The evolution of space-time and matters in the very early universe

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1. We proposed the delta-N formalism to treat the non-linear fluctuations at super-Hubble horizon scale. This provides us the powerful tool to link the very early universe to observational quantities. This formalism is often used by many peoples who are interested in the non-linear effects in cosmology.2. We proved the uniqueness theorem of static, asymptotically flat black holes in higher dimensions. While there is the Hawking's topology theorem in four dimensions, that is, the topology of event horizon is 2-sphere, this is not the case in higher dimensions. However, our new theorem implies that static black holes have topology of sphere.3. The genesis of Lepton, i. e., Leptogenesis, is most promising mechanism to explain the baryon number observed today. In this mechanism, we proposed a new model which explains the baryon number by the sign of the CP-violation in neutrino oscillations.4. We explored the gravitino decay process during the Big-bang nucleosynthesis and then had the limi … More t to the hadronic decay. This result provides us a strong limit on inflation models and baryogenesis.5. We investigated the evaporation of primordial black holes (PBH) formed in braneworld context. More precisely, using the observational limit on the gamma ray background and the abundance of anti-protons, we could have the limit on the abundance of PBH, the size of extra dimensions and so on.6. With high-resolution N-body simulations, we constructed the triaxial modeling halo density profiles empirically. Then we could explain the observed gravitational arc statistics with this model. This is first time to explain that.7. With Sloan Digital Sky Survey (SDSS) data we found that the evolution of non-Gaussian feature of probability distribution function (PDF) depends on the class of galaxies. Since we could pick up the secondary cause of the appearance of non-Gaussianity through the evolution of galaxy, we could have the basics to explore the initial condition for the density fluctuations. Less