Emergence of Riemannian geometry and the massive graviton

Abstract

We overview a new mechanism[14] whereby classical Riemannian geometry emerges out of the differential structure on quantum spacetime, as extension data for the classical algebra of differential forms. Outcomes for physics include a new formula for the standard Levi-Civita connection, a new point of view of the cosmological constant as a very small mass for the graviton of around 10-33ev, and a weakening of metric compatibility in the presence of torsion. The same mechanism also provides a new construction for quantum bimodule connections on quantum spacetimes and a new approach to the quantum Ricci tensor. © Owned by the authors, published by EDP Sciences, 2014.