  In this work, according to some evidence from being an asymmetry in the
number density of left and right-handed electrons, $\delta_L$, in-universe
motivate us to calculate the dominated contribution of this asymmetry in the
generation of B-mode power spectrum $C_{ B\,l}^{(S)}$. Note, in the standard
cosmological scenario, Compton scattering in the presence of scalar matter
perturbation can not generate magnetic like pattern in linear polarization
while in the case of polarized Compton scattering, we have shown
$C_{B\,l}^{(S)}\propto \delta_L^2$. We add up the spectrum of the B-mode
generated by the polarized Compton scattering to the spectra produced by weak
lensing effects and Compton scattering in the presence of tensor perturbations.
The results show a significant amplification in $C_{B\,l}$ in large scale
$l<500$ for $\delta_L>10^{-6}$ which will be observable in future high
resolution B-mode polarization detection. Finally, we have shown that $C_{
B\,l}^{(S)}$ generated by polarized Compton scattering can suppress the tensor
to scalar ratio, $r$ parameter so that this contamination can be comparable to
a primordial tensor-to-scalar ratio spatially for $\delta_L>10^{-5}$.
