Cosmological constant from quantum spacetime

Abstract

We show that a hypothesis that spacetime is quantum with coordinate algebra $[{x}^{i},t]={\ensuremath{\lambda}}_{P}{x}^{i}$, and spherical symmetry under rotations of the ${x}^{i}$, essentially requires in the classical limit that the spacetime metric is the Bertotti-Robinson metric, i.e., a solution of Einstein's equations with a cosmological constant and a non-null electromagnetic field. Our arguments do not give the value of the cosmological constant or the Maxwell field strength, but they cannot both be zero. We also describe the quantum geometry and the full moduli space of metrics that can emerge as classical limits from this algebra.