Cosmological perturbations and the physical meaning of gauge-invariant variables

Bruni, Marco; Dunsby, Peter K. S.; Ellis, George

doi:10.1086/171629

Cited by 261 publications

(490 citation statements)

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“…constant on the fluid flow lines). This is easily done by writing the Laplace-Beltrami operator for∇ a and defining our harmonics as the eigenfunction of the Helmoltz equation (see [27] for more details):…”

Section: B Harmonic Decompositionmentioning

confidence: 99%

Gauge invariant perturbations of scalar-tensor cosmologies: The vacuum case

2006

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Section: B Harmonic Decompositionmentioning

confidence: 99%

Gauge invariant perturbations of scalar-tensor cosmologies: The vacuum case

2006

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“…see [24], but the relation between these and the covariant ones used here has not yet been established; cf. [19,20] …”

Section: Brane Dynamicsmentioning

confidence: 99%

“…Scalar gauge-invariant perturbations can be described using covariantly defined variables (see [18,19] and references therein). In the brane scenario this formalism has been developed in [1,16] (see also [21]); here we shall follow the same approach, with minor modifications, and we refer to these papers for definitions.…”

Section: Density Perturbationsmentioning

confidence: 99%

Singularities on the brane are not isotropic

Bruni

Dunsby

2002

Phys. Rev. D

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Recent studies of homogeneous anisotropic universe models in the brane world scenario show that the cosmological singularity in this context is isotropic. It has therefore been suggested that this may be a generic feature of singularities on the brane, even in the inhomogeneous case. Using a perturbative approach, we show that this is not the case. As in the GR case, the presence of decaying modes in the perturbations signal the instability (in the past) of the isotropic singularity. The brane universe is therefore not born with isotropy built in: as in standard cosmology, the observed large-scale isotropy and homogeneity remains to be explained.

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“…The tensor [R αβµν ] is necessarily the solution of Eq. (24) corresponding to the initial data [R αβµν ] U . The results above for non-empty Einstein's equations G µν = −kT µν are easily proven due to the continuity of T µν through Σ and can be seen in Lichnerowicz, 1960 or Novello & Salim, 1985.…”

Section: Equivalence Between Qm Equations and Grmentioning

confidence: 99%

The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory

2014

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A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent quantities. We shall see that in the QM-scheme we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz et al that deals with perturbation in the standard Einstein framework. For completeness, we compare the QMscheme to the gauge-independent method of Bardeen, a procedure consisting on particular choices of the perturbed variables as a combination of gauge dependent quantities.

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Cosmological perturbations and the physical meaning of gauge-invariant variables

Cited by 261 publications

References 0 publications

Gauge invariant perturbations of scalar-tensor cosmologies: The vacuum case

Gauge invariant perturbations of scalar-tensor cosmologies: The vacuum case

Singularities on the brane are not isotropic

The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory

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