f(T) teleparallel gravity and cosmology

Abstract

Kibble equations F. Realizations of torsion tensors G. Torsion contributions to the energy-momentum tensor H. Torsion contributions to shear, expansion, vorticity and acceleration 1. The kinematical quantities 2. The Raychaudhuri equation III.

Bianchi I cosmological solutions in teleparallel gravity

“…Thus we can interpret regimes with H < 0 as contracting Universe and regimes with H > 0 as expanding one. Moreover if we substitute H = 0 into equation (20) we find that at the point of bounce Ṫ = 0 as well.…”

“…Now we have system of three equations (19)(20)(21) for three independent variables H, T , ρ with the first integral (13). It is interesting to note that variable ρ may be totally decoupled from the system: if derive matter density from constraint (13) and substitute it to equations ( 19)-( 20) we obtain closed system of two differential equations for two variables H and T , where matter will have influence only by equation of state's parameter w.…”

“…It is quite natural to suppose that lowest term is T , because f = T is equivalent to GR and we would like to have it as a limit. It means that instead of ( 19)- (20) we have for such kind of solution approximate system…”

A geometric view on local Lorentz transformations in teleparallel gravity

“…During the last decade, teleparallel gravity theories, which attribute the gravitational interaction to the torsion of a flat, metric-compatible connection instead of the curvature of the Levi-Civita connection, have received growing attention [1,2], and provided numerous models to address the open questions in gravity and cosmology [3][4][5]. An important notion, which is of particular relevance in these theories, is that of local Lorentz invariance, and its potential breaking in modified teleparallel gravity theories [6][7][8].…”

Spin connection and cosmological perturbations in f(T) gravity

“…all this values depend on all coordinates in the most general case. Now taking the tetrad ( 17) and all 24 independent components of ω A Bµ we can calculate all values which is needed for equation of motion (13), keeping only linear terms with respect to ψ, φ, ω A Bµ and their derivatives. As the expressions for T λ µν and S λ µν are rather combersome, we write down here final results only for torsion scalar and for S ikl ∂ l f T product because they are both important for equations of motion.…”