Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on Proper Frame

In this paper, we first develop a complete perturbation theory requiring only the perturbation of the fundamental quantities describing Teleparallel Gravity. We first obtain the physical quantities by perturbing the coframes taking into account the gauge metric and spin-connection conditions. We obtain the perturbed field equations involving these perturbed quantities. We will study some specific cases of perturbations of coframes and finally discuss the stability of the Minkowski background. Our perturbation framework is based on using a proper orthonormal frame throughout, which is possible since we remain with a theory of Teleparallel Gravity.Comment: 33 pages, submitted to a journa

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

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

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

Bianchi Type Cosmological Models in f(T)f(T) Tele-parallel Gravity

Symmetry assumptions on the geometrical framework have provided successful mechanisms to develop physically meaningful solutions to many problems. In tele-parallel gravity, invariance of the frame and spin-connection under a group of motions defines an affine symmetry group. Here, we assume there exists a three-dimensional group of affine symmetries acting simply transitively on a spatial hypersurface and that this group of symmetry actions defines our affine frame symmetry group. We determine the general form of the co-frame and spin connection for each spatially homogeneous Bianchi type. We then construct the corresponding field equations for $f(T)$ tele-parallel gravity. We show that if the symmetry group is of Bianchi type A ($I$, $II$, $VI_0$, $VII_0$, $VIII$ or $IX$) then there exists a co-frame/spin connection pair that is consistent with the antisymmetric part of the field equations of $f(T)$ tele-parallel gravity. For those geometries having a Bianchi type B symmetry group ($IV$, $V$, $VI_h$, $VII_h$), we find that in general these geometries are inconsistent with the antisymmetric part of the $f(T)$ tele-parallel gravity field equations unless the theory reduces to an analog of General Relativity with a cosmological constant.Comment: 28 page