Global properties of higher-dimensional cosmological spacetimes

We study global existence problems and asymptotic behavior of higher-dimensional inhomogeneous spacetimes with a compact Cauchy surface in the Einstein-Maxwell-dilaton (EMD) system. Spacelike $T^{D-2}$-symmetry is assumed, where $D\geq 4$ is spacetime dimension. The system of the evolution equations of the EMD equations in the areal time coordinate is reduced to a wave map system, and a global existence theorem for the system is shown. As a corollary of this theorem, a global existence theorem in the constant mean curvature time coordinate is obtained. Finally, for vacuum Einstein gravity in arbitrary dimension, we show existence theorems of asymptotically velocity-terms dominated singularities in the both cases which free functions are analytic and smooth.