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Title: Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

Abstract

We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of {phi}{sub v} order higher than the second-order terms where {phi}{sub v} is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have {delta}{phi}{approx}(3/5){phi}{sub v} to the linear order. Therefore, the pure general relativistic effects are of {phi}{sub v} order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropymore » of cosmic microwave background, we have ({delta}T/T){approx}(1/3){delta}{phi}{approx}(1/5){phi}{sub v}{approx}10{sup -5}. Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon.« less

Authors:
 [1];  [2]
  1. Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Taegu (Korea, Republic of)
  2. Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of)
Publication Date:
OSTI Identifier:
20711347
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 72; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.72.044012; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; COMPUTERIZED SIMULATION; CORRECTIONS; COSMIC RADIATION; COSMOLOGICAL CONSTANT; COSMOLOGY; DISTURBANCES; FIELD EQUATIONS; GAUGE INVARIANCE; GENERAL RELATIVITY THEORY; GRAVITATIONAL WAVES; NONLINEAR PROBLEMS; PERTURBATION THEORY; POTENTIALS; RADIOWAVE RADIATION; RELATIVISTIC RANGE; RELICT RADIATION

Citation Formats

Hwang, Jai-chan, and Noh, Hyerim. Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.044012.
Hwang, Jai-chan, & Noh, Hyerim. Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects. United States. https://doi.org/10.1103/PhysRevD.72.044012
Hwang, Jai-chan, and Noh, Hyerim. 2005. "Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects". United States. https://doi.org/10.1103/PhysRevD.72.044012.
@article{osti_20711347,
title = {Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects},
author = {Hwang, Jai-chan and Noh, Hyerim},
abstractNote = {We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of {phi}{sub v} order higher than the second-order terms where {phi}{sub v} is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have {delta}{phi}{approx}(3/5){phi}{sub v} to the linear order. Therefore, the pure general relativistic effects are of {phi}{sub v} order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have ({delta}T/T){approx}(1/3){delta}{phi}{approx}(1/5){phi}{sub v}{approx}10{sup -5}. Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon.},
doi = {10.1103/PhysRevD.72.044012},
url = {https://www.osti.gov/biblio/20711347}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 4,
volume = 72,
place = {United States},
year = {Mon Aug 15 00:00:00 EDT 2005},
month = {Mon Aug 15 00:00:00 EDT 2005}
}