Spacetime emergence in the Robertson-Walker universe from a matrix model

Abstract

Using a novel, string theory-inspired formalism based on a Hamiltonian constraint, we obtain a conformal mechanical system for the spatially flat four-dimensional Robertson-Walker Universe. Depending on parameter choices, this system describes either a relativistic particle in the Robertson-Walker background, or metric fluctuations of the Robertson-Walker geometry. Moreover we derive a tree-level M-theory matrix model in this time-dependent background. Imposing the Hamiltonian constraint forces the spacetime geometry to be fuzzy near the big bang, while the classical Robertson-Walker geometry emerges as the Universe expands. From our approach we also derive the temperature of the Universe interpolating between the radiation and matter dominated eras.