Cosmological Constant and Noncommutative Spacetime

TL;DR

This paper demonstrates that in a canonical noncommutative spacetime, the cosmological constant emerges as a Lagrange multiplier, leading to an unimodular noncommutative gravity framework that naturally addresses the cosmological constant problem.

Contribution

It introduces a novel connection between noncommutative spacetime and unimodular gravity, providing a natural explanation for the cosmological constant's value.

Findings

Cosmological constant appears as a Lagrange multiplier in noncommutative spacetime.

Noncommutative algebra restricts coordinate transformations to volume-preserving ones.

Results in the correct order of magnitude for the universe's critical density.

Abstract

We show that the cosmological constant appears as a Lagrange multiplier if nature is described by a canonical noncommutative spacetime. It is thus an arbitrary parameter unrelated to the action and thus to vacuum fluctuations. The noncommutative algebra restricts general coordinate transformations to four-volume preserving noncommutative coordinate transformations. The noncommutative gravitational action is thus an unimodular noncommutative gravity. We show that spacetime noncommutativity provides a very natural justification to an unimodular gravity solution to the cosmological problem. We obtain the right order of magnitude for the critical energy density of the universe if we assume that the scale for spacetime noncommutativity is the Planck scale.