Can Inhomogeneities Accelerate the Cosmic Volume Expansion?

If expanding and contracting regions coexist in the universe, the speed ofthe cosmic volume expansion can be accelerated. We construct simpleinhomogeneous dust-filled universe models in which the speed of the cosmicvolume expansion is accelerated for finite periods. These models areconstructed by removing spherical domains from the Einstein-de Sitter universeand filling each domain with a Lemaitre-Tolman-Bondi dust sphere possessing thesame gravitational mass as the removed region. This represents an exactsolution of the Einstein equations. We find that acceleration of the cosmicvolume expansion is realized in some cases when the size of the contractingregion is comparable to the horizon radius of the Einstein-de Sitter universethough this model is very different from the universe observed today. Thisresult implies that non-linear general relativistic effects of inhomogeneitiesare very important to realize the acceleration of the cosmic volume expansion.Comment: 12 pages,5 figures. version published in Progress of Theoretical Physic