Cosmological post-Newtonian equations from nonlinear perturbation theory
TL;DR: In this paper, the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact Cosmological perturbation theory in Einstein's gravity are derived, and the complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage.
Abstract: We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact, should include the former, and here we use this fact as a new derivation of the former. The complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinear processes occurring in cosmological structure formation. We consider an ideal fluid and include the cosmological constant.
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01 Jan 1988
TL;DR: The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables as discussed by the authors.
Abstract: The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables. The linearized perturbation equations written in these variables are simpler than the usual versions, and easily accommodate an arbitrary background equation of state, entropy perturbations, and anisotropic pressure perturbations. Particular attention is paid to how a scalar (density) perturbation might be generated by stress perturbations at very early times, when the non-gauge-invariant perturbation in the density itself is ill-defined. The amplitude of the fractional energy density perturbation at the particle horizon cannot be larger, in order of magnitude, than the maximum ratio of the stress perturbation to the background energy density at any earlier time, unless the perturbation is inherent in the initial singularity.
53 citations
01 Jan 1977
TL;DR: In this paper, forbidden decay modes of one-and two-electron ions, fine structure of helium, long range forces in quantum theory, simulated Compton scattering and related phenomena, field-theory on the light-cone and the Parton model, deep inelastic scattering, deep-inelastic processes, interactions of photons with nuclear matter, the hadronic properties of the photon, radiative corrections to electron form factors, Eikonal mechanisms at high energy, and unified theories of weak and electromagnetic interactions.
Abstract: Topics covered include: forbidden decay modes of one- and two-electron ions; fine structure of helium; long range forces in quantum theory; simulated Compton scattering and related phenomena; field-theory on the light-cone and the Parton model; deep inelastic scattering; deep inelastic processes; interactions of photons with nuclear matter; the hadronic properties of the photon; radiative corrections to electron form factors; Eikonal mechanisms at high energy; the quantum mechanics of chiral theories; and unified theories of weak and electromagnetic interactions. (GHT)
18 citations
TL;DR: In this article, the authors present fully nonlinear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields, without taking the temporal gauge condition in the Friedmann background.
Abstract: We present fully nonlinear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. For each fluid component we ignore the anisotropic stress. The multiple component nature, however, introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully nonlinear equations and the third-order perturbation equations of the nonrelativistic pressure fluids in the CDM-comoving gauge.
15 citations
Cites background or methods from "Cosmological post-Newtonian equatio..."
...…equations in the presence of a fluid or a minimally coupled scalar field (Hwang & Noh 2013a, Noh 2014) and applied the equations to various situations: Newtonian limit, Newtonian limit with general relativistic pressure, and post-Newtonian limit (Hwang & Noh 2013b, 2013c, Noh & Hwang 2013)....
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...In Noh & Hwang (2013) we have shown that the cosmological first-order post-Newtonian (1PN) equations (modulo anisotropic stress) in Hwang, Noh & Puetzfeld (2008) can be easily derived from our fully nonlinear cosmological formulation....
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...…derivation of the perturbation equations to any nonlinear order, the formulation was used to show the Newtonian limit, the first-order post-Newtonian approximation and the Newtonian hydrodynamic equations with general relativistic (gravitating) pressure (Hwang & Noh 2013b, 2013c, Noh & Hwang 2013)....
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TL;DR: In this article, the relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order were derived in the zero-shear gauge based on the fully nonlinear formulation of cosmological perturbation in Einstein's gravity.
Abstract: We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (\ref{mass-conservation-Mink})-(\ref{Poisson-eq-Mink}). The derivation is made in the zero-shear gauge based on the fully nonlinear formulation of cosmological perturbation in Einstein's gravity. The correction terms {\it differ} from many of the previously suggested forms in the literature based on hand-waving manners. We confirm our results by comparing with (i) the nonlinear perturbation theory, (ii) the first order post-Newtonian approximation, and (iii) the special relativistic limit, and by checking (iv) the consistency with full Einstein's equation.
11 citations
TL;DR: In this article, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein's theory of general relativity.
Abstract: Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein's theory of general relativity. An analysis is made in the maximal slicing, where the Poisson's equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
11 citations
References
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01 Jan 1992
2,867 citations
"Cosmological post-Newtonian equatio..." refers background or methods in this paper
...Nonlinear aspects of clustering process of the large-scale structure are mainly studied in the Newtonian context [1, 2, 3, 4, 5] except that the background evolution is provided by Friedmann equations based on Einstein’s gravity often with the cosmological constant....
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...These are the well known perturbed Newtonian hydrodynamic equations in the cosmological background; see Sections 7-9 of [1]....
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TL;DR: The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables as discussed by the authors.
Abstract: The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables. The linearized perturbation equations written in these variables are simpler than the usual versions, and easily accommodate an arbitrary background equation of state, entropy perturbations, and anisotropic pressure perturbations. Particular attention is paid to how a scalar (density) perturbation might be generated by stress perturbations at very early times, when the non-gauge-invariant perturbation in the density itself is ill-defined. The amplitude of the fractional energy density perturbation at the particle horizon cannot be larger, in order of magnitude, than the maximum ratio of the stress perturbation to the background energy density at any earlier time, unless the perturbation is inherent in the initial singularity.
2,114 citations
TL;DR: In this article, the authors review the formalism and applications of non-linear perturbation theory (PT) to understand the large-scale structure of the universe, from the linear to the nonlinear regime.
1,833 citations
1,663 citations