Superselection rule for the cosmological constant in three-dimensional spacetime

TL;DR

This paper demonstrates that in three-dimensional spacetime, a superselection rule prevents the universe from being in a quantum superposition of different cosmological constant values, unlike in higher dimensions.

Contribution

It establishes a superselection rule for the cosmological constant in 3D spacetime based on asymptotic symmetry algebra, a result not applicable in higher dimensions.

Findings

Superposition of different {} values is forbidden in 3D spacetime.

Superselection rule is derived from asymptotic symmetry algebra.

No such rule exists for higher-dimensional spacetimes.

Abstract

Efforts to understand the origin of the cosmological constant {\Lambda} and its observed value have led to consider it as a dynamical field rather than as a universal constant. Then the possibility arises that the universe, or regions of it, might be in a superposition of quantum states with different values of {\Lambda}, so that its actual value would not be definite. There appears to be no argument to rule out this possibility for a generic spacetime dimension D. However, as proved herein, for D=3 there exists a superselection rule that forbids such superpositions. The proof is based on the asymptotic symmetry algebra.