Universal behaviour of generalized Causal set d'Alembertians in curved spacetime

TL;DR

This paper demonstrates that a broad class of generalized causal set d'Alembertian operators in curved spacetime universally exhibit the same curvature coupling term, extending previous minimal operator results and relating to the Einstein Equivalence principle.

Contribution

It extends the universality of the curvature coupling term to all generalized causal set d'Alembertians in curved spacetime, beyond minimal operators.

Findings

All generalized causal set d'Alembertians include a -R/2 term in curved spacetime.

The universality of this term holds for a broad class of operators, not just minimal ones.

The results have implications for the Einstein Equivalence principle.

Abstract

Causal set non-local wave operators allow both for the definition of an action for Causal set theory and the study of deviations from local physics that may have interesting phenomenological consequences. It was previously shown that, in all dimensions, the (unique) minimal discrete operators give averaged continuum non-local operators that reduce to $\Box-R/2$ in the local limit. Recently, dropping the constraint of minimality, it was shown that there exist an infinite number of discrete operators satisfying basic physical requirements and with the right local limit in flat spacetime. In this work, we consider this entire class of Generalized Causal set d'Alembertins in curved spacetimes and extend to them the result about the universality of the $-R/2$ factor. Finally, we comment on the relation of this result to the Einstein Equivalence principle.