Physical implications of four dimensional braided noncommutative gravity

TL;DR

This paper explores two different noncommutative gravity models based on twisted and braided symmetries, showing they can have equivalent physical predictions despite different formulations, advancing understanding of noncommutative gravity theories.

Contribution

It establishes a connection between twisted and braided noncommutative diffeomorphism models, demonstrating their potential phenomenological equivalence in certain cases.

Findings

Both models share the same three-graviton vertex.

They exhibit identical simple vacuum solutions.

The work advances understanding of noncommutative gravity models.

Abstract

The formulation of gravity theories on noncommutative (NC) spacetimes has been an active area of research for some time. Various models and methods have been proposed in the literature. Even within the star-product formalism, there are several distinct approaches to constructing NC deformations of General Relativity (GR) and Einstein-Cartan-Palatini (ECP) gravity. Some models are based on the NC local Lorentz symmetry, while others rely on NC deformations of the diffeomorphism symmetry of GR. In this paper, we investigate the connection between two NC gravity models based on twisted and braided NC diffeomorphism symmetry. Although these two models yield different NC gravity actions, we show that, in certain cases, they lead to the same phenomenological consequences. In particular, they share identical three-graviton vertex and exhibit some simple common vacuum solutions. This work represents a step towards understanding the diverse landscape of NC gravity models constructed within the star-product framework.