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We propose a variation of spacetime noncommutative field theory to realizethe stringy spacetime uncertainty relation without breaking any of the globalsymmetries of the homogeneous isotropic universe. We study the spectrum ofmetric perturbations in this model for a wide class of accelerating backgroundcosmologies. Spacetime noncommutativity leads to a coupling between thefluctuation modes and the background cosmology which is nonlocal in time. Foreach mode, there is a critical time at which the spacetime uncertainty relationis saturated. This is the time when the mode is generated. These effects leadto a spectrum of fluctuations whose spectral index is different from what isobtained for commutative spacetime in the infrared region, but is unchanged inthe ultraviolet region. In the special case of an exponentially expandingbackground, we find a scale-invariant spectrum. but with a different magnitudethan in the context of commutative spacetime if the Hubble constant is abovethe string scale.Comment: 10 page

Noncommutative spacetime, stringy spacetime uncertainty principle, and density fluctuations