Primordial bispectrum information from CMB polarization

After the precise observations of the cosmic microwave background (CMB) anisotropy power spectrum, attention is now being focused on higher order statistics of the CMB anisotropies. Since linear evolution preserves the statistical properties of the initial conditions, observed non-Gaussianity of the CMB will mirror primordial non-Gaussianity. Single-field slow-roll inflation robustly predicts negligible non-Gaussianity so an indication of primordial non-Gaussianity will suggest alternative scenarios need to be considered. In this paper we calculate the information on primordial non-Gaussianity encoded in the polarization of the CMB. After deriving the optimal weights for a cubic estimator we evaluate the signal-to-noise ratio $(S/N)$ of the estimator for Wilkinson Microwave Anisotropy Probe, Planck, and an ideal cosmic variance limited experiment. We find that when the experiment can observe CMB polarization with good sensitivity, the sensitivity to primordial non-Gaussianity increases by roughly a factor of 2. We also test the weakly non-Gaussian assumption used to derive the optimal weight factor by calculating the degradation factor produced by the gravitational lensing induced connected four-point function. The physical scales in the radiative transfer functions are largely irrelevant for the constraints on the primordial non-Gaussianity. We show that the total $(S/N{)}^2$ is simply proportional to the number of observed pixels on the sky.