We investigate the effects of the nonminimal coupling between the scalar field dark energy (quintessence) and the dark matter on the two- point correlation function. It is well known that this coupling shifts the turnover scale as well as suppresses
the amplitude of the matter power spectrum. However, these effects are too small to be observed when we limit the coupling strength to be consistent with observations. Since the coupling of quintessence to baryons is strongly constrained, species dependent coupling may arise. This results in a baryon bias that is dif- ferent from unity. Thus, we look over the correlation function in this coupled model. We find that even the non-coupled quintessence model gives the better fit to the correlation function compared to the cosmo- logical constant model. We are also able to observe the enhancement of the baryon acoustic oscillation (BAO) peak due to the increasing bias factor of baryon from this species dependent coupling. In order to avoid the damping effect of the BAO signature in the matter power spectrum due to nonlinear clustering, we consider the coupling effect on the BAO bump in the linear regime. This provides an alternative method to constrain the coupling of dark energy to dark matter.
We discuss the ratio of the angular diameter distances from the source to the lens, $D_{ds}$, and to the observer at present, $D_{s}$, for various dark energy models. It is well known that the difference of $D_s$s between the models is apparent and t
his quantity is used for the analysis of Type Ia supernovae. However we investigate the difference between the ratio of the angular diameter distances for a cosmological constant, $(D_{ds}/D_{s})^{Lambda}$ and that for other dark energy models, $(D_{ds}/D_{s})^{rm{other}}$ in this paper. It has been known that there is lens model degeneracy in using strong gravitational lensing. Thus, we investigate the model independent observable quantity, Einstein radius ($theta_E$), which is proportional to both $D_{ds}/D_s$ and velocity dispersion squared, $sigma_v^2$. $D_{ds}/D_s$ values depend on the parameters of each dark energy model individually. However, $(D_{ds}/D_s)^{Lambda} - (D_{ds}/D_{s})^{rm{other}}$ for the various dark energy models, is well within the error of $sigma_v$ for most of the parameter spaces of the dark energy models. Thus, a single strong gravitational lensing by use of the Einstein radius may not be a proper method to investigate the property of dark energy. However, better understanding to the mass profile of clusters in the future or other methods related to arc statistics rather than the distances may be used for constraints on dark energy.
