Cosmological constant from quantum spacetime

TL;DR

This paper proposes that a quantum spacetime algebra with spherical symmetry naturally leads to a classical limit described by the Bertotti-Robinson metric, implying a non-zero cosmological constant and electromagnetic field.

Contribution

It demonstrates that quantum spacetime algebraic assumptions inherently produce a classical spacetime with a cosmological constant and electromagnetic field, revealing a deep link between quantum geometry and classical solutions.

Findings

Classical limit is the Bertotti-Robinson metric.

Both the cosmological constant and Maxwell field cannot be zero.

Describes quantum geometry and the moduli space of emergent metrics.

Abstract

We show that a hypothesis that spacetime is quantum with coordinate algebra $[x^i,t]=\lambda_P x^i$, 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 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.