Usually the effects of isotropic inhomogeneities are not seriously taken into account in the determination of the cosmological parameters because of Copernican principle whose statement is that we do not live in the privileged domain in the universe. But Copernican principle has not been observationally confirmed yet in sufficient accuracy, and there is the possibility that there are non-negligible large-scale isotropic inhomogeneities in our universe. In this paper, we study the effects of the isotropic inhomogeneities on the determination of the cosmological parameters and show the probability that non-Copernican isotropic inhomogeneities mislead us into believing, for example, the phantom energy of the equation of state, p = wρ with w < −1, even in case that w = −1 is the true value.

Usually, we assume that there is no inhomogeneity isotropic in terms of our location in our universe. This assumption has not been observationally confirmed yet in sufficient accuracy, and we need to consider the possibility that there are non-negligible large-scale isotropic inhomogeneities in our universe. The existence of large-scale isotropic inhomogeneities affects the determination of the cosmological parameters. In particular, from only the distance-redshift relation, we can not distinguish the inhomogeneous isotropic universe model from the homogeneous isotropic one, because of the ambiguity in the cosmological parameters. In this paper, in order to avoid such ambiguity, we consider three observables, the distance-redshift relation, the fluctuation spectrum of the cosmic microwave background radiation(CMBR) and the scale of the baryon acoustic oscillation(BAO), and compare these observables in two universe models; One is the inhomogeneous isotropic universe model with the cosmological constant and the other is the homogeneous isotropic universe model with the dark energy other than the cosmological constant. We show that these two universe models can not predict the same observational data of all three observables but the same ones of only two of three, as long as the perturbations are adiabatic. In principle, we can distinguish the inhomogeneous isotropic universe from the homogeneous isotropic one through appropriate three observables, if the perturbations are adiabatic.