Cosmic time evolution and propagator from a Yang–Mills matrix model

Abstract

We consider a solution of a IKKT-type matrix model which can be considered as a 1+1-dimensional space-time with Minkowski signature and a Big Bounce (BB)-like singularity. A suitable regularization of the Lorentzian matrix integral is proposed, which leads to the standard -prescription for the effective field theory. In particular, the Feynman propagator is recovered locally for late times. This demonstrates that a causal structure and time evolution can emerge in the matrix model, even on non-trivial geometries. We also consider the propagation of modes through the BB, and observe an interesting correlation between the post-BB and pre-BB sheets, which reflects the structure of the brane in target space.