scholarly journals Proper time reparametrization in cosmology: Möbius symmetry and Kodama charges

2021 ◽  
Vol 2021 (12) ◽  
pp. 005
Author(s):  
Jibril Ben Achour
Keyword(s):  
Proper Time ◽  
Conformal Symmetry ◽  
Cosmological Models ◽  
Conformal Weight ◽  
General Mapping ◽  
Gauge Fixing ◽  
Frw Model ◽  
Physical Symmetry ◽  
Time Reparametrization Invariance ◽  
Symmetry Structure

Abstract It has been noticed that for a large class of cosmological models, the gauge fixing of the time-reparametrization invariance does not completely fix the clock. Instead, the system enjoys a surprising residual Noether symmetry under a Möbius reparametrization of the proper time, which maps gauge-inequivalent solutions to the Friedmann equations onto each other. In this work, we provide a unified treatment of this hidden conformal symmetry and its realization in the homogeneous and isotropic sector of the Einstein-Scalar-Λ system. We consider the flat Friedmann-Robertson-Walker (FRW) model, the (A)dS cosmology and provide a first treatment of the model with spatial constant curvature. We derive the general condition relating the choice of proper time and the conformal weight of the scale factor, and give a detailed analysis of the conserved Noether charges generating this physical symmetry. Our approach allows us to identify new realizations of this symmetry while recovering previous results in a unified manner. We also present the general mapping onto the conformal particle and discuss the solution-generating nature of the transformations beyond the Möbius symmetry. Finally, we show that, at least in a restricted context, this hidden conformal symmetry is intimately related to the Kodama charges of spherically symmetric gravity. This new connection suggests that the Möbius invariance of cosmology is only the corner of a larger symmetry structure which could be relevant beyond cosmological models.

Symmetry structure of a wave equation on some classes of Bianchi cosmological models

2014 ◽  
Vol 89 (4) ◽  
pp. 411-416 ◽  
Author(s):  
S. Jamal ◽  
A. H. Kara ◽  
R. Narain ◽  
G. Shabbir
Keyword(s):  
Wave Equation ◽  
Cosmological Models ◽  
Symmetry Structure

Cosmological Models in Lyra Geometry with Linearly Varying Deceleration Parameter

2018 ◽  
Author(s):  
Kalyani Desikan
Keyword(s):  
Exact Solutions ◽  
Displacement Field ◽  
Deceleration Parameter ◽  
Lyra Geometry ◽  
Cosmological Models ◽  
Time Dependent ◽  
Linearly Varying Deceleration Parameter ◽  
Frw Model ◽  
Time Periods ◽  
The Universe

Cosmological models with linearly varying deceleration parameter in the cosmological theory based on Lyra’s geometry have been discussed. Exact solutions have been obtained for a spatially flat FRW model by considering a time dependent displacement field. We have also obtained the time periods during which the universe undergoes decelerated and accelerated expansions for a matter-dominated universe.

scholarly journals EFFECTIVE POTENTIAL FOR A NONRELATIVISTIC NON-ABELIAN CHERN-SIMONS MATTER SYSTEM IN CONSTANT BACKGROUND FIELDS

1995 ◽  
Vol 10 (29) ◽  
pp. 4187-4201
Author(s):  
DIDIER CAENEPEEL ◽  
MARTIN LEBLANC
Keyword(s):  
Effective Potential ◽  
Conformal Symmetry ◽  
Functional Method ◽  
Coupling Constant ◽  
Gauge Fixing ◽  
Matter System ◽  
Background Fields ◽  
Aharonov Bohm ◽  
Chern Simons ◽  
Matter Sector

We present the effective potential for nonrelativistic matter coupled to non-Abelian Chern-Simons gauge fields. We perform the calculation using a functional method in constant background fields to satisfy Gauss’s law and to simplify the computation. Both the quantum gauge and matter fields are integrated over. The gauge-fixing is achieved with an Rξ gauge in the ξ→0 limit. Divergences appearing in the matter sector are regulated via operator regularization. We find no correction to the Chern-Simons coupling constant and the system experiences conformal symmetry breaking to one-loop order except at the known value of self-duality. These results agree with previous analysis of the non-Abelian Aharonov-Bohm scattering.

scholarly journals Symmetries of the black hole interior and singularity regularization

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Marc Geiller ◽  
Etera R. Livine ◽  
Francesco Sartini
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Black Hole Physics ◽  
Proper Time ◽  
White Hole ◽  
Formula Group ◽  
Physical Symmetry ◽  
Black Hole Interior ◽  
Group Quantization

We reveal an \mathfrak{iso}(2,1)𝔦𝔰𝔬(2,1) Poincar'e algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincar'e group ISO(2,1)(2,1), which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS{}_22. At the Lagrangian level, this symmetry corresponds to M"obius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger \textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)BMS3=Diff(S1)⋉Vect(S1) group, where S^1S1 is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincar'e symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.

Conformal symmetric Bianchi type-I cosmologies in f(R) gravity

2018 ◽  
Vol 33 (23) ◽  
pp. 1850134 ◽  
Author(s):  
Dog̃ukan Taṣer ◽  
Melis Ulu Dog̃ru
Keyword(s):  
Perfect Fluid ◽  
Bianchi Type ◽  
Conformal Symmetry ◽  
Cosmological Models ◽  
Value Of Time ◽  
Type I ◽  
Field Equations ◽  
Bianchi Type I ◽  
Symmetry Properties ◽  
Bianchi Type I Universe

In this study, we investigate the Bianchi type-I cosmologies with string cloud attached to perfect fluid in f(R) gravity. The field equations and their exact solutions for Bianchi type-I cosmologies with string cloud attached to a perfect fluid are found by using the conformal symmetry properties. The obtained solutions under the varied selection of arbitrary constants indicate three cosmological models. Isotropy conditions for obtained cosmological models are investigated for large value of time. Whether or not the string cloud in conformal symmetric Bianchi type-I universe supports the isotropy condition for the large value of time has been investigated. Also, we examine the contracting and decelerating features of the obtained solutions by using Raychaudhuri equation. Finally, geometrical and physical results of the solutions are discussed.

scholarly journals GAUGE FIXING AND OBSERVABLES IN GENERAL RELATIVITY

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2475-2482 ◽  
Author(s):  
DONALD SALISBURY
Keyword(s):  
General Relativity ◽  
Transformation Group ◽  
Proper Time ◽  
Free Particle ◽  
Symmetry Transformation ◽  
Time Dependent ◽  
Canonical Variables ◽  
Time Translation ◽  
Field Dependent ◽  
Gauge Fixing

The conventional group of four-dimensional diffeomorphisms is not realizeable as a canonical transformation group in phase space. Yet there is a larger field-dependent symmetry transformation group which does faithfully reproduce 4-D diffeomorphism symmetries. Some properties of this group were first explored by Bergmann and Komar. More recently the group has been analyzed from the perspective of projectability under the Legendre map. Time translation is not a realizeable symmetry, and is therefore distinct from diffeomorphism-induced symmetries. This issue is explored further in this paper. It is shown that time is not "frozen". Indeed, time-like diffeomorphism invariants must be time-dependent. Intrinsic coordinates of the type proposed by Bergmann and Komar are used to construct invariants. Lapse and shift variables are retained as canonical variables in this approach, and therefore will be subject to quantum fluctuations in an eventual quantum theory. Concepts and constructions are illustrated using the relativistic classical and quantum free particle. In this example concrete time-dependent invariants are displayed and fluctuation in proper time is manifest.

scholarly journals GAUGE DEPENDENCE IN CHERN–SIMONS THEORY

1999 ◽  
Vol 14 (03) ◽  
pp. 463-479 ◽  
Author(s):  
F. A. DILKES ◽  
L. C. MARTIN ◽  
D. G. C. MCKEON ◽  
T. N. SHERRY
Keyword(s):  
Proper Time ◽  
Three Dimensional ◽  
Vacuum Expectation ◽  
Three Dimensions ◽  
Simons Theory ◽  
Gauge Parameter ◽  
Gauge Dependence ◽  
Gauge Fixing ◽  
Chern Simons ◽  
Chern Simons Theory

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern–Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter (α) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form [Formula: see text]. This is possible as in three dimensions α is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and ∊μλν is handled unambiguously since the system is three-dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this α dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.

scholarly journals CONFORMAL FIELD THEORY ON R × S3 FROM QUANTIZED GRAVITY

2009 ◽  
Vol 24 (16n17) ◽  
pp. 3073-3110 ◽  
Author(s):  
KEN-JI HAMADA
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Transformation ◽  
Conformal Symmetry ◽  
Conformal Factor ◽  
Combined System ◽  
Four Dimensions ◽  
Gravitational Fields ◽  
Conformal Field ◽  
Gauge Fixing

Conformal algebra on R × S3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess–Zumino action managing nonperturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically is given by a combination of naive conformal transformation and a certain field-dependent gauge transformation. The unitarity issue of gravity is discussed in the context of conformal field theory. We construct physical states by solving the conformal invariance condition and calculate their scaling dimensions. It is shown that the conformal symmetry mixes the positive-metric and the negative-metric modes and thus the negative-metric mode does not appear independently as a gauge invariant state at all.

ON THE CONSTRUCTION OF SHEARFREE COSMOLOGICAL MODELS

2001 ◽  
Vol 16 (20) ◽  
pp. 1321-1325 ◽  
Author(s):  
T. CHROBOK ◽  
Y. N. OBUKHOV ◽  
M. SCHERFNER
Keyword(s):  
Proper Time ◽  
Space Time ◽  
Cosmological Models ◽  
General Space ◽  
Time Description

Using the proper time description and the usual cosmological observer field, it is possible to construct general space–time metrics representing a class of shearfree cosmological models.

Sign in / Sign up

Export Citation Format

Share Document