Optimal estimator for resonance bispectra in the CMB

We propose an (optimal) estimator for a CMB bispectrum containing logarithmically spaced oscillations. There is tremendous theoretical interest in such bispectra, and they are predicted by a plethora of models, including axion monodromy models of inflation and initial state modifications. The number of resolved logarithmical oscillations in the bispectrum is limited due to the discrete resolution of the multipole bispectrum. We derive a simple relation between the maximum number of resolved oscillations and the frequency. We investigate several ways to factorize the primordial bispectrum, and conclude that a one-dimensional expansion in the sum of the momenta Sigma k(i) = k(t) is the most efficient and flexible approach. We compare the expansion to the exact result in multipole space and show for omega(eff) = 100 that O(10(3)) modes are sufficient for an accurate reconstruction. We compute the expected sigma(fNL) and find that within an effective field theory (EFT) the overall signal to noise scales as S/N proportional to omega(3/2). Using only the temperature data we find S/N similar to O(1-10(2)) for the frequency domain set by the EFT.