Covariant Fluid Dynamics: a Long Wave-Length Approximation

Abstract

In this paper we consider the Long-Wavelength Approximation Scheme (LWAS) in the framework of the covariant fluid approach to general relativistic dynamics, specializing to the particular case of irrotational dust matter. We discuss the dynamics of these models during the approach to any spacelike singularity where a BKL-type evolution is expected, studying the validity of this approximation scheme and the role of the magnetic part of the Weyl tensor, $H_{ab}$. Our analytic results confirm a previous numerical analysis: it is $H_{ab}$ that destroys the pure Kasner-like approach to the singularity and eventually produces the bounce to another Kasner phase. Expanding regions evolve as separate universes where inhomogeneities and anisotropies die away.

18 pages. LaTeX2e. IOP Style

References in corpus (3)

• Evolution of second-order cosmological perturbations
• Cosmological models from a geometric point of view
• 3+1 Approach to the Long Wavelength Iteration Scheme

Cited by in corpus (10)

• On cosmic acceleration without dark energy
• A novel approach to the dynamics of Szekeres dust models
• A solution to the anisotropy problem in bouncing cosmologies
• Einstein's signature in cosmological large-scale structure
• Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology
• Zel'dovich approximation and General Relativity
• Frame dragging and Eulerian frames in General Relativity
• Quasi-isotropic cycles and non-singular bounces in a Mixmaster cosmology
• A non-linear approximation for perturbations in ΛCDM
• fNL - gNL mixing in the matter density field at higher orders