Formation of Density Fluctuation and Spacetime structure in Extended Inflation Model

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The Inflationary Universe Model was greatly supported by the discovery of the fluctuations in cosmic background radiation by COBE,since the spectrum was just the same one predicted by this model. This model, however, still have some theoretical problems. In the present work, first we investigated by what conditions cosmic no hair conjecture holds, by using Regge Calculus Method. We found some constraints on the initial condition for inflation in homogeneous and anisotropic model, and now are extending this method to inhomogeneous model. Second, we investigated generation of the density fluctuations by global texture which is expected to be formed in early universe by phase transition of vacuum. We found it has a power law spectrum with non Gaussian fluctuations. Third we investigated the condition of formation of wormholes by phase transition of vacuum, and their evolution. We found traversable wormholes can exist in expanding universe in spite that weak energy condition is satisfied. This research was done as collaboration with M.Nagasawa, Y.Furihata and K.Narahara.