Consistency relations for sharp features in the primordial spectra

Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris; Soto, Alex

doi:10.1088/1475-7516/2015/10/062

Cited by 24 publications

(29 citation statements)

References 170 publications

(231 reference statements)

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“…With this study, we have all necessary tools for an application to the Planck data. Besides the resonance models which we focussed on in this paper, the methods presented here are also applicable to other types of rapidly varyings features in the power spectrum and bispectrum [16,19,21,[23][24][25][46][47][48][49][50] and should provide an efficient way to address multi-peak significance of these models. …”

Section: Discussionmentioning

confidence: 99%

Joint resonant CMB power spectrum and bispectrum estimation

2016

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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

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Section: Discussionmentioning

confidence: 99%

Joint resonant CMB power spectrum and bispectrum estimation

2016

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“…To capture the aforementioned situations, in [48], a one parameter relation between the Hubble slow-roll parameter η and the sound speed was proposed. This had the form…”

Section: Including the Effects Of A Varying Sound Speedmentioning

confidence: 99%

“…These time variations break -in a controlled way -the standard behavior required in single field slow-roll inflation, producing localized features in the spectra, though without invalidating inflation as a mechanism to explain the origin of primordial fluctuations in a way compatible with observations. Given that the source of features may be traced back to background parameters that affect the evolution of all perturbations, features appearing in different n-point correlation functions would be necessarily correlated [41][42][43][44][45][46][47][48][49][50][51][52]. In the case of scalar perturbations, a powerful way to study such time-dependent departures from slow-roll is the joint estimator analysis of two-and three-point correlation functions [52], since a detection of correlated signals in the power spectrum and bispectrum would increase the statistical significance of these features.…”

Section: Introductionmentioning

confidence: 99%

Scale invariance of the primordial tensor power spectrum

et al. 2017

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Future cosmic microwave background polarization experiments will search for evidence of primordial tensor modes at large angular scales, in the multipole range 4 ≤ ≤ 50. Because in that range there is some mild evidence of departures from scale invariance in the power spectrum of primordial curvature perturbations, one may wonder about the possibility of similar deviations appearing in the primordial power spectrum of tensor modes. Here we address this issue and analyze the possible presence of features in the tensor spectrum resulting from the dynamics of primordial fluctuations during inflation. We derive a general, model independent, relation linking features in the spectra of curvature and tensor perturbations. We conclude that even with large deviations from scale invariance in the curvature power spectrum, the tensor spectrum remains scale invariant for all observational purposes.

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“…Hence this leads us to consider a class of potential functions that have a step-like feature, with a height, width, and location that we shall take as adjustable parameters (related work includes Refs. [8,9,10] and references therein). We find that with these potentials and using the slow-roll approximations to obtain the power spectrum we can obtain moderate improvement in the data compared to standard potentials without this feature.…”

Section: Introductionmentioning

confidence: 99%

Exploring the CMB power suppression in canonical inflation models

Gonzalez

Hertzberg

2019

J. Cosmol. Astropart. Phys.

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There exists some evidence of a suppression in power in the CMB multipoles around l ∼ 20 − 30. If taken seriously, this is in tension with the simplest inflationary models driven by a single scalar field with a standard type of slowly varying potential function V (φ). Such potential functions generate a nearly scale invariant spectrum and so they do not possess the requisite suppression in power. In this paper we explore if canonical two-derivative inflation models, with a step-like feature in the potential, can improve agreement with data. We find that improvement can be made when one utilizes the standard slow-roll approximation formula for the power spectrum. However, we find that in order to have a feature in the power spectrum that is sufficiently localized so as to not significantly disrupt higher l or lower l, the potential's step-like feature must be so sharp that the standard slow-roll approximations break down. This leads us to perform an exact computation of the power spectrum by solving for the Bunch-Davies mode functions numerically. We find that the corresponding CMB multipoles do not provide a good agreement with the data. We conclude that, unless there is fine-tuning, canonical inflation models do not fit this suppression in the data. *

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Consistency relations for sharp features in the primordial spectra

Cited by 24 publications

References 170 publications

Joint resonant CMB power spectrum and bispectrum estimation

Joint resonant CMB power spectrum and bispectrum estimation

Scale invariance of the primordial tensor power spectrum

Exploring the CMB power suppression in canonical inflation models

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