We study the cosmological evolutions of the equation of state for dark energy $w_{\mathrm{DE}}$ in the exponential and logarithmic as well as their combination $f(T)$ theories. We show that the crossing of the phantom divide line of $w_{\mathrm{DE}} = -1$ can be realized in the combined $f(T)$ theory even though it cannot be in the pure exponential or logarithmic $f(T)$ theory. In particular, the crossing is from $w_{\mathrm{DE}} > -1$ to $w_{\mathrm{DE}} < -1$, in the opposite manner from $f(R)$ gravity models. We also demonstrate that this feature is favored by the recent observational data.

We explore the generation of large-scale magnetic fields from inflation in teleparallelism, in which the gravitational theory is described by the torsion scalar instead of the scalar curvature in general relativity. In particular, we examine the case that the conformal invariance of the electromagnetic field during inflation is broken by a non-minimal gravitational coupling between the torsion scalar and the electromagnetic field. It is shown that for a power-law type coupling, the magnetic field on 1~Mpc scale with its strength of $\sim 10^{-9}$~G at the present time can be generated.

We study teleparallel gravity in five-dimensional spacetime with particular discussions on Kaluza-Klein (KK) and braneworld theories. We directly perform the dimensional reduction by differential forms. In the braneworld theory, the teleparallel gravity formalism in the Friedmann-Lema\^{i}tre-Robertson-Walker cosmology is equivalent to GR due to the same Friedmann equation, whereas in the KK case the reduction of our formulation does not recover the effect as GR of 4-dimensional spacetime due to an additional coupling between the derivative of scalar field and torsion, which results in some different behavior from general relativity.

We study the cosmological evolutions of the equation of state for dark energy $w_{\mathrm{DE}}$ in the exponential and logarithmic as well as their combination $f(T)$ theories. We show that the crossing of the phantom divide line of $w_{\mathrm{DE}} = -1$ can be realized in the combined $f(T)$ theory even though it cannot be in the pure exponential or logarithmic $f(T)$ theory. In particular, the crossing is from $w_{\mathrm{DE}} > -1$ to $w_{\mathrm{DE}} < -1$, in the opposite manner from $f(R)$ gravity models. We also demonstrate that this feature is favored by the recent observational data.

We explore the generation of large-scale magnetic fields from inflation in teleparallelism, in which the gravitational theory is described by the torsion scalar instead of the scalar curvature in general relativity. In particular, we examine the case that the conformal invariance of the electromagnetic field during inflation is broken by a non-minimal gravitational coupling between the torsion scalar and the electromagnetic field. It is shown that for a power-law type coupling, the magnetic field on 1~Mpc scale with its strength of $\sim 10^{-9}$~G at the present time can be generated.

We study teleparallel gravity in five-dimensional spacetime with particular discussions on Kaluza-Klein (KK) and braneworld theories. We directly perform the dimensional reduction by differential forms. In the braneworld theory, the teleparallel gravity formalism in the Friedmann-Lema\^{i}tre-Robertson-Walker cosmology is equivalent to GR due to the same Friedmann equation, whereas in the KK case the reduction of our formulation does not recover the effect as GR of 4-dimensional spacetime due to an additional coupling between the derivative of scalar field and torsion, which results in some different behavior from general relativity.

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