Generalized relative locality and causal sets

TL;DR

This paper introduces a new framework for phenomenological quantum gravity that distinguishes between observer-independent and observer-dependent spacetimes, linking relative locality with causal set structures.

Contribution

It presents a coordinate-independent formalism using fibre bundles to unify spacetime and relative locality effects in quantum gravity models.

Findings

Relative locality can be derived in general PQG models regardless of momentum-space curvature.

The formalism links spacetime symmetries directly to relative locality effects.

Causality is manifest in the new fibre bundle approach, enabling cosmological applications.

Abstract

In this paper we introduce a new general framework for the study of phenomenological quantum gravity theories (PQG). The key idea is the introduction of two different types of spacetime, an observer-independent spacetime (modeled by a smooth orientable manifold) and an observer-dependent one (which has an inherently discrete causal set structure). The interaction between the two allows us to prove the main result of the paper: relative locality can be obtained in general PQG models, regardless of momentum-space curvature. {We also discuss the treatment of spacetime symmetries in our model, and introduce a direct link between spacetime symmetries and relative locality effects.} Our construction is presented in a coordinate-independent way and is based on fibre bundles where spacetime, rather than momentum-space, is the base manifold. This makes causality manifest even in general models with relative locality. Furthermore, it allows for the application of this formalism to cosmology on general backgrounds, something which is not clearly possible in the canonical approach to relative locality, where momentum-space serves as the base manifold.