Are braneworlds born isotropic?

It has recently been suggested that an isotropic singularity may be a generic feature of brane cosmologies, even in the inhomogeneous case. Using the covariant and gauge-invariant approach we present a detailed analysis of linear perturbations of the isotropic model ${\cal F}_b$ which is a past attractor in the phase space of homogeneous Bianchi models on the brane. We find that for matter with an equation of state parameter $\gamma > 1$, the dimensionless variables representing generic anisotropic and inhomogeneous perturbations decay as $t\to 0$, showing that the model ${\cal F}_b$ is asymptotically stable in the past. We conclude that brane universes are born with isotropy naturally built-in, contrary to standard cosmology. The observed large-scale homogeneity and isotropy of the universe can therefore be explained as a consequence of the initial conditions if the brane-world paradigm represents a description of the very early universe.Comment: Changed to match published versio

Observational Cosmology in Macroscopic Gravity

We discuss the construction of cosmological models within the framework of Macroscopic Gravity (MG), which is a theory that models the effects of averaging the geometry of space-time on large scales. We find new exact spatially homogeneous and isotropic FLRW solutions to the MG field equations, and investigate large-scale perturbations around them. We find that any inhomogeneous perturbations to the averaged geometry are severely restricted, but that possible anisotropies in the correlation tensor can have dramatic consequences for the measurement of distances. These calculations are a first step within the MG approach toward developing averaged cosmological models to a point where they can be used to interpret real cosmological data, and hence to provide a working alternative to the "concordance" LCDM model.Comment: 22 page

Spherically Symmetric Solutions in Macroscopic Gravity

Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's solution is essentially based on an ideal theory of gravitation, where all inhomogeneities are ignored. Therefore, any generalization of the Schwarzschild solution should take into account the effects of small perturbations that may be present in the gravitational field. The theory of Macroscopic Gravity characterizes the effects of the inhomogeneities through a non-perturbative and covariant averaging procedure. With similar assumptions on the geometry and matter content, a solution to the averaged field equations as dictated by Macroscopic Gravity are derived. The resulting solution provides a possible explanation for the flattening of galactic rotation curves, illustrating that Dark Matter is not real but may only be the result of averaging inhomogeneities in a spherically symmetric background.Comment: 14 pages, added and updated references, some paragraphs rewritten for clarity, typographical errors fixed, results have not change

Scaling solution, radion stabilization, and initial condition for brane-world cosmology

We propose a new, self-consistent and dynamical scenario which gives rise to well-defined initial conditions for five-dimensional brane-world cosmologies with radion stabilization. At high energies, the five-dimensional effective theory is assumed to have a scale invariance so that it admits an expanding scaling solution as a future attractor. The system automatically approaches the scaling solution and, hence, the initial condition for the subsequent low-energy brane cosmology is set by the scaling solution. At low energies, the scale invariance is broken and a radion stabilization mechanism drives the dynamics of the brane-world system. We present an exact, analytic scaling solution for a class of scale-invariant effective theories of five-dimensional brane-world models which includes the five-dimensional reduction of the Horava-Witten theory, and provide convincing evidence that the scaling solution is a future attractor.Comment: 17 pages; version accepted for PRD, references adde

Irreversible Processes in Inflationary Cosmological Models

By using the thermodynamic theory of irreversible processes and Einstein general relativity, a cosmological model is proposed where the early universe is considered as a mixture of a scalar field with a matter field. The scalar field refers to the inflaton while the matter field to the classical particles. The irreversibility is related to a particle production process at the expense of the gravitational energy and of the inflaton energy. The particle production process is represented by a non-equilibrium pressure in the energy-momentum tensor. The non-equilibrium pressure is proportional to the Hubble parameter and its proportionality factor is identified with the coefficient of bulk viscosity. The dynamic equations of the inflaton and the Einstein field equations determine the time evolution of the cosmic scale factor, the Hubble parameter, the acceleration and of the energy densities of the inflaton and matter. Among other results it is shown that in some regimes the acceleration is positive which simulates an inflation. Moreover, the acceleration decreases and tends to zero in the instant of time where the energy density of matter attains its maximum value.Comment: 13 pages, 2 figures, to appear in PR

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Renormalization Group Approach to Generalized Cosmological models

We revisit here the problem of generalized cosmology using renormalization group approach. A complete analysis of these cosmologies, where specific models appear as asymptotic fixed-points, is given here along with their linearized stability analysis.Comment: 10 pages, to appear in the International Journal of Theoretical Physic

The Dynamics of Brane-World Cosmological Models

Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or {\em brane} embedded in a higher-dimensional {\em bulk} spacetime. Ordinary matter fields are confined to the brane while the gravitational field can also propagate in the bulk, leading to modifications of Einstein's theory of general relativity at high energies. In particular, the Randall-Sundrum-type models are self-consistent and simple and allow for an investigation of the essential non-linear gravitational dynamics. The governing field equations induced on the brane differ from the general relativistic equations in that there are nonlocal effects from the free gravitational field in the bulk, transmitted via the projection of the bulk Weyl tensor, and the local quadratic energy-momentum corrections, which are significant in the high-energy regime close to the initial singularity. In this review we discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models containing both a perfect fluid and a scalar field close to the initial singularity. Using dynamical systems techniques it is found that, for models with a physically relevant equation of state, an isotropic singularity is a past-attractor in all orthogonal spatially homogeneous models (including Bianchi type IX models). In addition, we describe the dynamics in a class of inhomogeneous brane-world models, and show that these models also have an isotropic initial singularity. These results provide support for the conjecture that typically the initial cosmological singularity is isotropic in brane-world cosmology.Comment: Einstein Centennial Review Article: to appear in CJ