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

TL;DR

This paper demonstrates how a Lorentzian matrix model can produce emergent causal structure and time evolution, including a Big Bounce scenario, with a consistent Feynman propagator and mode propagation analysis.

Contribution

It introduces a regularization scheme for Lorentzian matrix integrals that yields standard quantum field theory prescriptions and shows emergent causality in a non-trivial geometry.

Findings

Feynman propagator recovered at late times

Causal structure emerges in the matrix model

Mode propagation across the Big Bounce shows correlations

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-like singularity. A suitable $i\varepsilon$ regularization of the Lorentzian matrix integral is proposed, which leads to the standard $i\varepsilon$-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 Big Bounce, and observe an interesting correlation between the post-BB and pre-BB sheets, which reflects the structure of the brane in target space.