Covariant perturbations in a multifluid cosmological medium

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

doi:10.1086/171630

Cited by 135 publications

(180 citation statements)

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“…The vectors and tensors can be also expanded in harmonics by introducing the vector and tensor spherical harmonics [56,57,59]. The even (electric) and odd (magnetic) parity vector harmonics are 41) and the vector Ψ a can be expanded as…”

Section: Harmonic Expansionmentioning

confidence: 99%

“…By using a covariant approach, one circumvents these problems by using the spatial curvature rather than the metric as the defining variables [36,37]. In this way, a set of gauge-invariant perturbation variables can be easily identified as the ones that vanish on the chosen background [38][39][40][41][42][43][44]50]. This feature of the covariant approach makes it a very versatile method for studying perturbations on a variety of backgrounds and physical situations and relating the results obtained in a unified way [45][46][47][48][49] In this paper we present for the first time a general treatment of the vorticity-free perturbations of Kantowski-Sachs cosmologies with positive cosmological constant, extending earlier work [51], which focused only on the scalar perturbation sector.…”

Section: Introductionmentioning

confidence: 99%

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Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Keresztes

Forsberg

Bradley

et al. 2015

J. Cosmol. Astropart. Phys.

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Abstract. A general treatment of vorticity-free, perfect fluid perturbations of KantowskiSachs models with a positive cosmological constant are considered within the framework of the 1+1+2 covariant decomposition of spacetime. The dynamics is encompassed in six evolution equations for six harmonic coefficients, describing gravito-magnetic, kinematic and matter perturbations, while a set of algebraic expressions determine the rest of the variables. The six equations further decouple into a set of four equations sourced by the perfect fluid, representing forced oscillations and two uncoupled damped oscillator equations. The two gravitational degrees of freedom are represented by pairs of gravito-magnetic perturbations. In contrast with the Friedmann case one of them is coupled to the matter density perturbations, becoming decoupled only in the geometrical optics limit. In this approximation, the even and odd tensorial perturbations of the Weyl tensor evolve as gravitational waves on the anisotropic Kantowski-Sachs background, while the modes describing the shear and the matter density gradient are out of phase dephased by π/2 and share the same speed of sound.

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Section: Harmonic Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Keresztes

Forsberg

Bradley

et al. 2015

J. Cosmol. Astropart. Phys.

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show abstract

“…‡ Strictly speaking, the variables defined in [18][19][20] and those defined in the same way in the brane context [1,16,21] are 4-d; they are however easily generalised to 5-d. Bardeen like variables [22,23] have been defined in 5-d in order to carry out a brane-bulk analysis, e.g. see [24], but the relation between these and the covariant ones used here has not yet been established; cf.…”

Section: Brane Dynamicsmentioning

confidence: 99%

“…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%

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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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1+3 Covariant Cosmic Microwave Background Anisotropies II: The Almost-Friedmann–Lemaı̂tre Model

2000

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This is the second of a series of papers extending the 1+3 covariant and gauge-invariant treatment of kinetic theory to an examination of cosmic microwave background temperature anisotropies arising from inhomogeneities in the early universe. The first paper (Paper I) dealt with algebraic issues, representing anisotropies in a covariant and gauge-invariant way by means of projected symmetric and trace-free tensors. Here we derive the mode form of the integrated Boltzmann equations, first, giving a covariant version of the standard derivation using the mode recursion relations, second, demonstrating the link to the the multipole divergence equations and finally various analytic ways of solving the resulting equations are discussed. A general integral form of solution is obtained for the equations with Thomson scattering. The covariant Friedmann Lema@^tre multipole form of the transport equations are found near tight-coupling using the covariant and gauge-invariant generalization of the Peebles and Yu expansion in Thompson scattering time. The dispersion relations and damping scale are then obtained from the covariant approach. The equations are integrated to give the covariant and gauge-invariant equivalent of the canonical scalar sourced anisotropies in the K=0 (flat background) case. We carry out a simple treatment of the matter dominated free-streaming projection, slow-decoupling, and tight-coupling cases in covariant and gaugeinvariant theory, with the aim of both giving a unified transparent derivation of this range of results and clarifying the formal connection between the usual approaches (for example, works by Hu and Sugiyama) and the covariant and gauge-invariant like treatments for scalar perturbations (for example, works by Challinor and Lasenby).

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Covariant perturbations in a multifluid cosmological medium

Cited by 135 publications

References 0 publications

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Singularities on the brane are not isotropic

1+3 Covariant Cosmic Microwave Background Anisotropies II: The Almost-Friedmann–Lemaı̂tre Model

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