Quantifying the redshift space distortion of the bispectrum I: primordial non-Gaussianity

The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors k(1), k(2), k(3) with respect to the line of sight. Here, we have decomposed the redshift space bispectrum in spherical harmonics which completely quantify this anisotropy. To illustrate this, we consider linear redshift space distortion of the bispectrum arising from primordial non-Gaussianity. In the plane-parallel approximation, only the first four even l multipoles have non-zero values, and we present explicit analytical expressions for all the non-zero multipoles, that is, upto l = 6 and m = 4. The ratio of the different multipole moments to the real-space bispectrum depends only on beta(1) the linear redshift distortion parameter and the shape of the triangle. Considering triangles of all possible shapes, we have studied how this ratio depends on the shape of the triangle for beta(1) = 1. We have also studied the beta(1) dependence for some of the extreme triangle shapes. If measured in future, these multipole moments hold the potential of constraining beta(1). The results presented here are also important if one wishes to constrain f(NL) using redshift surveys.