We study the noncommutative inflation with a time-dependent noncommutativity
between space and time. From the numerical analysis of power law inflation,
there are clues that the CMB spectrum indicates a nonconstant noncommutative
inflation. Then we extend our treatment to the inflation models with more
general noncommutativity and find that the scalar perturbation power spectrum
depends sensitively on the time varying of the spacetime noncommutativity. This
stringy effect may be probed in the future cosmological observations.Comment: 15 pages, 2 figure
