An Estimator for statistical anisotropy from the CMB bispectrum
  Various data analyses of the Cosmic Microwave Background (CMB) provide
observational hints of statistical isotropy breaking. Some of these features
can be studied within the framework of primordial vector fields in inflationary
theories which generally display some level of statistical anisotropy both in
the power spectrum and in higher-order correlation functions. Motivated by
these observations and the recent theoretical developments in the study of
primordial vector fields, we develop the formalism necessary to extract
statistical anisotropy information from the three-point function of the CMB
temperature anisotropy. We employ a simplified vector field model and
parametrize the bispectrum of curvature fluctuations in such a way that all the
information about statistical anisotropy is encoded in some parameters
lambda_{LM} (which measure the anisotropic to the isotropic bispectrum
amplitudes). For such a template bispectrum, we compute an optimal estimator
for lambda_{LM} and the expected signal-to-noise ratio. We estimate that, for
f_{NL} ~ 30, an experiment like Planck can be sensitive to a ratio of the
anisotropic to the isotropic amplitudes of the bispectrum as small as 10%. Our
results are complementary to the information coming from a power spectrum
analysis and particularly relevant for those models where statistical
anisotropy turns out to be suppressed in the power spectrum but not negligible
in the bispectrum.
