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Title: Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

Abstract

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, ormore » rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and velocity perturbations including the rotation coincide with the ones in Newton's gravity. All equations in this work include the cosmological constant in the background world model. We emphasize that our relativistic/Newtonian correspondences in several situations and pure general relativistic corrections in the context of Newtonian equations are mainly about the dynamic equations of density and velocity perturbations without using the gravitational potential (metric perturbations). Consequently, our relativistic/Newtonian correspondences do not imply the absence of many space-time (i.e., pure general relativistic) effects like frame dragging, and redshift and deflection of photons even in such cases. We also present the case of multiple minimally coupled scalar fields, and properly derive the large-scale conservation properties of curvature perturbation variable in various temporal gauge conditions to the second order.« less

Authors:
;  [1]
  1. Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Taegu (Korea, Republic of)
Publication Date:
OSTI Identifier:
21027820
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 76; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.76.103527; (c) 2007 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; CORRECTIONS; COSMOLOGICAL CONSTANT; COSMOLOGY; DENSITY; EQUATIONS OF MOTION; FLUIDS; GENERAL RELATIVITY THEORY; GRAVITATION; GRAVITATIONAL WAVES; PERTURBATION THEORY; PHOTONS; POTENTIALS; RED SHIFT; RELATIVISTIC RANGE; ROTATION; SCALAR FIELDS; SPACE-TIME

Citation Formats

Hwang, Jai-chan, Noh, Hyerim, and Korea Astronomy and Space Science Institute, Daejon. Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.76.103527.
Hwang, Jai-chan, Noh, Hyerim, & Korea Astronomy and Space Science Institute, Daejon. Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation. United States. https://doi.org/10.1103/PHYSREVD.76.103527
Hwang, Jai-chan, Noh, Hyerim, and Korea Astronomy and Space Science Institute, Daejon. 2007. "Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation". United States. https://doi.org/10.1103/PHYSREVD.76.103527.
@article{osti_21027820,
title = {Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation},
author = {Hwang, Jai-chan and Noh, Hyerim and Korea Astronomy and Space Science Institute, Daejon},
abstractNote = {We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and velocity perturbations including the rotation coincide with the ones in Newton's gravity. All equations in this work include the cosmological constant in the background world model. We emphasize that our relativistic/Newtonian correspondences in several situations and pure general relativistic corrections in the context of Newtonian equations are mainly about the dynamic equations of density and velocity perturbations without using the gravitational potential (metric perturbations). Consequently, our relativistic/Newtonian correspondences do not imply the absence of many space-time (i.e., pure general relativistic) effects like frame dragging, and redshift and deflection of photons even in such cases. We also present the case of multiple minimally coupled scalar fields, and properly derive the large-scale conservation properties of curvature perturbation variable in various temporal gauge conditions to the second order.},
doi = {10.1103/PHYSREVD.76.103527},
url = {https://www.osti.gov/biblio/21027820}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 10,
volume = 76,
place = {United States},
year = {Thu Nov 15 00:00:00 EST 2007},
month = {Thu Nov 15 00:00:00 EST 2007}
}