Tilt and phantom cosmology

We show that in tilting perfect fluid cosmological models with an ultra-radiative equation of state, generically the tilt becomes extreme at late times and, as the tilt instability sets in, observers moving with the tilting fluid will experience singular behaviour in which infinite expansion is reached within a finite proper time, similar to that of phantom cosmology (but without the need for exotic forms of matter).Comment: 9 pages, v2: more discussion, added reference

Spikes and matter inhomogeneities in massless scalar field models

We shall discuss the general relativistic generation of spikes in a massless scalar field or stiff perfect fluid model. We first investigate orthogonally transitive (OT) G 2 stiff fluid spike models both heuristically and numerically, and give a new exact OT G 2 stiff fluid spike solution. We then present a new two-parameter family of non-OT G 2 stiff fluid spike solutions, obtained by the generalization of non-OT G 2 vacuum spike solutions to the stiff fluid case by applying Geroch's transformation on a Jacobs seed. The dynamics of these new stiff fluid spike solutions is qualitatively different from that of the vacuum spike solutions in that the matter (stiff fluid) feels the spike directly and the stiff fluid spike solution can end up with a permanent spike. We then derive the evolution equations of non-OT G 2 stiff fluid models, including a second perfect fluid, in full generality, and briefly discuss some of their qualitative properties and their potential numerical analysis. Finally, we discuss how a fluid, and especially a stiff fluid or massless scalar field, affects the physics of the generation of spikes

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

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

The initial singularity of ultrastiff perfect fluid spacetimes without symmetries

We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is `generic' in the sense that it depends on as many free functions as a general solution, i.e., without imposing any symmetry assumptions, of the Einstein-Euler equations. The method we use is a that of a Fuchsian reduction.Comment: 16 pages, journal versio

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

Anisotropic cosmological models with a perfect fluid and a Λ\Lambda term

We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual equation of state, i.e., p = \zeta \ve, with $\zeta \in [0, 1]$ or a van der Waals equation of state. Role of the $\Lambda$ term in the evolution of the BI Universe has been studied.Comment: 8 pages, 8 Figure

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

Notes on f(T)f(T) Theories

The cosmological models based on teleparallel gravity with nonzero torsion are considered. To investigate the evolution of this theory, we consider the phase-space analysis of the $f(T)$ theory. It shows when the tension scalar can be written as an inverse function of $x$ where $x=\rho_{e}/(3m_{pl}^{2}H^{2})$ and $T=g(x)$, the system is an autonomous one. Furthermore,the $\omega_{e}-\omega'_{e}$ phase analysis is given out. We perform the dynamical analysis for the models $f(T)=\beta T\ln(T/T_{0})$ and $f(T)=\alpha m_{pl}^{2}(-T/m_{pl}^{2})^{n}$ particularly. We find that the universe will settle into de-Sitter phase for both models. And we have examined the evolution behavior of the power law form in the $\omega_{ep}-\omega'_{ep}$ plane.Comment: 13 pages, 2 figure