Narrow Results

Usually, in order to investigate the evolution of a theory, one may find the critical points of the system and then perform perturbations around these critical points to see whether they are stable or not. This local method is very useful when the initial values of the dynamical variables are not far away from the critical points. Essentially, the nonlinear effects are totally neglected in such kind of approach. Therefore, one cannot tell whether the dynamical system will evolute to the stable critical points or not when the initial values of the variables do not close enough to these critical points. Furthermore, when there are two or more stable critical points in the system, local analysis cannot provide the information on which the system will finally evolute to. In this paper, we have further developed the nullcline method to study the bifurcation phenomenon and global dynamical behavior of the f(T) theory. We overcome the shortcoming of local analysis. And, it is very clear to see the evolution of the system under any initial conditions.

In this paper, we study the growth index of matter density perturbations for the power law model in f(T) gravity. Using the parametrization γ(z) = γ₀ + γ₁(z/1 + z) for the growth index, which approximates the real evolution of γ(z) very well, and the observational data of the growth factor, we find that, at the 1σ confidence level, the power law model in f(T) gravity is consistent with the observations, since the obtained theoretical values of γ₀ and γ₁ are in the allowed region.

The issue of causality in f(T) gravity is investigated by examining the possibility of existence of the closed timelike curves in the Gödel-type metric. By assuming a perfect fluid as the matter source, we find that the fluid must have an equation of state parameter greater than minus one in order to allow the Gödel solutions to exist, and furthermore the critical radius r_c, beyond which the causality is broken down, is finite and it depends on both matter and gravity. Remarkably, for certain f(T) models, the perfect fluid that allows the Gödel-type solutions can even be normal matter, such as pressureless matter or radiation. However, if the matter source is a special scalar field rather than a perfect fluid, then r_c → ∞ and the causality violation is thus avoided.