= Sachs-Wolfe projection of a constant bispectrum
{c}
{title2=$b_{\ell_1\ell_2\ell_3}=\frac{4\pi^4f_{\rm NL}\Delta_\zeta^4}{125\prod_i(2\ell_i+1)}\left(\frac1{L+3}+\frac1L\right),\quad L=\sum_i\ell_i$}
For a <constant primordial bispectrum> and large-angle transfer function $\Delta_\ell(k)=j_\ell(kR)/5$, the <spherical Bessel product integral> reduces the radial projection to $\int_0^1r^{L+2}\,dr+\int_1^\infty r^{-L-1}\,dr$. For $L>0$ this equals $1/(L+3)+1/L$, giving the displayed <reduced CMB bispectrum>. All powers of the distance $R$ cancel. Under common large-multipole scaling it behaves as $\ell^{-4}$ at fixed shape; this is angular scale invariance, not a constant angular bispectrum. The all-monopole case $L=0$ has a logarithmically divergent radial tail and is excluded.
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