Joint resonant CMB power spectrum and bispectrum estimation

TL;DR

This paper introduces an efficient method to jointly analyze CMB power spectrum and bispectrum data for resonant features, reducing computational costs while accurately assessing their statistical significance.

Contribution

It presents a Gaussian approximation approach using Fisher matrices to quickly evaluate the significance of resonant features in CMB data, streamlining the analysis process.

Findings

Gaussian approximation closely matches full simulation results

Cosmology and foreground parameters minimally affect amplitude estimates

Method enables rapid significance testing of candidate signatures

Abstract

We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large number of simulations to derive the probability density function (PDF) of the feature-amplitude in the Gaussian case. Although these simulations are tractable for the power spectrum, for the bispectrum they require significant computational resources. We show that, by assuming that the PDF is given by a multi-variate Gaussian where the covariance is determined by the Fisher matrix of the sine and cosine terms, we can efficiently produce spectra that are statistically close to those derived from full simulations. By drawing a large number of spectra from this PDF, both for the power spectrum and the bispectrum, we can quickly determine the statistical significance of candidate signatures in the CMB, considering both single frequency and multi-frequency estimators. We show that for resonance models, cosmology and foreground parameters have little influence on the estimated amplitude, which allows to simplify the analysis considerably. A more precise likelihood treatment can then be applied to candidate signatures only. We also discuss a modal expansion approach for the power spectrum, aimed at quickly scanning through large families of oscillating models.