A renormalization group method for studying the early universe in the Lorentzian IIB matrix model

Abstract: We propose a new method for studying the early universe in the Lorentzian version of the IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. This method is based on the idea of renormalization group, and it enables us to study the time-evolution of the universe for much longer time than in the previous work, which showed that the SO(9) rotational symmetry is spontaneously broken down to SO(3) after a "critical time". We demonstrate how this method works in a simplified model, which is expected to capture the behaviors of the original model when the space is not so large. In particular, we present clear evidence that the three-dimensional space expands exponentially after the critical time in this simplified model.