skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Light-cone observables and gauge-invariance in the geodesic light-cone formalism

Abstract

The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.

Authors:
;  [1]
  1. Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zürich, Winterthurerstrasse 190, CH-8057, Zürich (Switzerland)
Publication Date:
OSTI Identifier:
22676179
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 06; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPUTERIZED SIMULATION; DISTANCE; GAUGE INVARIANCE; LIGHT CONE; LUMINOSITY; PERTURBATION THEORY; RED SHIFT; UNIVERSE

Citation Formats

Scaccabarozzi, Fulvio, and Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch. Light-cone observables and gauge-invariance in the geodesic light-cone formalism. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/06/007.
Scaccabarozzi, Fulvio, & Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch. Light-cone observables and gauge-invariance in the geodesic light-cone formalism. United States. doi:10.1088/1475-7516/2017/06/007.
Scaccabarozzi, Fulvio, and Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch. Thu . "Light-cone observables and gauge-invariance in the geodesic light-cone formalism". United States. doi:10.1088/1475-7516/2017/06/007.
@article{osti_22676179,
title = {Light-cone observables and gauge-invariance in the geodesic light-cone formalism},
author = {Scaccabarozzi, Fulvio and Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch},
abstractNote = {The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.},
doi = {10.1088/1475-7516/2017/06/007},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 06,
volume = 2017,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}
  • The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodesic-deviation equation, and thus to derive an exact expression for the Jacobi map J{sup A}{sub B}(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J{sup A}{sub B} factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J{sup A}{sub B} is simply given by expressing the GLC quantities in terms of the corresponding ones inmore » the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on light-like signals.« less
  • Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems. This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their theoretical description is verified by checking its gauge-invariance. We argue that cosmological observables are invariant scalars under diffeomorphisms and their theoretical description is gauge-invariant, only at linear order in perturbations. Beyond linear order, they are usually not gauge-invariant, and we provide the general law for the gauge-transformation that the perturbation part of an observable does obey. We apply this finding to derive the second-order expression for the observational light-conemore » average in cosmology and demonstrate that our expression is indeed invariant under diffeomorphisms.« less
  • The difficulty in renormalizing Yang-Mills theory in the light-cone gauge is examined in the Becchi-Rouet-Stora (BRS) invariance formalism. It is shown that the BRS-invariant and nonlocal counterterms, which are necessary for the consistent determination of the divergent coefficients, cannot be absorbed by redefining the fields in the action. A set of renormalization constants for Green's functions is also given.
  • The N = 4 supersymmetric Yang-Mills self-energy is calculated, to one-loop order, in a light-cone gauge that respects power counting and locality of the integrals. The calculation is general, including both physical and unphysical modes (fields). It is found that the self-energy satisfies the Ward identity and that is is infrared finite, but ultraviolet divergent.
  • Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007 (2004)], we construct a system of light-cone coordinates based at a geodesic world line of an arbitrary curved spacetime. The construction involves (i) an advanced-time or a retarded-time coordinate that labels past or future light cones centered on the world line (ii) a radial coordinate that is an affine parameter on the null generators of these light cones, and (iii) angular coordinates that are constant on each generator. The spacetime metric is calculated in the light-cone coordinates, and it is expressed as an expansion in powers of themore » radial coordinate in terms of the irreducible components of the Riemann tensor evaluated on the world line. The formalism is illustrated in two simple applications, the first involving a comoving world line of a spatially flat cosmology, the other featuring an observer placed on the axis of symmetry of Melvin's magnetic universe.« less