Reduced CMB bispectrum (source code)

= Reduced CMB bispectrum
{title2=$b_{\ell_1\ell_2\ell_3}$}

A statistically isotropic <Cosmic microwave background anisotropy> has $\langle a_{\ell_1m_1}a_{\ell_2m_2}a_{\ell_3m_3}\rangle=\mathcal G^{\ell_1\ell_2\ell_3}_{m_1m_2m_3}b_{\ell_1\ell_2\ell_3}$, where $\mathcal G$ is the integral of the three <spherical harmonics>. The reduced CMB bispectrum removes this angular geometric factor and retains the primordial and transfer-function dependence. A <Sachs-Wolfe projection of a constant bispectrum> is an analytic large-angle example.