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

Scaccabarozzi, Fulvio; Yoo, Jaiyul

doi:10.1088/1475-7516/2017/06/007

Cited by 19 publications

(28 citation statements)

References 34 publications

(136 reference statements)

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“…We provide the connection between two approaches adopted in this paper. The key quantity is the photon wave-vector k µ expressed both in a FRW coordinate and a GLC coordinate (see [48] for details). The photon wave-vector in a FRW coordinate can be expressed as , are sufficient for us to solve the geodesic equations for the wave vector k ν ∇ ν k µ = 0, i.e.…”

Section: B Comparison Of the Photon Wave-vector In Two Approachesmentioning

confidence: 99%

Non-linear general relativistic effects in the observed redshift

Fanizza

Yoo

Biern

2018

J. Cosmol. Astropart. Phys.

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We present the second-order expression for the observed redshift, accounting for all the relativistic effects from the light propagation and from the frame change at the observer and the source positions. We derive the generic gauge-transformation law that any observable quantities should satisfy, and we verify our second-order expression for the observed redshift by explicitly checking its gauge transformation property. This is the first time an explicit verification is made for the second-order calculations of observable quantities. We present our results in popular gauge choices for easy use and discuss the origin of disagreements in previous calculations. arXiv:1805.05959v2 [gr-qc]

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Section: B Comparison Of the Photon Wave-vector In Two Approachesmentioning

confidence: 99%

Non-linear general relativistic effects in the observed redshift

Fanizza

Yoo

Biern

2018

J. Cosmol. Astropart. Phys.

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“…In order to find the θ a o (γ) map, we must thus go beyond the GLC framework, i.e. we need to invoke the tetrad vectors at the observer (see [12]). More precisely, one first needs to consider some other "Cartesian-like" coordinate system x ′µ in which the metric is non-singular at o and k ′µ contains the angular information of the photon geodesic, in order to define a non-singular tetrad and get observed angles through k A o = e ′A µ k ′µ o .…”

Section: Discussionmentioning

confidence: 99%

“…The problem with this manipulation, however, is that one needs to know the map θ a o (γ) beforehand, i.e. one needs to consider the tetrad construction described in the previous section to make the connection [12]. The question we wish to answer here is whether it is possible to determine the θ a o (γ) map within the GLC framework alone, i.e.…”

Section: Observed Vs Glc Anglesmentioning

confidence: 99%

Observed angles and geodesic light-cone coordinates

Mitsou

Scaccabarozzi

Fanizza

2018

Class. Quantum Grav.

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We discuss the interpretation of the angles in the Geodesic Light-Cone (GLC) coordinates. In particular, we clarify the way in which these angles can be identified with the observed ones. We show that, although this identification is always possible in principle, one cannot implement it in the usual gauge-fixing way, i.e. through a set of conditions on the GLC metric. Rather, one needs to invoke a tetrad at the observer and a Cartesian-like coordinate system in order to obtain the desired map globally on the observed sky. *

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“…From the previous paragraph we understand that the 3-cylinder construction is clearly distinct from the observational coordinate [68,69] and geodesic light-cone coordinate [22,42,[69][70][71][72][73][74][75][76][77][78][79][80][81] formalisms, where the angles associated with incoming light-rays are part of a specific coordinate system on M. Although these angles are not defined at the observer, they are an unambiguous parametrization of the incoming light-like geodesics because they are constant along these paths, by construction. There is, however, an important disadvantage in this approach.…”

Section: Caustic Resolutionmentioning

confidence: 99%

“…In particular, caustics of light rays now correspond to the map C → M being non-injective, not to singularities, so our observable maps are definable and computable in the presence of strong lensing as well. This absence of obstruction in resolving caustics is another important feature of our formalism and stands in contrast with the observational coordinate [68,69] and geodesic light-cone coordinate [22,42,[69][70][71][72][73][74][75][76][77][78][79][80][81] approaches for cosmological observables. At the practical level, one no longer needs to compute redshift fluctuations and angular deflections with respect to some reference parametrization (e.g.…”

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confidence: 99%

Tetrad formalism for exact cosmological observables

Mitsou,

Yoo

2019

Preprint

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The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. The corresponding corrections must be taken into account for reliable results at non-linear orders. This can be accomplished by introducing an orthonormal basis, or "tetrad", at the observer point, representing the frame with respect to which observations are performed. In this paper we consider the tetrad formalism of General Relativity, thus associating tetrads to sources as well, and develop a new formalism for describing cosmological observables. It is based on a manifold which we call the "observer space-time", whose coordinates are the proper time, redshift and angles an observer uses to parametrize measurements, and on which the rest of the observables are defined. This manifold does not have to be diffeomorphic to the true space-time and allows us to resolve caustics in the latter, in contrast with similar coordinate-based formalisms. As a concrete example, we work out the definitions and equations for the angular diameter distance, weak lensing and number count observables. As for the observables associated to the CMB, they lie inside the phase space matrix distribution of the photon fluid evaluated at the observer point and pulled back on the observer sky. The second part of this paper is therefore devoted to general-relativistic matrix kinetic theory. Here too the tetrad formalism appears as the natural approach for relating the macroscopic dynamics to the microscopic QFT and therefore for constructing the matrix Boltzmann equations. Part of the presented material is known and is included for completeness, but we provide more detailed discussions over some subtle issues and we also consider an alternative construction of the collision term which deviates from the standard one at higher order in the loop corrections. In summary, the present paper contains all the required structures for computations in cosmology with exact and model-independent cosmological observables. The associated linear perturbation theory will be given in a companion paper.

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

Cited by 19 publications

References 34 publications

Non-linear general relativistic effects in the observed redshift

Non-linear general relativistic effects in the observed redshift

Observed angles and geodesic light-cone coordinates

Tetrad formalism for exact cosmological observables

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