 Reduced CMB bispectrum

A statistically isotropic Cosmic microwave background anisotropy has $⟨a_{{\ell }_1{m}_1}{a}_{{\ell }_2{m}_2}{a}_{{\ell }_3{m}_3}⟩={\mathcal{G}}_{m_1{m}_2{m}_3}^{{\ell }_1{\ell }_2{\ell }_3}{b}_{{\ell }_1{\ell }_2{\ell }_3}$, 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.