Progressing wave gravitational perturbations of Robertson-Walker space-times

In a series of papers Janis and coworkers found a family of Robertson-Walker space-times whose most general radiative purely gravitational perturbations could be expressed as progressing waves. In this paper we significantly generalize, simplify, and extend, their results.     

Progressing waves on spherical spacetimes

A family of spherically symmetrical spacetimes that are transparent to minimally coupled scalar multipole waves is investigated. The concept of transparency is reformulated in terms of the established concept of progressing waves. The set of spherically symmetric spacetimes and the family of wave equations for which the transparency condition can be shown to hold is generalized.     

Evolution of nonlinear cosmological perturbations

We define fully nonperturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our nonlinear generalizations are defined geometrically, independently of any coordinate system. We give the equations governing their evolution on all scales. Also, in order to make contact with previous works on first- and second-order perturbations, we introduce a coordinate system and show that previous results can be recovered, on large scales, in a remarkably simple way, after restricting our definitions to first and second orders in a perturbative expansion.     

Conservation laws for cosmological perturbations

We briefly recall the problem of defining conserved quantities such as energy in general relativity, and the solution given by introducing a symmetric background. We apply the general formalism to perturbed Robertson-Walker spacetimes with de Sitter geometry as background. We relate the obtained conserved quantities to Traschen's integral constraints and mention a few applications in cosmology.     

Two-fluid cosmological models in Gödel-type spacetimes

Solutions of the Einstein field equations are considered when the metric is of Gödel type and the sources are two fluids either with or without an electromagnetic field. It is shown that there are solutions that are spacetime homogeneous and spacetime inhomogeneous.     

Remarks on cosmological spacetimes and constant mean curvature surfaces

We give a general condition which ensures the existence of constant mean curvature (CMC) Cauchy surfaces in cosmological spacetimes. However, there is an example of a spacetime which does not satisfy this condition and does not admit any CMC Cauchy surfaces. We discuss conditions under which CMC surfaces may exist.     

Magnetic field generation from cosmological perturbations

In this Letter, we discuss the generation of magnetic field from cosmological perturbations. We consider the evolution of three component plasma (electron, proton, and photon) evaluating the collision term between electrons and photons up to the second order. The collision term is shown to induce electric current, which then generates magnetic field. There are three contributions, two of which can be evaluated from the first-order quantities, while the other one is fluid vorticity, which is purely second order. We estimate the magnitudes of the former contributions and show that the amplitude of the produced magnetic field is about approximately 10(-19) G at 10 Mpc comoving scale at the decoupling. Compared to astrophysical and inflationary mechanisms for seed-field generation, our study suffers from much less ambiguities concerning unknown physics and/or processes.     

Evolution of cosmological perturbations in a brane-universe

In our present Letter, we analyze the impact of the existence of extra dimensions on cosmology, in particular, on the evolution of cosmological perturbations. For a five-dimensional anti-de Sitter spacetime where ordinary matter is confined to a brane-universe, the equations governing the cosmological perturbations are presented in a form very close to the equations of standard cosmology. Two types of corrections appear: corrections due to the unconventional evolution of the homogeneous solution, which change the background-dependent coefficients of the equations, and corrections due to the curvature along the fifth dimension, which act as source terms in the evolution equations.     

Density perturbations in a Brans-Dicke cosmological model

A very general flat solution for Brans-Dicke cosmology with a perfect-fluid, Robertson-Walker metric and a perfect gas law of state is examined regarding density perturbations. The model has growing instabilities, but not of exponential character.     

Gauge-invariant perturbations in anisotropie homogeneous cosmological models

In a recent paper K. Tomita and M. Den found a set of coupled differential equations for spatially flat, anisotropic homogeneous,N- dimensional cosmological models. Some particular exact solutions of those differential equations for a few specific equations of state were obtained by D. Lorentz-Petzold. In the present work we solve those differential equations completely.