The Effect of Anisotropic Extra Dimension in Cosmology

We consider five dimensional conformal gravity theory which describes an anisotropic extra dimension. Reducing the theory to four dimensions yields Brans-Dicke theory with a potential and a hidden parameter $z$ which implements the anisotropy between the four dimensional spacetime and the extra dimension. We find that a range of value of the parameter $z$ can address the current dark energy density compared to the Planck energy density. Constraining the parameter $z$ and the other cosmological model parameters using the recent observational data consisting of the Hubble parameters, type Ia supernovae, and baryon acoustic oscillations, together with the Planck or WMAP 9-year data of the cosmic microwave background radiation, we find $z>-2.05$ for Planck data and $z>-2.09$ for WMAP 9-year data at 95\% confidence level. We also obtained constraints on the rate of change of the effective Newtonian constant~($G_{\rm eff}$) at present and the variation of $G_{\rm eff}$ since the epoch of recombination to be consistent with observation.