AUTHOR=Nesterov Alexander I. , Mata Héctor TITLE=How Nonassociative Geometry Describes a Discrete Spacetime JOURNAL=Frontiers in Physics VOLUME=7 YEAR=2019 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00032 DOI=10.3389/fphy.2019.00032 ISSN=2296-424X ABSTRACT=

Nonassociative geometry, providing a unified description of discrete and continuum spaces, is a valuable candidate for the study of discrete models of spacetime. Within the framework of nonassociative geometry we propose a model of emergent spacetime. In our approach, the evolution of spacetime geometry is governed by a random/stochastic process. This leads to a natural appearance of causal structure and arrow of time. We apply our approach to study a toy model of discrete (2+1)-D spacetime and Friedmann-Robertson-Walker cosmological model. We show that in a continuous limit the evolution of the discrete spacetime corresponds to a radiation epoch of the standard cosmological model.