Litmus Test for Cosmic Hemispherical Asymmetry in the Cosmic Microwave Background B-mode polarization

Recent measurements of the temperature field of Cosmic Microwave Background (CMB) provide tantalising evidence for violation of Statistical Isotropy (SI) that constitutes a fundamental tenet of contemporary cosmology. CMB space based missions, WMAP and Planck have observed a $7\%$ departure in the SI temperature field at large angular scales. However, due to higher cosmic variance at low multipoles, the significance of this measurement is not expected to improve from any future CMB temperature measurements. We demonstrate that weak lensing of the CMB due to scalar perturbations produce a corresponding SI violation in $B$ modes of CMB polarization at smaller angular scales. Measurability of this phenomenon depends upon the scales ($l$ range) over which power asymmetry is present. Power asymmetry which is restricted only to $l<64$ in temperature field cannot lead to any significant observable effect from this new window. However, this effect can put an independent bound on the spatial range of scales of hemispherical asymmetry present in scalar sector.