We study teleparallel gravity in the emph{original} Kaluza-Klein (KK) scenario. Our calculation of the KK reduction of teleparallel gravity indicates that the 5-dimensional torsion scalar $^{(5)}T$ generates the non-Brans-Dicke type effective Lagrang
ian in 4-dimension due to an additional coupling between the derivative of the scalar field and torsion, but the result is equivalent to that in general relativity. We also discuss the cosmological behavior in the FLRW universe based on the effective teleparallel gravity.
We investigate the viable exponential $f(R)$ gravity in the metric formalism with $f(R)=-beta R_s (1-e^{-R/R_s})$. The latest sample of the Hubble parameter measurements with 23 data points is used to place bounds on this $f(R)$ model. A joint analys
is is also performed with the luminosity distances of Type Ia supernovae and baryon acoustic oscillations in the clustering of galaxies, and the shift parameters from the cosmic microwave background measurements, which leads to $0.240<Omega_m^0<0.296$ and $beta>1.47$ at 1$sigma$ confidence level. The evolutions of the deceleration parameter $q(z)$ and the effective equations of state $omega_{de}^{eff}(z)$ and $omega_{tot}^{eff}(z)$ are displayed. By taking the best-fit parameters as prior values, we work out the transition redshift (deceleration/acceleration) $z_T$ to be about 0.77. It turns out that the recent observations are still unable to distinguish the background dynamics in the $Lambda$CDM and exponential $f(R)$ models.
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 grav
ity 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.
We study finite quantum corrections for several well known neutrino mixing matrices and find that it is hard to account for the large value of theta_13 recently reported by T2K and MINOS. To nicely reproduce all experimentally favored neutrino mixing
angles and masses, we propose a new neutrino mixing pattern. We also demonstrate a simple realization by slightly extending the standard model to illustrate the quantum corrections.
