Joint resonant CMB power spectrum and bispectrum estimation

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. Contents

Probing primordial features with future galaxy surveys

“…The case of periodic oscillations in axion monodromy inflation [21,22] fall in this broad class of models [23]. These features in the power spectrum are accompanied by specific templates in the bispectrum (see [24] for a review): therefore primordial features can also be searched in the bispectrum [25] or jointly in the power spectrum and bispectrum [26][27][28]. At present, no inflationary model fitting these features has been found to be preferred at a statistical significant level over more standard models [4,25].…”

Robust predictions for an oscillatory bispectrum in Planck 2015 data from transient reductions in the speed of sound of the inflaton

“…(9) [12], and this significantly enhances the signal-to-noise of highly oscillatory features [45]. If the features corresponding to these modes are actually present in the data, combined searches in both the power spectrum and bispectrum are expected to greatly raise the significance of the fits [13,15], hopefully to detection-like levels.…”

“…When models with correlated features are tested against the data in a joint approach for different observables at the same time, the significance of possible fits is expected to increase, as has been reported in particular for oscillatory feature searches combining CMB power spectrum and bispectrum [13][14][15] (see also [16] for a model-independent approach).…”

Planck2015 results

“…Due to the high computational demands of this analysis, we have only exactly assessed the look-elsewhere effect for SMICA T data, for which we find an expected maximum peak of 3.5σ ± 0.4σ in the case of Gaussian maps, to be compared to 3.7σ in the SMICA T data, demonstrating that the results are fully consistent with Gaussianity. The expected maximum peak for Gaussian maps was calculated from the Fisher matrix with the method described in Meerburg et al (2016). The average over component separation methods as well as the T+E data is even less significant.…”