Covariant fluid dynamics: a long wavelength approximation

Bruni, Marco; Sopuerta, Carlos F.

doi:10.1088/0264-9381/20/24/003

Cited by 16 publications

(23 citation statements)

References 44 publications

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“…[48] and [53]). A patch in our model not evolving to a pancake unavoidably asymp-totically approaches de Sitter [46] (cf.…”

Section: Discussionmentioning

confidence: 99%

“…In other words, if a decaying mode is present then the initial singularity is velocity dominated (see [51], cf. also [53] and references therein) and Kasner-like, while when we only have a growing mode, the initial singularity is matter dominated and effectively isotropic: in approaching the singularity, the growing mode decreases and our spacetime becomes FLRW with a small perturbation.…”

Section: B Classification Of Singularitiesmentioning

confidence: 93%

“…However, the "silent" approximation with H ab = ω ab = 0 holds true for first-order scalar perturbations [65] and at second order outside the horizon [75]. It also corresponds, in the covariant description, to the so called long wavelength approximation in gravitational collapse (see [76] and references therein), with H ab only becoming non-negligible in between different Kasner phases [53].…”

Section: Covariant Variables a Deriving The Variables From The Mementioning

confidence: 99%

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Exact nonlinear inhomogeneities inΛCDMcosmology

Meures¹,

Bruni²

2011

Phys. Rev. D

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At a time when galaxy surveys and other observations are reaching unprecedented sky coverage and precision it seems timely to investigate the effects of general relativistic nonlinear dynamics on the growth of structures and on observations. Analytic inhomogeneous cosmological models are an indispensable way of investigating and understanding these effects in a simplified context.In this paper, we develop exact inhomogeneous solutions of general relativity with pressureless matter (dust, describing cold dark matter) and cosmological constant Λ, which can be used to model an arbitrary initial matter distribution along one line of sight. In particular, we consider the second class Szekeres models with Λ and split their dynamics into a flat ΛCDM background and exact nonlinear inhomogeneities, obtaining several new results. One single metric function Z describes the deviation from the background. We show that F , the time dependent part of Z, satisfies the familiar linear differential equation for δ, the first-order density perturbation of dust, with the usual growing and decaying modes. In the limit of small perturbations, δ ≈ F as expected, and the growth of inhomogeneities links up exactly with standard perturbation theory. In particular, we exhibit an exact conserved curvature variable, necessary for the existence of the growing mode, which is the nonlinear extension of the first-order curvature perturbation. We provide analytic expressions for the exact nonlinear δ and the growth factor in our models. For the case of overdensities we find that, depending on the initial conditions, the growing mode may or may not lead to a pancake singularity, analogous to a Zel'dovich pancake. This is in contrast with the Λ = 0 pure Einstein-de-Sitter background where, at any given point in comoving (Lagrangian) coordinates pancakes will always occur. Analyzing the covariant variables associated with the space-time, we derive the associated dynamical system, which we are able to decouple and reduce to two differential equations, one for ΩΛ representing the background dynamics and one for δ describing the dynamics of the inhomogeneities. Our models are Petrov type D, which we show by explicitly deriving the only nonzero Weyl scalar Ψ2, which does not depend on Λ. Since this is the only Weyl contribution to the geodesic deviation equation, Λ can only contribute to lensing through its contribution to the background expansion.

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“…[48] and [53]). A patch in our model not evolving to a pancake unavoidably asymp-totically approaches de Sitter [46] (cf.…”

Section: Discussionmentioning

confidence: 99%

Section: B Classification Of Singularitiesmentioning

confidence: 93%

Section: Covariant Variables a Deriving The Variables From The Mementioning

confidence: 99%

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Exact nonlinear inhomogeneities inΛCDMcosmology

Meures¹,

Bruni²

2011

Phys. Rev. D

Self Cite

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“…where we used (24), (32), (33), (34) and (35). For the alternative system (36a)-(36d) the appropriate choice of initial value functions is furnished by the set {H qi , Ω q0 , S, P, Q}.…”

Section: Alternative Scalar Representationsmentioning

confidence: 99%

A novel approach to the dynamics of Szekeres dust models

Sussman

Bolejko

2012

Class. Quantum Grav.

137

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Abstract. We obtain an elegant and useful description of the dynamics of Szekeres dust models (in their full generality) by means of "quasi-local" scalar variables constructed by suitable integral distributions that can be interpreted as weighed proper volume averages of the local covariant scalars. In terms of these variables, the field equations and basic physical and geometric quantities are formally identical to their corresponding expressions in the spherically symmetric LTB dust models. Since we can map every Szekeres model to a unique LTB model, rigorous results valid for the latter models can be readily generalized to a nonspherical Szekeres geometry. The new variables lead naturally to an initial value formulation in which all scalars are expressed as scaling laws in terms of their values at an arbitrary initial space slice. These variables also yield a significant simplification of numerical work, since the fluid flow evolution equations become a system of autonomous ordinary differential equations subjected to algebraic constraints containing the information on the deviations from spherical symmetry. As an example of how this formalism can be applied, we show that spherical symmetry is stable against small dipole-like perturbations. This new approach to the dynamics of the Szekeres solutions has an enormous potential for dealing with a wide variety of theoretical issues and for constructing non-spherical models of cosmological inhomogeneities to fit observational data.

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“…The 3-metric γ ij (t, q) is given in Eq. (5), and describes the gravitational evolution of an irrotational dust component in an EdS Universe. The reported synchronous metric can be obtained e.g.…”

Section: Discussionmentioning

confidence: 99%

Frame dragging and Eulerian frames in general relativity

Rampf

2014

Phys. Rev. D

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The physical interpretation of cold dark matter perturbations is clarified by associating Bertschinger's Poisson gauge with a Eulerian frame of reference. We obtain such an association by using a Lagrangian approach to relativistic cosmological structure formation. Explicitly, we begin with the second-order solution of the Einstein equations in a synchronous/comoving coordinate system, which defines the Lagrangian frame, and transform it to a Poissonian coordinate system. The generating vector of this coordinate/gauge transformation is found to be the relativistic displacement field. The metric perturbations in the Poissonian coordinate system contain known results from standard/Eulerian Newtonian perturbation theory but contain also purely relativistic corrections. On subhorizon scales, these relativistic corrections are dominated by the Newtonian bulk part. These corrections, however, set up nonlinear (initial) constraints for the density and for the velocity that become important on scales close to the horizon. Furthermore, we report the occurrence of a transverse component in the displacement field and find that it induces a nonlinear frame dragging as seen in the Eulerian frame, which is subdominant at late times and subhorizon scales. Finally, we find two other gauges that can be associated with a Eulerian frame. We argue that the Poisson gauge is to be preferred because it comes with the simplest physical interpretation.

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Covariant fluid dynamics: a long wavelength approximation

Cited by 16 publications

References 44 publications

Exact nonlinear inhomogeneities inΛCDMcosmology

Exact nonlinear inhomogeneities inΛCDMcosmology

A novel approach to the dynamics of Szekeres dust models

Frame dragging and Eulerian frames in general relativity

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