  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.
