AUTHOR=Nesterov Alexander I. , Mata Héctor 

TITLE=How Nonassociative Geometry Describes a Discrete Spacetime

JOURNAL=Frontiers in Physics

VOLUME=Volume 7 - 2019

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 provides an unified algebraic description of continuum and 
discrete spaces, making it a valuable candidate for the study of discrete spacetime. In the framework of the nonassociative geometry we propose the model of emergent spacetime. At the Planckian scales the spacetime is described by a so-called diodular discrete structure, but at large scales it ``looks like'' a differentiable manifold. In our model, 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 $(2+1)$-D discrete spacetime and a discrete Friedmann-Robertson-Walker cosmological model. We show that in a continuous limit the evolution of the discrete spacetime corresponds to the radiation epoch of the standard cosmological model.