Post-Newtonian Cosmology

Szekeres, Peter; Rainsford, Tamath

doi:10.1023/a:1001976317159

Cited by 16 publications

(37 citation statements)

References 5 publications

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“…Then, for a set of initial data (ω i (x i , 0), ρ(t 0 ), φ(t 0 )) the set of homogeneous Newtonian cosmologies may be found since (6), (7) and (8) can be uniquely solved for θ, ω ij and ρ, and, a ii can be determined from (4) and a ij from (9). This is very different to the fully general relativistic case where there are nine possible symmetry groups.…”

Section: Newtonian Homogeneous Anisotropic Cosmologymentioning

confidence: 99%

“…Let us explore how far the post-Newtonian approximation [9] goes in overcoming this difficulty. The post-Newtonian theory is known to be well-posed in the general case of anisotropy and inhomogeneity [9].…”

Section: Newtonian Homogeneous Anisotropic Cosmologymentioning

confidence: 99%

“…Reformulating the field equations of the O(c −6 ) limit as wavelike equations defines the post-Newtonian theory used here (see [9]). …”

Section: Post-newtonian Approximations Of Anisotropic Homogeneous Cosmentioning

confidence: 99%

“…However, in a recent paper [9], it is shown that the Newtonian approximation has some difficulties. To begin with the Newtonian approximation is incomplete in the sense that the Bianchi identities cannot be obtained from the field equations.…”

Section: Introductionmentioning

confidence: 99%

“…It is generally accepted that Newtonian theory is a specialization of the linearized approximation of general relativity cut off at the c −2 -level. However, information is lost in this cut-off procedure, and it is shown that cutting off at the c −4 -level results in a theory in which the Bianchi identities are obtainable from the field equations, [9]. Moreover, the Newtonian theory has no initial value problem when applied to cosmology because there are no boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Anisotropic Homogeneous Cosmologies in the Post-Newtonian Approximation

Rainsford

2001

General Relativity and Gravitation

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In this paper we explore how far the post-Newtonian theory, [9] goes in overcoming the difficulties associated with anisotropic homogeneous cosmologies in the Newtonian approximation. It will be shown that, unlike in the Newtonian case, the cosmological equations of the post-Newtonian approximation are much more in the spirit of general relativity with regard to the nine Bianchi types and issues of singularities.The situations of vanishing rotation and vanishing shear are treated separately. The homogeneous Bianchi I model is considered as an example of a rotation-free cosmology with anisotropy. It is found in the Newtonian approximation that there are arbitrary functions that need to be given for all time if the initial value problem is to be well-posed, while in the post-Newtonian case there is no such need. For the general case of a perfect fluid only the post-Newtonian theory can satisfactorily describe the effects of pressure. This is in accordance with findings in [7] where the post-Newtonian approximation was applied to homogeneous cosmologies.For a shear-free anisotropic homogeneous cosmology the Newtonian theory of Heckmann and Schücking, [2] is explored. Comparisons with its relativistic and post-Newtonian counterparts are made. In the Newtonian theory solutions exist to which there are no analogues in general relativity. The post-Newtonian approximation may provide a way out.

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Section: Newtonian Homogeneous Anisotropic Cosmologymentioning

confidence: 99%

Section: Newtonian Homogeneous Anisotropic Cosmologymentioning

confidence: 99%

“…Reformulating the field equations of the O(c −6 ) limit as wavelike equations defines the post-Newtonian theory used here (see [9]). …”

Section: Post-newtonian Approximations Of Anisotropic Homogeneous Cosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anisotropic Homogeneous Cosmologies in the Post-Newtonian Approximation

Rainsford

2001

General Relativity and Gravitation

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Equations of Motion in an Expanding Universe

Kopeikin

Петров

2015

Fundamental Theories of Physics

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Dynamic field theory and equations of motion in cosmology

Kopeikin

Петров

2014

Annals of Physics

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We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays a role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein's equations in the form of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ ≤ 1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ ≫ 1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress-energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein's equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.

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Post-Newtonian Cosmology

Cited by 16 publications

References 5 publications

Anisotropic Homogeneous Cosmologies in the Post-Newtonian Approximation

Anisotropic Homogeneous Cosmologies in the Post-Newtonian Approximation

Equations of Motion in an Expanding Universe

Dynamic field theory and equations of motion in cosmology

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