  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.
