Note On A Super-Horizon-Scale Inhomogeneous Cosmological Model

Many observations of large-scale and cosmological structures in the universe have been collected, but so far there is no consistent theoretical explanation. In the region within 100 Mpc from us, the observed two-point correlations of galaxies and clusters of galaxies can be described well by low-density homogeneous cosmological models (Bahcall & Cen 1993; Suto 1993). On the other hand, the observed anisotropies of the cosmic microwave background radiation have been explained well by comparatively high-density cosmological models such as the Einstein-de Sitter model (Bunn & Sugiyama 1994). In the intermediate scale, the angular sizes of the cores of quasars have been measured and their redshift dependence has been shown to be more consistent with the Einstein-de Sitter model than with the low-density models (Kellermann 1993). The number count-magnitude relation for remote galaxies supports low-density models with a nonzero cosmological constant (for example, Fukugita et al. 1990), but these models may be inconsistent with the observed distribution of Lyα clouds (Fukugita & Lahav 1991).