TL;DR
This paper derives a master equation for the evolution of a two-dimensional universe using simplicial quantum gravity, analyzes its phases analytically, and discusses their cosmological implications.
Contribution
It introduces an analytical framework for understanding the phases of a two-dimensional universe's evolution based on a master equation derived from simplicial quantum gravity.
Findings
Identifies three phases: expanding, elongating, and collapsing.
Provides asymptotic solutions for key statistical quantities in each phase.
Discusses the cosmological significance of each phase.
Abstract
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.
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