Birth and Growth of Two-dimensional Universe

A master equation for the evolution of two-dimensional universe is derived based on the simplicial quantum gravity regarding the evolution as the Markov process of a space-time lattice. Three typical phases, expanding, elongating and collapsing phase, which have been found in the numerical simulation, are studied together with their boundaries, analytically. Asymptotic solutions of the evolution equation for statistical quantities, such as averaged area, boundary length, and correlation of fluctuations, are obtained for each phase and boundary.After introducing a physical time the cosmological significance of each phase is discussed.