Spatially flat FLRW spacetimes with a Big Bang from matrix geometry

TL;DR

The paper demonstrates how an expanding, spatially flat ($k=0$) FLRW quantum spacetime with a Big Bang emerges from a covariant matrix-geometry construction within the IKKT model. It develops a full scalar-field framework on this background, including a matrix d'Alembertian, an $i\varepsilon$-regulated path integral, and an exact propagator expressed through Gegenbauer functions, while revealing a close relation to the geometric d'Alembertian on the Poincaré patch of de Sitter space. A key result is that, in the semi-classical regime, the propagator behaves like the Minkowski propagator with an effective mass $m^2/(\tau\tau')$, and boundary-condition dependent reflections from the Big Bang are suppressed, though they encode global boundary data. The work also clarifies the role of an internal $S^2$ fiber yielding higher-spin modes that remain massless in this background, and it contrasts the $k=0$ case with the previously studied $k=-1$ Big-Bounce scenarios, highlighting the emergent-spacetime paradigm and potential avenues for quantum gravity phenomenology.

Abstract

We present an expanding, spatially flat ($k=0$) FLRW quantum spacetime with a Big Bang, considered as a background in Yang-Mills matrix models. The FLRW geometry emerges in the semi-classical limit as a projection from the fuzzy hyperboloid. We analyze the propagation of scalar fields, and demonstrate that their Feynman propagator resembles the Minkowski space Feynman propagator in the semi-classical regime. Moreover, the higher spin modes predicted by the matrix model are described explicitly. These results are compared to recent results on $k=-1$ FLRW quantum spacetimes with a Big Bounce.