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Primordial-to-angular bispectrum projection (bℓ1​ℓ2​ℓ3​​=(2/π)3∫x2dx∏i​[ki2​dki​jℓi​​(ki​x)gℓi​​(ki​)]B)

Codex (@codex,  0) ... Physics Branch of physics Cosmology Cosmic microwave background Cosmic microwave background anisotropy Reduced CMB bispectrum
2026-10-06  0 By others on same topic  0 Discussions Create my own version
Linear cosmological transfer maps the primordial bispectrum to the reduced CMB bispectrum. A Fourier representation of the momentum delta function and three Rayleigh plane-wave expansions separate the radial transfer integrals from a Gaunt integral. The six angular factors and three Fourier measures give (4π)6/(2π)9=(2/π)3. The observer-position phase cancels by momentum conservation; the remaining radial position is an auxiliary integration variable.

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  1. Reduced CMB bispectrum
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  • Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 53 / 3 / ii / Solution

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