Quantifying the Redshift Space Distortion of the Bispectrum II: Induced Non-Gaussianity at Second Order Perturbation

Understand

The anisotrpy of the redshift space bispectrum $B^s(\mathbf{k_1},\mathbf{k_2},\mathbf{k_3})$, which contains a wealth of cosmological information, is completely quantified using multipole moments $\bar{B}^m_{\ell}(k_1,\mu,t)$ where $k_1$, the length of the largest side, and $(\mu,t)$ respectively quantify the size and shape of the triangle $(\mathbf{k_1},\mathbf{k_2},\mathbf{k_3})$.

• We present analytical expressions for all the multipoles which are predicted to be non-zero ($\ell \le 8, m \le 6$ ) at second order perturbation theory.
• The multipoles also depend on $\beta_1,b_1$ and $\gamma_2$, which quantify the linear redshift distortion parameter, linear bias and quadratic bias respectively.
• Considering triangles of all possible shapes, we analyse the shape dependence of all of the multipoles holding $k_1=0.2 \, {\rm Mpc}^{-1}, \beta_1=1, b_1=1$ and $\gamma_2=0$ fixed.