Density perturbations in cosmological models

Olson, Donald W.

doi:10.1103/physrevd.14.327

Cited by 88 publications

(81 citation statements)

References 20 publications

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“…However, the variables in Bardeen's theory are defined with respect to a particular coordinate system, making their geometrical and physical meaning not very transparent See the discussion in [35]. 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].…”

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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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: 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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“…Bardeen's approach, however, is of considerable complexity as it determines a set of gauge-invariant quantities that are related to density perturbations but are not perturbations themselves. Building on earlier work by Hawking (1966), Stewart & Walker (1974) and Olson (1976), Ellis & Bruni (1989) [12] formulated a fully covariant gauge-invariant treatment of cosmological perturbations. Their approach, which is of high mathematical elegance and physical transparency, has the additional advantage of starting from the fully non-linear equations before linearizing them about a chosen background.…”

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confidence: 99%

Magnetized cosmological perturbations

2000

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The aim of these lecture notes is to familiarize graduate students and beginning postgraduates with the basic ideas of linear cosmological perturbation theory and of structure formation scenarios. We present both the Newtonian and the general relativistic approaches, derive the key equations and then apply them to a number of characteristic cases. The gauge problem in cosmology and ways to circumvent it are also discussed. We outline the basic framework of the baryonic and the non-baryonic structure formation scenarios and point out their strengths and shortcomings. Fundamental concepts, such as the Jeans length, Silk damping and collisionless dissipation, are highlighted and the underlying mathematics are presented in a simple and straightforward manner. IntroductionLooking up into the night sky we see structure everywhere. Star clusters, galaxies, galaxy clusters, superclusters and voids are evidence that on small and moderate scales, that is up to 10 Mpc, our universe is very lumpy. As we move to larger and larger scales, however, the universe seems to smooth out. This is evidenced by the isotropy of the x-ray background, the number counts of radio sources and, of course, by the high isotropy of the Cosmic Microwave Background (CMB) radiation. The latter also provides a fossil record of our observable universe when it was roughly 10 5 years old and about 10 3 times smaller than today. So, the universe was very smooth at early times and it is very lumpy now. How did this happen? Although the details are still elusive, cosmologists believe that the reason is "gravitational instability". Small fluctuations in the density of the primeval cosmic fluid that grew gravitationally into the galaxies, the clusters and the voids we observe today. The idea of gravitational instability is not new. It was first introduced in the early 1900s by Jeans, who showed that a homogeneous and isotropic fluid is unstable to small perturbations in its density [1]. What Jeans demonstrated was that density inhomogeneities grow in time when the pressure support is weak compared to the gravitational pull. In retrospect, this is not surprising given that gravity is always attractive. As long as pressure is negligible, an overdense region will keep accreting material from its surroundings, becoming increasingly unstable until it eventually collapses into a gravitationally bound object. Jeans, however, applied his analysis to a static Newtonian fluid in an attempt to understand * e-mail address: ctsagas@maths.uct.ac.za 1 the formation of planets and stars. In modern cosmology we need to account for the expansion of the universe as well as for general relativistic effects.Despite the lack, as yet, of a detailed scenario, the rather simple idea that the observed structure in our universe has resulted from the gravitational amplification of weak primordial fluctuations seems to work remarkably well. These small perturbations grew slowly over time until they were strong enough to separate from the background expansion, turn around, and c...

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“…A solution for this difficulty was found by looking for gauge-independent combinations which are written in terms of the metric tensor and its derivatives by many authors (cf. Bardeen 1980, Hawking 1966, Jones 1976, Olson 1976, Brandenberger 1983, Vishniac 1990.…”

Section: Perturbation Theory In Qm Formalismmentioning

confidence: 99%

“…One could imaginewhich has been used a number of times in the literature (Hawking 1966, Olson 1976)-that for FRW cosmology the perturbations of its main characteristics (the energy density, δρ the scalar of curvature δR and the Hubble expansion factor δθ) would be natural quantities to be considered as basic for the perturbation scheme. However, these are not "good" scalars, since they are not zero in the background 13 .…”

Section: Friedman Universe: Scalar Perturbationsmentioning

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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Density perturbations in cosmological models

Cited by 88 publications

References 20 publications

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Magnetized cosmological perturbations

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

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