Noncommutative geometry and the primordial dipolar imaginary power spectrum

We argue that noncommutative space-times lead to an anisotropic dipolar imaginary primordial power spectrum. We define a new product rule, which allows us to consistently extract the power spectrum in such space-times. The precise nature of the power spectrum depends on the model of noncommutative geometry. We assume a simple dipolar model which has a power dependence on the wave number, $$k$$k, with a spectral index, $$\alpha $$α. We show that such a spectrum provides a good description of the observed dipole modulation in the cosmic microwave background radiation (CMBR) data with $$\alpha \approx 0$$α≈0. We extract the parameters of this model from the data. The dipole modulation is related to the observed hemispherical anisotropy in the CMBR data, which might represent the first signature of quantum gravity.