A Complete Cosmological Solution to the Averaged Einstein Field Equations as found in Macroscopic Gravity

A formalism for analyzing the complete set of field equations describing Macroscopic Gravity is presented. Using this formalism, a cosmological solution to the Macroscopic Gravity equations is determined. It is found that if a particular segment of the connection correlation tensor is zero and if the macroscopic geometry is described by a flat Robertson-Walker metric, then the effective correction to the averaged Einstein Field equations of General Relativity i.e., the backreaction, is equivalent to a positive spatial curvature term. This investigation completes the analysis of [Phys. Rev. Lett., vol. 95, 151102, (2005)] and the formalism developed provides a possible basis for future studies.Comment: 11 page

Technologie verplicht

Overheidsorganisaties maken in toenemende mate gebruik van geavanceerde technologie. Hierdoor zijn zij in staat gebleken de kwaliteit én de snelheid van hun werkzaamheden aanzienlijk te verbeteren en het eind van de nieuwe mogelijkheden lijkt nog lang niet in zicht. Veel overheidsorganisaties volgen de technologische ontwikkelingen dan ook op de voet. Moderne technologie schept naast mogelijkheden echter ook verplichtingen. Immers, als overheidsorganisaties hun werk beter kunnen doen met behulp van technologie, moeten zij dat ook doen. Dit zou wel eens een belangrijke nieuwe verplichting in het recht kunnen worden: de verplichting om technologie te gebruiken. De stelling wordt, wat het openbaar ministerie betreft, ondersteund door arresten van het Hof Amsterdam en van de Hoge Raad

Bianchi IX Brane-world Cosmologies

We shall investigate the asymptotic properties of the Bianchi type IX cosmological model in the Brane-world scenario. The matter content is assumed to be a combination of a perfect fluid and a minimimally coupled scalar field that is restricted to the Brane. A detailed qualitative analysis of the Bianchi type IX braneworld containing a scalar field having an exponential potential is undertaken. It is found that the Brane-Robertson Walker solution is a local source for the expanding Bianchi IX models, and if $k^2<2$ the expanding Bianchi IX models asymptote to the power-law inflationary solution. The only other local sink is the contracting Brane-Robertson Walker solution. An analysis of the Bianchi IX models with a scalar field with a general potential is discussed, and it is shown that in the case of expanding models, for physical scalar field potentials close to the initial singularity, the scalar field is effectively massless, and the solution is approximated by the Brane-Robertson Walker model.Comment: 28 pages, RevTe

Brane-world Cosmologies with non-local bulk effects

It is very common to ignore the non-local bulk effects in the study of brane-world cosmologies using the brane-world approach. However, we shall illustrate through the use of three different scenarios, that the non-local bulk-effect ${\cal P}_{\mu\nu}$ does indeed have significant impact on both the initial and future behaviour of brane-world cosmologies.Comment: 17 pages, no figures, iopart.cls, submitted to CQ

Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach

Teleparallel gravity and its popular generalization $f(T)$ gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel gravity and its generalizations can be found in the literature, especially regarding their local Lorentz invariance. We describe how these misunderstandings may have arisen and attempt to clarify the situation. In particular, the central point of confusion in the literature appears to be related to the inertial spin connection in teleparallel gravity models. While inertial spin connections are commonplace in special relativity, and not something inherent to teleparallel gravity, the role of the inertial spin connection in removing the spurious inertial effects within a given frame of reference is emphasized here. The careful consideration of the inertial spin connection leads to the construction of a fully invariant theory of teleparallel gravity and its generalizations. Indeed, it is the nature of the spin connection that differentiates the relationship between what have been called good tetrads and bad tetrads and clearly shows that, in principle, any tetrad can be utilized. The field equations for the fully invariant formulation of teleparallel gravity and its generalizations are presented and a number of examples using different assumptions on the frame and spin connection are displayed to illustrate the covariant procedure. Various modified teleparallel gravity models are also briefly reviewed.Comment: v2: 72 pages, revised version, references added, matches published versio

Scalar Field Cosmologies with Barotropic Matter: Models of Bianchi class B

We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter content is composed of two non-interacting components; the first component is described by a barotropic fluid having a gamma-law equation of state, whilst the second is a non-interacting scalar field (phi) with an exponential potential V=Lambda exp(k phi). In particular, we study the asymptotic properties of the models both at early and late times, paying particular attention on whether the models isotropize (and inflate) to the future, and we discuss the genericity of the cosmological scaling solutions.Comment: 18 pages, 1 figure, uses revtex and epsf to insert figur

Qualitative Viscous Cosmology

The Full (non--truncated) Israel--Stewart theory of bulk viscosity is applied to dissipative FRW spacetimes. Dimensionless variables and dimensionless equations of state are used to write the Einstein--thermodynamic equations as a plane autonomous system and the qualitative behaviour of this system is determined. Entropy production in these models is also discussed.Comment: 13 pages, REVTeX, accepted for publication in Physical Review

Dynamics of Generalized Assisted Inflation

We study the dynamics of multiple scalar fields and a barotropic fluid in an FLRW-universe. The scalar potential is a sum of exponentials. All critical points are constructed and these include scaling and de Sitter solutions. A stability analysis of the critical points is performed for generalized assisted inflation, which is an extension of assisted inflation where the fields mutually interact. Effects in generalized assisted inflation which differ from assisted inflation are emphasized. One such a difference is that an (inflationary) attractor can exist if some of the exponential terms in the potential are negative.Comment: 27 page

The Dynamics of Multi-Scalar Field Cosmological Models and Assisted Inflation

We investigate the dynamical properties of a class of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials. We show that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions asymptotically the curvature is not dynamically negligible). Consequently, we find that in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behaviour, contrary to what is commonly believed. The early-time and intermediate behaviour of the models is also studied. In particular, n-scalar field models are investigated and the structure of the saddle equilibrium points corresponding to inflationary m-field scaling solutions and non-inflationary m-field matter scaling solutions are also studied (where m<n), leading to interesting transient dynamical behaviour with new physical scenarios of potential importance.Comment: 27 pages, uses REVTeX Added an appendix illustrating some of the details needed to compute the stability of the assisted inflationary solutio