Monte Carlo studies on the expanding behavior of the early universe in the Lorentzian type IIB matrix model

Abstract

The type IIB matrix model is a conjectured nonperturbative formulation of superstring theory. Recently the Lorentzian version of the model has been studied by Monte Carlo simulation, and it has been shown that only three out of nine spatial directions start to expand after a critical time. We extend this work by investigating the expanding behavior for much longer time. We find that the 3d space expands exponentially for some period of time, which may be interpreted as inflation. We also simulate a simplified model, which is expected to capture some qualitative features of the original model at much later times. We observe that the exponential expansion eventually changes into a power-law t^(1/2) behavior, which agrees with the expanding behavior of the Friedmann-Robertson-Walker (FRW) universe in the radiation dominated era.