Dynamic field theory and equations of motion in cosmology

Journal Article · Sat Nov 15 00:00:00 EST 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2014.07.029· OSTI ID:22403444

Kopeikin, Sergei M., E-mail: [e-mail] ^[1]; Petrov, Alexander N., E-mail: [e-mail] ^[2]

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1. Department of Physics and Astronomy, University of Missouri, 322 Physics Bldg., Columbia, MO 65211 (United States)
2. Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetskij Prospect 13, Moscow 119992 (Russian Federation)

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 the 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.

• OSTI ID: 22403444
• Journal Information: Annals of Physics (New York), Vol. 350; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASTROPHYSICS
ASYMPTOTIC SOLUTIONS
BARYONS
DISTURBANCES
EINSTEIN FIELD EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
GALAXIES
GAUGE INVARIANCE
GRAVITATION
LAGRANGIAN FUNCTION
NONLUMINOUS MATTER
RELATIVISTIC RANGE
SERIES EXPANSION
STARS
TENSORS
VARIATIONAL METHODS