Friedmann-like universes with torsion

We consider spatially homogeneous and isotropic cosmologies with non-zero torsion. Given the high symmetry of these universes, we adopt a specific form for the torsion tensor that preserves the homogeneity and isotropy of the spatial surfaces. Employing both covariant and metric-based techniques, we derive the torsional versions of the continuity, the Friedmann and the Raychaudhuri equations. These formulae demonstrate how, by playing the role of the spatial curvature, or that of the cosmological constant, torsion can drastically change the evolution of the classic homogeneous and isotropic Friedmann universes. In particular, torsion alone can lead to exponential expansion. For instance, in the presence of torsion, the Milne and the Einstein-de Sitter universes evolve like the de Sitter model. We also show that, by changing the expansion rate of the early universe, torsion can affect the primordial nucleosynthesis of helium-4. We use this sensitivity to impose strong cosmological bounds on the relative strength of the associated torsion field, requiring that its ratio to the Hubble expansion rate lies in the narrow interval ($-0.005813,\,+0.019370$) around zero. Interestingly, the introduction of torsion can \textit{reduce} the production of primordial helium-4, unlike other changes to the standard thermal history of an isotropic universe. Finally, turning to static spacetimes, we find that there exist torsional analogues of the classic Einstein static universe, with all three types of spatial geometry. These models can be stable when the torsion field and the universe's spatial curvature have the appropriate profiles.Comment: Revised article. Section on BBN limits on torsion added. References added and update

Magnetic Brane-worlds

We investigate brane-worlds with a pure magnetic field and a perfect fluid. We extend earlier work to brane-worlds, and find new properties of the Bianchi type I brane-world. We find new asymptotic behaviours on approach to the singularity and classify the critical points of the dynamical phase space. It is known that the Einstein equations for the magnetic Bianchi type I models are in general oscillatory and are believed to be chaotic, but in the brane-world model this chaotic behaviour does not seem to be possible.Comment: 21 pages, 3 ps figures; To appear in CQ

Gauge-invariant magnetic perturbations in perfect-fluid cosmologies

We develop further our extension of the Ellis-Bruni covariant and gauge-invariant formalism to the general relativistic treatment of density perturbations in the presence of cosmological magnetic fields. We present detailed analysis of the kinematical and dynamical behaviour of perturbed magnetized FRW cosmologies containing fluid with non-zero pressure. We study the magnetohydrodynamical effects on the growth of density irregularities during the radiation era. Solutions are found for the evolution of density inhomogeneities on small and large scales in the presence of pressure, and some new physical effects are identified.Comment: Revised version (some minor changes - few equations added). 26 pages. No figures. To appear in Classical and Quantum Gravit

Averaging anisotropic cosmologies

We examine the effects of spatial inhomogeneities on irrotational anisotropic cosmologies by looking at the average properties of anisotropic pressure-free models. Adopting the Buchert scheme, we recast the averaged scalar equations in Bianchi-type form and close the standard system by introducing a propagation formula for the average shear magnitude. We then investigate the evolution of anisotropic average vacuum models and those filled with pressureless matter. In the latter case we show that the backreaction effects can modify the familiar Kasner-like singularity and potentially remove Mixmaster-type oscillations. The presence of nonzero average shear in our equations also allows us to examine the constraints that a phase of backreaction-driven accelerated expansion might put on the anisotropy of the averaged domain. We close by assessing the status of these and other attempts to define and calculate `average' spacetime behaviour in general relativity.Comment: revised version, to appear in CQ

Structure and stability of the Lukash plane-wave spacetime

We study the vacuum, plane-wave Bianchi $VII{}_{h}$ spacetimes described by the Lukash metric. Combining covariant with orthonormal frame techniques, we describe these models in terms of their irreducible kinematical and geometrical quantities. This covariant description is used to study analytically the response of the Lukash spacetime to linear perturbations. We find that the stability of the vacuum solution depends crucially on the background shear anisotropy. The stronger the deviation from the Hubble expansion, the more likely the overall linear instability of the model. Our analysis addresses rotational, shear and Weyl curvature perturbations and identifies conditions sufficient for the linear growth of these distortions.Comment: Revised version, references added. To appear in Class. Quantum Gra

Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh

Using dynamical systems theory and a detailed numerical analysis, the late-time behaviour of tilting perfect fluid Bianchi models of types IV and VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are studied and the important result that the only future attracting equilibrium points for non-inflationary fluids are the plane-wave solutions in Bianchi type VII$_h$ models is discussed. A tiny region of parameter space (the loophole) in the Bianchi type IV model is shown to contain a closed orbit which is found to act as an attractor (the Mussel attractor). From an extensive numerical analysis it is found that at late times the normalised energy-density tends to zero and the normalised variables 'freeze' into their asymptotic values. A detailed numerical analysis of the type VII$_h$ models then shows that there is an open set of parameter space in which solution curves approach a compact surface that is topologically a torus.Comment: 30 pages, many postscript figure

Dynamical Systems Approach to Magnetised Cosmological Perturbations

Assuming a large-scale homogeneous magnetic field, we follow the covariant and gauge-invariant approach used by Tsagas and Barrow to describe the evolution of density and magnetic field inhomogeneities and curvature perturbations in a matter-radiation universe. We use a two parameter approximation scheme to linearize their exact non-linear general-relativistic equations for magneto-hydrodynamic evolution. Using a two-fluid approach we set up the governing equations as a fourth order autonomous dynamical system. Analysis of the equilibrium points for the radiation dominated era lead to solutions similar to the super-horizon modes found analytically by Tsagas and Maartens. We find that a study of the dynamical system in the dust-dominated era leads naturally to a magnetic critical length scale closely related to the Jeans Length. Depending on the size of wavelengths relative to this scale, these solutions show three distinct behaviours: large-scale stable growing modes, intermediate decaying modes, and small-scale damped oscillatory solutions.Comment: 15 pages RevTeX, 5 figures. Accepted for publication in Physical Review

Anisotropic stresses in inhomogeneous universes

Anisotropic stress contributions to the gravitational field can arise from magnetic fields, collisionless relativistic particles, hydrodynamic shear viscosity, gravitational waves, skew axion fields in low-energy string cosmologies, or topological defects. We investigate the effects of such stresses on cosmological evolution, and in particular on the dissipation of shear anisotropy. We generalize some previous results that were given for homogeneous anisotropic universes, by including small inhomogeneity in the universe. This generalization is facilitated by a covariant approach. We find that anisotropic stress dominates the evolution of shear, slowing its decay. The effect is strongest in radiation-dominated universes, where there is slow logarithmic decay of shear.Comment: 7 pages Revte

Vorticity production and survival in viscous and magnetized cosmologies

We study the role of viscosity and the effects of a magnetic field on a rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal magnetohydrodynamic approximation. Our results confirm that viscosity can generate vorticity in inhomogeneous environments, while the magnetic tension can produce vorticity even in the absence of fluid pressure and density gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we find that viscosity adds to the diluting effect of the universal expansion. Typically, however, the dissipative viscous effects are confined to relatively small scales. We also identify the characteristic length bellow which the viscous dissipation is strong and beyond which viscosity is essentially negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic presence is found to slow down the standard decay-rate of linear vortices, thus leading to universes with more residual rotation than generally anticipated.Comment: Minor changes. References added and updated. Published versio