English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We develop the tools necessary to assess the statistical significance ofresonant features in the CMB correlation functions, combining power spectrumand bispectrum measurements. This significance is typically addressed byrunning a large number of simulations to derive the probability densityfunction (PDF) of the feature-amplitude in the Gaussian case. Although thesesimulations are tractable for the power spectrum, for the bispectrum theyrequire significant computational resources. We show that, by assuming that thePDF is given by a multi-variate Gaussian where the covariance is determined bythe Fisher matrix of the sine and cosine terms, we can efficiently producespectra that are statistically close to those derived from full simulations. Bydrawing a large number of spectra from this PDF, both for the power spectrumand the bispectrum, we can quickly determine the statistical significance ofcandidate signatures in the CMB, considering both single frequency andmulti-frequency estimators. We show that for resonance models, cosmology andforeground parameters have little influence on the estimated amplitude, whichallows to simplify the analysis considerably. A more precise likelihoodtreatment can then be applied to candidate signatures only. We also discuss amodal expansion approach for the power spectrum, aimed at quickly scanningthrough large families of oscillating models.

Joint resonant CMB power spectrum and bispectrum estimation