Cosmological constant and noncommutative spacetimeX. Calmet
Université Libre de Bruxelles, Service de Physique Théorique - CP 225, Boulevard du Triomphe (Campus plaine), B-1050 Brussels, Belgium
received 30 August 2006; accepted in final form 7 November 2006; published January 2007
published online 3 January 2007
We show that the cosmological constant appears as an integration constant 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-volumepreserving noncommutative coordinate transformations. The noncommutative gravitational action is thus a unimodular noncommutative gravity. We show that spacetime noncommutativity provides a very natural justification to a 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.
98.80.-k - Cosmology .
11.10.Nx - Noncommutative field theory .
04.20.-q - Classical general relativity .
© Europhysics Letters Association 2007