Emergence of Riemannian geometry and the massive graviton
School of Mathematical Sciences Queen Mary University of London Theory Group, CERN 327 Mile End Rd London E1 4NS
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Published online: 29 April 2014
We overview a new mechanism 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.
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