Abstract
Recently the cosmological dynamics of an anisotropic Universe in f(T) gravity became an area of intense investigations. Some earlier papers devoted to this issue contain contradictory claims about the nature and propertied of vacuum solutions in this theory. The goal of the present paper is to clarify this situation. We compare properties of f(T) and f(R) vacuum solutions and outline differences between them. The Kasner solution appears to be an exact solution for the T=0 branch, and an asymptotic solution for the T ne 0 branch. It is shown that the Kasner solution is a past attractor if T<0, being a past and future attractor for the T>0 branch.
Highlights
If the equations of motion are of the second order, as in general relativity (GR), the power-law solution for the scale factor is an asymptotic solution
In the high-curvature regime, these two conditions for power exponents are different from those in the GR Kasner solution [4–6], while the GR Kasner solution is an asymptotic solution in the low-curvature regime
A new class of modified gravity theories has started to attract much attention. It is based on the Teleparallel Equivalent to General Relativity (TEGR)—a theory first considered by Einstein in the 1920s [9–11] where the LeviCivita connection has been replaced by Weitzenböck connection [12], and curvature scalar R in the action by the torsion scalar T
Summary
If the equations of motion are of the second order, as in GR (that is, in Gauss–Bonnet gravity), the power-law solution for the scale factor is an asymptotic solution. We will see below that none of the two quadratic gravity alternatives regarding a Kasner solution can be true for f (T ) cosmology where we meet a third, different situation.
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