Covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations

Challinor, A.; Lasenby, A.

doi:10.1103/physrevd.58.023001

Cited by 50 publications

(84 citation statements)

References 13 publications

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“…We use units with c = G = 1 throughout, so that the constant in the Einstein equation is κ = 8π. It should be noted that our convention for the metric signature, which coincides with that in our earlier work on CMB anisotropies in the 1+3 covariant approach [31,32,35], differs from much of the 1+3 covariant literature. It is straightforward to transform from our conventions to those in [34]: g ab → −g ab , ∇ a → ∇ a , and so R abc d → R abc d .…”

Section: Introductionmentioning

confidence: 99%

Microwave background anisotropies from gravitational waves: the 1 + 3 covariant approach

Challinor

2000

Class. Quantum Grav.

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149

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Abstract. We present a 1+3 covariant discussion of the contribution of gravitational waves to the anisotropy of the cosmic microwave background radiation (CMB) in an almost-Friedmann-Robertson-Walker (FRW) universe. Our discussion is based in the covariant approach to perturbations in cosmology, which provides a physically transparent and gauge-invariant methodology for CMB physics. Applying this approach to linearised gravitational waves, we derive a closed set of covariant equations describing the evolution of the shear and the Weyl tensor, and the angular multipoles of the CMB intensity, valid for an arbitrary matter description and background spatial curvature. A significant feature of the present approach is that the normal mode expansion of the radiation distribution function, which arises naturally here, preserves the simple quadrupolar nature of the anisotropic part of the Thomson scattering source terms, and provides a direct characterisation of the power in the CMB at a given angular multipole, as in the recently introduced total angular momentum method. We provide the integral solution of the multipole equations, and analytic solutions for the shear and the Weyl tensor, for models with arbitrary spatial curvature. Numerical results for the CMB power spectrum in open models are also presented, which provide an independent verification of the calculations of other groups.

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Section: Introductionmentioning

confidence: 99%

Microwave background anisotropies from gravitational waves: the 1 + 3 covariant approach

Challinor

2000

Class. Quantum Grav.

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149

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“…In a series of papers [1][2][3][4][5][6][7][8][9][10], a 1+3 covariant and gauge-invariant formalism has been developed with a view to giving a model-independent framework in which to study the physics of the CMB. The approach is based on the projected symmetric trace-free (PSTF) representation of relativistic kinetic theory due to Ellis, Treciokas, and Matravers [11], and Thorne [12], and builds on the covariant and gauge-invariant approach to perturbations in cosmology (e.g.…”

Section: Introductionmentioning

confidence: 99%

Microwave background polarization in cosmological models

Challinor¹

2000

Phys. Rev. D

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130

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We introduce a new multipole formalism for polarized radiative transfer in general spacetime geometries. The polarization tensor is expanded in terms of coordinate-independent, projected symmetric trace-free (PSTF) tensorvalued multipoles. The PSTF representation allows us to discuss easily the observer dependence of the multipoles of the polarization, and to formulate the exact dynamics of the radiation in convenient 1+3 covariant form. For the case of an almost-Friedmann-Robertson-Walker (FRW) cosmological model we recast the Boltzmann equation for the polarization in to a hierarchy of multipole equations. This allows us to give a rigorous treatment of the generation and propagation of the polarization of the cosmic microwave background in almost-FRW models (with open, closed or flat geometries) without recourse to any harmonic decomposition of the perturbations. We also show how expanding the intensity and polarization multipoles in derivatives of harmonic functions gives a streamlined derivation of the mode-expanded multipole hierarchies. Integral solutions to these hierarchies are provided, and the relation of our formalism to others in the literature is discussed.

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“…Equations (12)(13)(14)(15)(16)(17)(18)(19)(20) allow us to find the transformation rule for all kinematic variables. The first one we shall consider is the acceleration of the curves defined by v µ .…”

Section: Covariant Form Of Cosmological Perturbations: Bardeen Xmentioning

confidence: 99%

“…After a quite long discussion, it appeared in the literature two main approaches to deal with such difficulties. In a pioneering paper [3] Hawking introduced the so called covariant approach, which was later used by many authors [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] to define gauge invariant (GI) variables associated with the gradients of background scalar quantities and the Weyl tensor. The second approach was developed by Gerlach and Sengupta [22] and then by Bardeen [23] in the cosmological scenario.…”

Section: Introductionmentioning

confidence: 99%

Covariant Bardeen perturbation formalism

2014

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In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem. Using our mixed and pure tensors approach, we were able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hyper-surface dependence inherent to the covariant approach. Finally, through the use of this map, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hyper-surface invariant variables at any order.

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Covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations

Cited by 50 publications

References 13 publications

Microwave background anisotropies from gravitational waves: the 1 + 3 covariant approach

Microwave background anisotropies from gravitational waves: the 1 + 3 covariant approach

Microwave background polarization in cosmological models

Covariant Bardeen perturbation formalism

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