Generic inference of inflation models by non-Gaussianity and primordial power spectrum reconstruction

Abstract

We present a generic inference method for inflation models from observational data by the usage of higher-order statistics of the curvature perturbation on uniform density hypersurfaces. This method is based on the calculation of the posterior for the primordial non-Gaussianity parameters $f_{\text{NL}}$ and $g_{\text{NL}}$, which in general depend on specific parameters of inflation and reheating models, and enables to discriminate among the still viable inflation models. To keep analyticity as far as possible to dispense with numerically expensive sampling techniques a saddle-point approximation is introduced, whose precision is validated for a numerical toy example. The mathematical formulation is done in a generic way so that the approach remains applicable to cosmic microwave background data as well as to large scale structure data. Additionally, we review a few currently interesting inflation models and present numerical toy examples thereof in two and three dimensions to demonstrate the efficiency of the higher-order statistics method. A second quantity of interest is the primordial power spectrum. Here, we present two Bayesian methods to infer it from observational data, the so called critical filter and an extension thereof with smoothness prior, both allowing for a non-parametric spectrum reconstruction. These methods are able to reconstruct the spectra of the observed perturbations and the primordial ones of curvature perturbation even in case of non-Gaussianity and partial sky coverage. We argue that observables like $T-$ and $B-$modes permit to measure both spectra. This also allows to infer the level of non-Gaussianity generated since inflation.

version 2: few new references added, minor changes

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Cited by in corpus (13)

• Wiggly Whipped Inflation
• Compatibility of Planck and BICEP2 in the Light of Inflation
• Primordial features and Planck polarization
• Probing features in inflaton potential and reionization history with future CMB space observations
• Constraints on features in the inflationary potential from future Euclid data
• Sharp inflaton potentials and bi-spectra: Effects of smoothening the discontinuity
• Stochastic determination of matrix determinants
• Degeneracy in the spectrum and bispectrum among featured inflaton potentials
• All-sky reconstruction of the primordial scalar potential from WMAP temperature data
• Bayesian inference methodology for Primordial Power Spectrum reconstructions from Large Scale Structure
• Probing inflation with large-scale structure data: the contribution of information at small scales
• J-PAS: forecast on the primordial power spectrum reconstruction
• Generic inference of inflation models by local non-Gaussianity