Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

TL;DR

This study demonstrates that a simplified bosonic Lorentzian type IIB matrix model can dynamically produce a (3+1)D expanding universe with a power-law growth, providing insights into the emergence of cosmological behavior from string theory models.

Contribution

The paper shows that a bosonic matrix model, without fermions, can exhibit a dynamically emerging (3+1)D universe with power-law expansion, extending previous work with larger matrix sizes.

Findings

(3+1)D universe emerges for N > 110

Power-law expansion t^{1/2} observed at late times

Large-N scaling property confirmed

Abstract

Recent studies on the Lorentzian version of the type IIB matrix model show that (3+1)D expanding universe emerges dynamically from (9+1)D space-time predicted by superstring theory. Here we study a bosonic matrix model obtained by omitting the fermionic matrices. With the adopted simplification and the usage of a large-scale parallel computer, we are able to perform Monte Carlo calculations with matrix size up to $N=512$, which is twenty times larger than that used previously for the studies of the original model. When the matrix size is larger than some critical value $N_{\rm c}\simeq 110$, we find that (3+1)D expanding universe emerges dynamically with a clear large-$N$ scaling property. Furthermore, at sufficiently late times, we observe a power-law behavior $t^{1/2}$ of the spatial extent with respect to time $t$, which is reminiscent of the expanding behavior of the Friedmann-Robertson-Walker universe in the radiation dominated era. We discuss possible implications of this result on the original model including fermionic matrices.