Cosmological constant from quantum spacetime

2014/12/06 by Shahn Majid, Majid, Shahn, Wen-Qing Tao +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #gr-qc #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.1412.2285

13 pages latex no figures. Compared to version 1, we put in the correct name `Bertotti-Robinson' and its context

arxiv created 2014/12/15 · arxiv updated 2014/12/16

Abstract

We show that a hypothesis that spacetime is quantum with coordinate algebra [xⁱ,t]=λ_P xⁱ, and spherical symmetry under rotations of the xⁱ, essentially requires in the classical limit that the spacetime metric is the Bertotti-Robinson metric, i.e. a solution of Einstein's equations with 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.

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