Covariant analysis of gravitational waves in a cosmological context

Dunsby, Peter K. S.; Bassett, Bruce A.; Ellis, George

doi:10.1088/0264-9381/14/5/023

Cited by 105 publications

(162 citation statements)

References 12 publications

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“…Section 3 begins with a discussion of the covariant description of gravitational waves in cosmology, and presents linearised wave equations, valid for a general matter stress-energy tensor, for the electric and magnetic parts of the Weyl tensor and the shear. These equations extend the perfect-fluid equations given in [37]. Following an expansion in tensor harmonics, in section 4 we give analytic solutions for the shear and the Weyl tensor during matter and radiation domination, extending the solutions given in [37] to the case of nonflat spatial sections.…”

Section: Introductionmentioning

confidence: 75%

“…These equations extend the perfect-fluid equations given in [37]. Following an expansion in tensor harmonics, in section 4 we give analytic solutions for the shear and the Weyl tensor during matter and radiation domination, extending the solutions given in [37] to the case of nonflat spatial sections. We also provide the integral solutions to the mode-expanded radiation multipole equations in the general case.…”

Section: Introductionmentioning

confidence: 75%

“…The 1+3 covariant description of gravitational waves in a cosmological context has been considered by Hawking [42], and more recently by Dunsby, Bassett, & Ellis [37]. Linearised gravitational waves are described by the transverse degrees of freedom in the electric and magnetic parts of the Weyl tensor.…”

Section: Gravitational Waves In An Almost-frw Universementioning

confidence: 99%

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

Challinor

2000

Class. Quantum Grav.

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: 75%

Section: Introductionmentioning

confidence: 75%

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

Challinor

2000

Class. Quantum Grav.

149

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“…Taking an orthonormal eigenframe B of H ab , we may assume that H 22 = H 33 . In this case the (22), (33) and (23) components of (25), (26) immediately give q 1 = −r 1 , σ 23 = 0, n 33 = n 22 and h 1 = 0 (such that h 3 = −h 2 ), while the (12), and (13) components of (25), (26) together with the (2,3) components of (24) lead to…”

Section: Proofmentioning

confidence: 99%

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Wylleman

Bergh

2006

Phys. Rev. D

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Recently the class of purely magnetic non-rotating dust spacetimes has been shown to be empty (Wylleman, Class. Quant. Grav. 23, 2727). It turns out that purely magnetic rotating dust models are subject to severe integrability conditions as well. One of the consequences of the present paper is that also rotating dust cannot be purely magnetic when it is of Petrov type D or when it has a vanishing spatial gradient of the energy density. For purely magnetic and non-rotating perfect fluids on the other hand, which have been fully classified earlier for Petrov type D (Lozanovski, Class. Quant. Grav. 19, 6377), the fluid is shown to be non-accelerating if and only if the spatial density gradient vanishes. Under these conditions, a new and algebraically general solution is found, which is unique up to a constant rescaling, which is spatially homogeneous of Bianchi type V I0, has degenerate shear and is of Petrov type I(M ∞ ) in the extended Arianrhod-McIntosh classification.The metric and the equation of state are explicitly constructed and properties of the model are briefly discussed. We finally situate it within the class of normal geodesic flows with degenerate shear tensor.

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“…We use the gauge-invariant and covariant perturbation approach of Ellis and Bruni [1]. This technique has previously been used to study aspects of gravitational wave propagation in isotropic cosmologies which differ from those considered here (see, for example, [2], [3]). …”

Section: Introductionmentioning

confidence: 99%

Gravitational wave propagation in isotropic cosmologies

Hogan

O’Shea

2002

Phys. Rev. D

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We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modelled as small perturbations of the background Robertson-Walker geometry. The perfect fluid matter distribution of the isotropic background is, in general, modified by small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl tensor is radiative (i.e. type N in the Petrov classification), we construct explicit examples for which the presence of the anisotropic stress is shown to be essential and the histories of the wave-fronts in the background Robertson-Walker geometry are shear-free null hypersurfaces. The examples derived in this case are analogous to the Bateman waves of electromagnetic theory.

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Covariant analysis of gravitational waves in a cosmological context

Cited by 105 publications

References 12 publications

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

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

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Gravitational wave propagation in isotropic cosmologies

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