Expanding (3+1)-Dimensional Universe from a Lorentzian Matrix Model for Superstring Theory in (9+1) Dimensions

Abstract

We reconsider the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. Unlike the previous works in which the Wick rotation was used to make the model well defined, we regularize the Lorentzian model by introducing infrared cutoffs in both the spatial and temporal directions. Monte Carlo studies reveal that the two cutoffs can be removed in the large-N limit and that the theory thus obtained has no parameters other than one scale parameter. Moreover, we find that three out of nine spatial directions start to expand at some "critical time," after which the space has SO(3) symmetry instead of SO(9).

Recent developments in the type IIB matrix model

“…(Such a constraint is analogous to the one that appeared in the model inspired by space-time uncertainty principle [26].) Without loss of generality, we set L = 1 in (7), and thus we arrive at the model [10] …”

“…[10] we performed Monte Carlo simulation of the model (8). In order to extract the "time evolution", we diagonalize A 0 , and define the eigenvectors |t a corresponding to the eigenvalues t a of A 0 (a = 1, .…”

“…Real-time evolution can be extracted from matrix configurations that dominate the path integral. It was shown that expanding three-dimensional space appears after a critical time [10], and the possibility of observing Inflation and the Big Bang has been discussed [11,12]. The behavior at much later times has been studied by solving the classical equation of motion [13], and a natural solution to the cosmological constant problem has been suggested [14].…”

“…On the other hand, it was found that the Lorentzian model can be made well-defined by introducing infrared cutoffs and removing them in the large-N limit [10]. Real-time evolution can be extracted from matrix configurations that dominate the path integral.…”

Matrix theory origins of non-geometric fluxes

“…[5] and it was studied further in numerous instances. These range from the study of non-commutative Yang-Mills theories [6], the structure and dimensionality of spacetime [7][8][9] and the emergence of geometry and gravity [10] to applications in particle physics [11,12] and cosmology [13,14]. It is worth mentioning that these studies use both analytical tools and/or Monte Carlo simulations.…”