Can we remove the systematic error due to isotropic inhomogeneities?

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 cosmological parameters. In particular, from only the distance-redshift relation, we cannot 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, and the scale of the baryon acoustic oscillation—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 dark energy other than the cosmological constant. We show that these two universe models cannot 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 the appropriate three observables, if the perturbations are adiabatic.

Figure 1

We depict $\mathrm{\Delta }{d}_{\mathrm{z}}(0.35)$ as a heat map on the $w_1-w_0$ plane. The difference in the form of a point represents the difference of the density contrast $\mathrm{\Delta }$ at the observer. A circle means a point that the absolute value of the density contrast $|\mathrm{\Delta }|$ at the observer is less than 0.1, whereas triangles mean a point that $|\mathrm{\Delta }|$ at the observer is more than 0.1. The lower left corner of the blank is the domain in which the linear perturbation approximation is not valid.

Figure 2

We depict $\mathrm{\Delta }{d}_{\mathrm{z}}(0.35)$ as a function of the $w_0$ with various $w_1$.

Figure 3

We depict $\mathrm{\Delta }{d}_{\mathrm{z}}$ as a function of $z$ in the domain $0<z<2$, for several pairs of $w_0$ and $w_1$ on the curve in the $w_1-w_0$ plane along which $\mathrm{\Delta }{d}_{\mathrm{z}}(0.35)$ vanishes.

Figure 4

We depict $\mathrm{\Delta }{d}_{\mathrm{z}}$ as a function of the redshift $\mathrm{z}$. The FLRW universe model is filled with nonrelativistic matter and the dark energy of various $w_0$ and $w_1=0$.