Joint resonant CMB power spectrum and bispectrum estimation
arXiv:1510.01756 · doi:10.1103/PhysRevD.93.043536
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.
17 pages, 11 figures. This version: Added refs, fixed typos and some rewrites
References in corpus (14)
- Monodromy in the CMB: Gravity Waves and String Inflation
- PolyChord: nested sampling for cosmology
- Enhanced Non-Gaussianity from Excited Initial States
- New Universal Local Feature in the Inflationary Perturbation Spectrum
- Folded Resonant Non-Gaussianity in General Single Field Inflation
- Combining power spectrum and bispectrum measurements to detect oscillatory features
- Polyspectra searches for sharp oscillatory features in cosmic microwave sky data
- Untangling features in the primordial spectra
- Alleviating the tension at low multipole through Axion Monodromy
- An optimal estimator for resonance bispectra in the CMB
- Consistency relations for sharp features in the primordial spectra
- Impact of Uncertainties in the Cosmological Parameters on the Measurement of Primordial non-Gaussianity
- Minimal cut-off vacuum state constraints from CMB bispectrum statistics
- Optimal CMB estimators for bispectra from excited states
Cited by in corpus (34)
- Planck 2018 results. X. Constraints on inflation
- Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
- Planck 2018 results. IX. Constraints on primordial non-Gaussianity
- Exploring Cosmic Origins with CORE: Inflation
- Productive Interactions: heavy particles and non-Gaussianity
- Probing primordial features with future galaxy surveys
- The Future of Primordial Features with Large-Scale Structure Surveys
- The Future of Primordial Features with 21 cm Tomography
- Primordial Features from Linear to Nonlinear Scales
- Scratches from the Past: Inflationary Archaeology through Features in the Power Spectrum of Primordial Fluctuations
- Precise measurements of inflationary features with 21 cm observations
- Primordial Non-Gaussianity
- Non-linear damping of superimposed primordial oscillations on the matter power spectrum in galaxy surveys
- Constraints on inflation with LSS surveys: features in the primordial power spectrum
- Probing primordial features with next-generation photometric and radio surveys
- Constraints on holographic multi-field inflation and models based on the Hamilton-Jacobi formalism
- Higher N-point function data analysis techniques for heavy particle production and WMAP results
- Euclid: The search for primordial features
- Direct search for features in the primordial bispectrum
- Robust predictions for an oscillatory bispectrum in Planck 2015 data from transient reductions in the speed of sound of the inflaton
- High-resolution CMB bispectrum estimator with flexible modal basis
- Probing primordial features with the primary CMB
- Consistency relations for sharp inflationary non-Gaussian features
- Effect of damped oscillations in the inflationary potential
- Correlated primordial spectra in effective theory of inflation
- Resonant Reconciliation of Convex Models and the Planck
- Isocurvature modes: joint analysis of the CMB power spectrum and bispectrum
- Shapes and features of the primordial bispectrum
- Scale invariance of the primordial tensor power spectrum
- Refining the nonlinear modelling of primordial oscillatory features
- Observable Quantum Loop Effects in the Sky
- A search for super-imposed oscillations to the primordial power spectrum in Planck and SPT-3G 2018 data
- Inflation Story: slow-roll and beyond
- Cross-tests of CMB features in the primordial spectra