Primordial non-Gaussian signatures in CMB polarization

We study the signatures of local type primordial non-Gaussianity, parametrized by $\text{fnl}$, of scalar perturbations in CMB polarization using the probability distribution functions, Minkowski Functionals and Betti numbers. We show that the lowest order non-Gaussian deviation of the PDF of the total polarization intensity is at order $(\text{fnl}\sigma {)}^2$. We calculate the non-Gaussian deviations of Minkowski Functionals and Betti numbers from simulated polarization maps. We find that $E$ mode polarization provides independent and equally strong constraint on $\text{fnl}$ as temperature fluctuations. The non-Gaussian signal in the total polarization intensity, however, is much weaker and has a relatively large cosmic variance and hence may not be useful for detecting local type non-Gaussianity.