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In the standard model of cosmology, the B-mode polarization of the cosmic microwave background can be generated due to the tensor perturbation of metric which is related to gravitational effects in the inflation epoch and scalar perturbation cannot explain B-mode polarization. We consider Compton scattering in the Non-Commutative framework and show that Compton scattering in presence of Non-Commutative background and scalar mode of perturbation, besides generating circularly polarized microwave, can lead to B-mode polarization of the Cosmic Microwave Background. We estimate that generated V-mode $C_{Vl}$ can be expressed as linearly polarized power spectrum $C_{Pl}$ as well as B-mode power spectrum $C_{Bl}$ as a function of $C_{Vl}$. We show that $C_{Vl}$ ($C_{Bl}$) for NC-scale $\Lambda_{\tiny{NC}}\sim 20$ TeV are in the range of $\mathcal{O}(nK^2)$ ($\mathcal{O}(pK^2)$) and higher, respectively, which are in the range of observational data.

The generation of B-mode and circular polarization of cosmic photons due to NonCommutative space-Time background