Cosmological observations in the inhomogeneous Universe and the evolution of a local inhomo geneity

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Parameters characterizing homogeneous and isotropic cosmological models (Hubble constant HィイD20ィエD2 and deceleration parameter, and so on) are determined on the basis of statistical analyses for the spatial distribution and velocities of astronomical objects. The values of Hubble constant are scattered even at present, and there is a tendency that HィイD20ィエD2 【approximately equal】 72km sィイD1-1ィエD1 and MpcィイD1-1ィエD1 in the range within 100 Mpc and HィイD20ィエD2 60 km sィイD1-1ィエD1 and MpcィイD1-1ィエD1 in the range of 100〜400Mpc. According to recent observation due to supernovae of type Ia, moreover, the deceleration parameter is found to be negative (i.e. the acceleration of the Universe).On the other hand, the bulk flow existing within 100 Mpc is not compatible with the homogeneity of cosmological models, which was discovered by Hudson et al. (1999) and Willick (1999). If we assume the existence of this bulk flow, a possible way is to consider an inhomogeneous cosmological (void) model in order to make the theory and observation compatible. This model consists of the outer region with high-density and smaller Hubble constant and the inner (void) spherical region with low-density and larger Hubble constant, and our observer (O) is assumed to be in a position deviated from the center (C). This local void-like region plays an important role similar to the cosmological constant.In the present project, we treated (1) an inhomogeneous cosmological model with the above two regions to investigate the observational aspects of inhomogeneous models, and (2) numerical simulations of gravitational lensing the null-geodesic equation, in order to study the cosmological parameters in inhomogeneous models. Due to these works we have found the consistency between above various observations and theoretical models, and fruitful possibilities of inhomogeneous models.