC DISSERTATION An Introduction to Loop Quantum Gravity with Application to Cosmology Author: Supervisor: Wan Mohamad Husni Wan Mokhtar Prof. Jo~ao Magueijo September 2014 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London Abstract The development of a quantum theory of gravity has been ongoing in the theoretical physics community for about 80 years, yet it remains unsolved. In this dissertation, we review the loop quantum gravity approach and its application to cosmology, better known as loop quantum cosmology. In particular, we present the background formalism of the full theory together with its main result, namely the discreteness of space on the Planck scale. For its application to cosmology, we focus on the homogeneous isotropic universe with free massless scalar field. We present the kinematical structure and the features it shares with the full theory. Also, we review the way in which classical Big Bang singularity is avoided in this model. Specifically, the spectrum of the operator corresponding to the classical inverse scale factor is bounded from above, the quantum evolution is governed by a difference rather than a differential equation and the Big Bang is replaced by a Big Bounce. i Acknowledgement In the name of Allah, the Most Gracious, the Most Merciful. All praise be to Allah for giving me the opportunity to pursue my study of the fundamentals of nature. In particular, I am very grateful for the opportunity to explore loop quantum gravity and its application to cosmology for my MSc dissertation. -
Asymptotically Flat Boundary Conditions for the U(1)3 Model for Euclidean Quantum Gravity
universe Article Asymptotically Flat Boundary Conditions for the U(1)3 Model for Euclidean Quantum Gravity Sepideh Bakhoda 1,2,* , Hossein Shojaie 1 and Thomas Thiemann 2,* 1 Department of Physics, Shahid Beheshti University, Tehran 1983969411, Iran; [email protected] 2 Institute for Quantum Gravity, FAU Erlangen—Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany * Correspondence: [email protected] (S.B.); [email protected] (T.T.) 3 Abstract: A generally covariant U(1) gauge theory describing the GN ! 0 limit of Euclidean general relativity is an interesting test laboratory for general relativity, specially because the algebra of the Hamiltonian and diffeomorphism constraints of this limit is isomorphic to the algebra of the corresponding constraints in general relativity. In the present work, we the study boundary conditions and asymptotic symmetries of the U(1)3 model and show that while asymptotic spacetime translations admit well-defined generators, boosts and rotations do not. Comparing with Euclidean general relativity, one finds that the non-Abelian part of the SU(2) Gauss constraint, which is absent in the U(1)3 model, plays a crucial role in obtaining boost and rotation generators. Keywords: asymptotically flat boundary conditions; classical and quantum gravity; U(1)3 model; asymptotic charges Citation: Bakhoda, S.; Shojaie, H.; 1. Introduction Thiemann, T. Asymptotically Flat In the framework of the Ashtekar variables in terms of which General Relativity (GR) Boundary Conditions for the U(1)3 is formulated as a SU(2) gauge theory [1–3], attempts to find an operator corresponding to Model for Euclidean Quantum the Hamiltonian constraint of the Lorentzian vacuum canonical GR led to the result [4] that Gravity. -
Observational Test of Inflation in Loop Quantum Cosmology
AEI-2011-042 Observational test of inflation in loop quantum cosmology Martin Bojowald1, Gianluca Calcagni2, and Shinji Tsujikawa3 1Institute for Gravitation and the Cosmos, The Pennsylvania State University 104 Davey Lab, University Park, PA 16802, U.S.A. 2Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am M¨uhlenberg 1, D-14476 Golm, Germany 3Department of Physics, Faculty of Science, Tokyo University of Science 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan E-mail: [email protected], [email protected], [email protected] Abstract: We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous set- tings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulas for the scalar/tensor power spectra under the slow-roll approximation, by taking into ac- count corrections of order higher than the runnings. We place observational bounds on the inverse-volume quantum correction δ a−σ (σ> 0, a is the scale factor) and arXiv:1107.1540v1 [gr-qc] 8 Jul 2011 ∝ the slow-roll parameter ǫV for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on δ for two pivot wavenumbers k0 for several values of δ. The quadratic potential can be compatible with the data even in the presence of the LQC correc- tions, but the quartic potential is in tension with observations. -
On Superstatistics and Black Hole Quasinormal Modes
On superstatistics and black hole quasinormal modes. Aldo Mart´ınez-Merinoa , M. Sabidob a Departamento de Ciencias Naturales y Exactas, CU Valles, Universidad de Guadalajara. Carretera Guadalajara - Ameca Km. 45.5, C.P. 46600, Ameca, Jalisco, M´exico. b Departamento de F´ısicade la Universidad de Guanajuato, A.P. E-143, C.P. 37150, Le´on,Guanajuato, M´exico. Abstract It is known that one can determine that lowest value of spin is jmin = 1, by using the quasinormal modes of black holes, the Bekenstein-Hawking entropy and Boltzmann-Gibbs statistics. In this paper, to determine jmin, we have used non extensive entropies that depend only on the probability (known as Obregon’s entropies and have been derived from superstatistics), as well as non extensive entropies that have free parameters . We find that jmin depends on the area and the non extensive parameter. In particular, for the non extensive entropies that only depend on the probability and find that the modification is only present for micro black holes. For classical black holes, the results are the same as for the Boltzmann-Gibbs statistics. 1. Introduction Black holes are one of the most enigmatic and enticing objects of study and just recently, a direct verification of their existence was provided by Event Horizon Telescope collaboration [1]. Despite the amount of research on the subject there are several unanswered questions. Quantization of black holes was proposed in the pioneering work of Bekenstein [2], he suggested that the surface gravity is proportional to its temperature and that the area of its event horizon is proportional to its entropy. -
Gravitational Axial Perturbations and Quasinormal Modes of Loop Quantum Black Holes
Eur. Phys. J. C (2019) 79:157 https://doi.org/10.1140/epjc/s10052-019-6565-2 Regular Article - Theoretical Physics Gravitational axial perturbations and quasinormal modes of loop quantum black holes M. B. Cruz1,a,C.A.S.Silva2,b,F.A.Brito1,3,c 1 Departamento de Física, Universidade Federal da Paraíba, João Pessoa, Paraíba 58051-970, Brazil 2 Instituto Federal de Educação Ciência e Tecnologia da Paraíba (IFPB), Campus Campina Grande-Rua Tranquilino Coelho Lemos 671, Jardim Dinamérica I, João Pessoa, Brazil 3 Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, Campina Grande 58429-900, Paraíba, Brazil Received: 3 November 2018 / Accepted: 3 January 2019 / Published online: 21 February 2019 © The Author(s) 2019 Abstract Loop quantum gravity (LQG) is a theory that pro- ular, in the context of this theory, a black hole metric known as poses a way to model the behavior of the spacetime in sit- loop quantum black hole (LQBH), or self-dual black hole, has uations where its atomic characteristic arises. Among these been proposed [10,11]. This solution corresponds to a quan- situations, the spacetime behavior near the Big Bang or black tum corrected Schwarzschild solution and possess the inter- hole’s singularity. The detection of gravitational waves, on esting property of self-duality. From this property, the black the other hand, has opened the way to new perspectives in the hole singularity is removed and replaced by another asymp- investigation of the spacetime structure. In this work, by the totically flat region, which is an expected effect in a quantum use of a WKB method introduced by Schutz and Will (Astro- gravity regime. -
Quantum Gravity Effects in Scalar, Vector and Tensor Field Propagation
QUANTUM GRAVITY EFFECTS IN SCALAR, VECTOR AND TENSOR FIELD PROPAGATION ANINDITA DUTTA Bachelor of Science, West Bengal State University, 2012 Master of Science, RKM Vivekananda University, 2014 A Thesis Submitted to the School of Graduate Studies of the University of Lethbridge in Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE Department of Physics and Astronomy University of Lethbridge LETHBRIDGE, ALBERTA, CANADA c Anindita Dutta, 2016 QUANTUM GRAVITY EFFECTS IN SCALAR, VECTOR AND TENSOR FIELD PROPAGATION ANINDITA DUTTA Date of Defense: December 12, 2016 Dr. Arundhati Dasgupta Supervisor Associate Professor Ph.D. Dr. Ken Vos Committee Member Associate Professor Ph.D. Dr. Stacey Wetmore Committee Member Professor Ph.D. Dr. Viqar Husain External Committee Member Professor Ph.D. Dr. Mark Walton Chair, Thesis Examination Com- Professor Ph.D. mittee Dedication To my Parents for supporting me all the way. And to my Teachers who made me who I am. iii Abstract Quantum theory of gravity deals with the physics of the gravitational field at Planck length scale (10−35 m). Even though it is experimentally hard to reach the Planck length scale, one can look for evidence of quantum gravity that is detectable in astrophysics. In this thesis, we try to find effects of loop quantum gravity corrections on observable phenomena. We show that the quantum fluctuation strain for LIGO data would be 10−125 on the Earth. The correction is, however, substantial near the black hole horizon. We discuss the effect of this for scalar field propagation followed by vector and tensor fields. For the scalar field, the correction introduces a new asymmetry; for the vector field, we found a new perturbation solution and for the tensor field, we found the corrected Einstein equations which are yet to solve. -
On the Relations Between Gravity and BF Theories⋆
Symmetry, Integrability and Geometry: Methods and Applications SIGMA 8 (2012), 032, 15 pages On the Relations between Gravity and BF Theories? Laurent FREIDEL y and Simone SPEZIALE z y Perimeter Institute, 31 Caroline St N, Waterloo ON, N2L 2Y5, Canada E-mail: [email protected] z Centre de Physique Th´eorique,CNRS-UMR 7332, Luminy Case 907, 13288 Marseille, France E-mail: [email protected] Received January 23, 2012, in final form May 18, 2012; Published online May 26, 2012 http://dx.doi.org/10.3842/SIGMA.2012.032 Abstract. We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell{ Mansouri action. Key words: Plebanski action; MacDowell{Mansouri action; BF gravity; TQFT; modified theories of gravity 2010 Mathematics Subject Classification: 83C45 1 Introduction It is an intriguing fact that general relativity can be given a polynomial action principle which relates it to topological BF theory. The fundamental variable is a connection, and the metric is a derived quantity. For BF theory alone, a Lagrange multiplier, B, enforces the curvature of the connection to be constant. This type of theories require no metric to be formulated, and posses no local degrees of freedom. The relation with general relativity is established through the extraction of metric degrees of freedom from the fundamental fields. There are mainly two ways of achieving this that have appeared in the literature, based on original work by Plebanski [77] and by MacDowell and Mansouri [66].