The Komatsu Spergel Wandelt estimator for oscillations in the cosmic microwave background bispectrum

Münchmeyer, Moritz; Bouchet, F. R.; Jackson, Mark G.; Wandelt, B. D.

doi:10.1051/0004-6361/201424179

Cited by 16 publications

(21 citation statements)

References 32 publications

(28 reference statements)

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“…Particularly, the new fast bispectrum estimator of oscillatory features from Ref. [74] should be able to cover the frequency where the most significant mode that we found is located. If those predictions are right, these signals in polarization spectra and temperature bispectrum may be observed with the upcoming Planck data release in 2015, though it is by now unclear whether the sensitivity level of the Planck full-mission data will be high enough to claim a detection.…”

Section: Discussionmentioning

confidence: 99%

Searching for primordial localized features with CMB and LSS spectra

Torrado

2015

Phys. Rev. D

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Inspired by the study of mild transient reductions in the speed of sound of the adiabatic mode during inflation, we search for a primordial localized feature imprinted in cosmic microwave background and large-scale structure formation observables. We find some common oscillatory patterns both in the Planck CMB temperature-temperature power spectrum and the WiggleZ galaxy spectrum. By performing independent searches with these two data sets, we find a coincidence in the most significant mode previously found by Achúcarro et al. in 2013 by using only Planck data. Furthermore, the joint data analysis shows that the oscillation frequency of the feature gets better constrained, and the amplitude marginally deviates from zero, unlike what was observed using only Planck data. Besides the parameter estimation, we also discuss the Bayesian evidence. The addition of WiggleZ data mildly enhances the significance of the best mode found in the Planck data.

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Section: Discussionmentioning

confidence: 99%

Searching for primordial localized features with CMB and LSS spectra

Torrado

2015

Phys. Rev. D

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“…As the bispectrum in Eq. (15) is separable, it allows the construction of a KSW estimator (Münchmeyer et al 2014) for direct bispectrum estimation at any given frequency. The bispectrum can be written as a sum of sine and cosine components which can be estimated separately (equivalent to measuring the amplitude and phase above) and this method was used to constrain frequencies up to ω = 3000.…”

Section: Feature Modelsmentioning

confidence: 99%

Planck2015 results

Ade

Aghanim

Arnaud

et al. 2016

A&A

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256

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The Planck full mission cosmic microwave background (CMB) temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gaussianity (NG). Using three classes of optimal bispectrum estimators -separable template-fitting (KSW), binned, and modalwe obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result from temperature alone f local NL = 2.5 ± 5.7, f equil NL = −16 ± 70, and f ortho NL = −34 ± 33 (68% CL, statistical). Combining temperature and polarization data we obtain f local NL = 0.8 ± 5.0, f equil NL = −4 ± 43, and f ortho NL = −26 ± 21 (68% CL, statistical). The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are consistent with estimators based on measuring the Minkowski functionals of the CMB. The effect of time-domain de-glitching systematics on the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization data as preliminary, owing to a known mismatch of the noise model in simulations and the data. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and derive constraints on early universe scenarios that generate primordial NG, including general single-field models of inflation, axion inflation, initial state modifications, models producing parityviolating tensor bispectra, and directionally dependent vector models. We present a wide survey of scale-dependent feature and resonance models, accounting for the "look elsewhere" effect in estimating the statistical significance of features. We also look for isocurvature NG, and find no signal, but we obtain constraints that improve significantly with the inclusion of polarization. The primordial trispectrum amplitude in the local model is constrained to be g local NL = (−9.0 ± 7.7) × 10 4 (68% CL statistical), and we perform an analysis of trispectrum shapes beyond the local case. The global picture that emerges is one of consistency with the premises of the ΛCDM cosmology, namely that the structure we observe today was sourced by adiabatic, passive, Gaussian, and primordial seed perturbations.

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“…Our expansion in a basis of linear oscillations differs from the usual modal expansion [39] in that it is effectively one dimensional, so only relatively few modes are needed to obtain high overlap even for very high frequencies. At the same time, the existing pipeline developed to look for linear oscillations [43] can be utilized to search for log oscillations at relatively little additional computational cost. We computed the expected signal to noise of a cosmic variance limited experiment with max = 2000.…”

Section: Discussionmentioning

confidence: 99%

“…An optimal estimator for linear spaced oscillations has been presented in [43] and in [44] the angular correlation function was considered as an alternative to the bispectrum. The developers of the mode expansion method have recently presented important work on possible issues with jointly measuring oscillations in the power and bi-spectrum [45].…”

Section: Introductionmentioning

confidence: 99%

Optimal estimator for resonance bispectra in the CMB

2015

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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 ki = kt is the most efficient and flexible approach. We compare the expansion to the exact result in multipole space and show for ω eff = 100 that O(10 3 ) modes are sufficient for an accurate reconstruction. We compute the expected σ f NL and find that within an effective field theory (EFT) the overall signal to noise scales as S/N ∝ ω 3/2 . Using only the temperature data we find S/N ∼ O(1 − 10 2 ) for the frequency domain set by the EFT.

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The Komatsu Spergel Wandelt estimator for oscillations in the cosmic microwave background bispectrum

Cited by 16 publications

References 32 publications

Searching for primordial localized features with CMB and LSS spectra

Searching for primordial localized features with CMB and LSS spectra

Planck2015 results

Optimal estimator for resonance bispectra in the CMB

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