Litmus Test for Cosmic Hemispherical Asymmetry in the Cosmic Microwave Background $B$-Mode Polarization

Recent measurements of the temperature field of the cosmic microwave background (CMB) provide tantalizing 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 produces a corresponding SI violation in $B$ modes of CMB polarization at smaller angular scales. The 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 the 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 the scalar sector.

Figure 1

(a) We plot six different types of scale dependent modulation strength ${\alpha }_l$ with spatial extent up to $l_{\max }=25$, 40, 70, 100, 200, and 400 which are considered in our analysis. (b) BIPOSH coefficients for $B$-mode polarization that arise due to joint contributions from dipole modulated scalar perturbation in both lensing potential $\mathrm{\Phi }$ and $E$ modes are plotted in dashed lines. The contributions only from $E$ mode polarization are plotted by squares.