Evolution of density perturbations in large void universe
  We study the evolution of linear density perturbations in a large spherical
void universe which accounts for the acceleration of the cosmic volume
expansion without introducing dark energy. The density contrast of this void is
not large within the light cone of an observer at the center of the void.
Therefore, we describe the void structure as a perturbation with a
dimensionless small parameter $\kappa$ in a homogeneous and isotropic universe
within the region observable for the observer. We introduce additional
anisotropic perturbations with a dimensionless small parameter $\epsilon$,
whose evolution is of interest. Then, we solve perturbation equations up to
order $\kappa \epsilon$ by applying second-order perturbation theory in the
homogeneous and isotropic universe model. By this method, we can know the
evolution of anisotropic perturbations affected by the void structure. We show
that the growth rate of the anisotropic density perturbations in the large void
universe is significantly different from that in the homogeneous and isotropic
universe. This result suggests that the observation of the distribution of
galaxies may give a strong constraint on the large void universe model.
