Cosmological power spectrum in a noncommutative spacetime

We propose a generalized star product which deviates from the standard product when the fields at evaluated at different space-time points. This produces no changes in the standard Lagrangian density in non-commutative space-time but produces a change in the cosmological power spectrum. We show that the generalized star product leads to physically consistent results and can fit the observed data on hemispherical anisotropy in the cosmic microwave background radiation.