An optimal estimator for resonance bispectra in the CMB

TL;DR

This paper develops an optimal estimator for oscillatory bispectra in the CMB, enabling efficient detection of models like axion monodromy, and analyzes the signal-to-noise scaling with frequency.

Contribution

It introduces a simple, flexible factorization method for the bispectrum and derives the relation between oscillation resolution and frequency.

Findings

The estimator effectively reconstructs bispectra with ~1000 modes for accurate analysis.

Signal-to-noise scales as frequency to the power of 1.5 within the EFT framework.

Temperature data can detect signals with S/N between 1 and 100 for relevant frequencies.

Abstract

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 $\sum k_i = k_t$ is the most efficient and flexible approach. We compare the expansion to the exact result in multipole space and show for $\omega_{\rm eff}=100$ that $\mathcal{O}(10^3)$ modes are sufficient for an accurate reconstruction. We compute the expected $\sigma_{f_{\rm NL}}$ and find that within an effective field theory (EFT) the overall signal to noise scales as $S/N\propto \omega^{3/2}$. Using only the temperature data we find $S/N\sim\mathcal{O}(1-10^2)$ for the frequency domain set by the EFT.