Superselection rule for the cosmological constant in three-dimensional spacetime

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.