M. Liguori

Constraining running non-gaussianity

The primordial non-Gaussian parameter fNL has been shown to be scale-dependent in several models of inflation with a variable speed of sound, such as Dirac-Born-Infeld (DBI) models. We perform a Fisher matrix analysis of the bispectra of the temperature and polarization of the Cosmic Microwave Background (CMB) radiation and derive the expected constraints on the parameter nNG that quantifies the running of fNL(k) for current and future CMB missions. We find that CMB information alone, in the event of a significant detection of the non-Gaussian component, corresponding to fNL = 50 for the local model and fNL = 100 for the equilateral model of non-Gaussianity, is able to determine nNG with a 1-σ uncertainty of nNG 0.1 and ΔnNG 0.3, respectively, for the Planck mission and a factor of two better for CMBPol. In addition, we show how future large-scale structure observations should achieve results comparable to or even better than those from the CMB, while showing some complementarity due to the different distribution of the non-Gaussian signal over the relevant range of scales. Finally, we compare our findings to the predictions on the amplitude and running of non-Gaussianity of DBI inflation, showing how the constraints on a scale-dependent fNL(k) translate into constraints on the parameter space of the theory.

General CMB and primordial bispectrum estimation: Mode expansion, map making, and measures of F{sub NL}

We present a detailed implementation of two parallel bispectrum estimation methods which can be applied to general nonseparable primordial and cosmic microwave background (CMB) bispectra. The method exploits bispectrum mode decompositions on the tetrahedral domain of allowed wave number or multipole values, using both separable basis functions and related orthonormal modes. We provide concrete examples of such modes constructed from symmetrized tetrahedral polynomials, demonstrating the rapid convergence of expansions describing nonseparable bispectra. We use these modes to create rapid and robust pipelines for generating simulated CMB maps of high resolution (

Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies

lg2000

An Estimate of the Primordial Non-Gaussianity Parameter f_NL Using the Needlet Bispectrum from WMAP

) given an arbitrary primordial power spectrum and bispectrum or an arbitrary late-time CMB angular power spectrum and bispectrum. By extracting coefficients for the same separable basis functions from an observational map, we are able to present an efficient

The CMB Bispectrum

{f}_{mathrm{NL}}

Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background II: Partial Sky Coverage and Inhomogeneous Noise

estimator for a given theoretical model with a nonseparable bispectrum. The estimator has two manifestations, comparing the theoretical and observed coefficients at either primordial or late times, thus encompassing a wider range of models, including secondary anisotropies and lensing as well as active models, such as cosmic strings. We provide examples and validation of both

CMB lensing and primordial non-Gaussianity

{f}_{mathrm{NL}}

Directional Variations of the Non-Gaussianity Parameter f_NL

estimation methods by direct comparison with simulations in a WMAP-realistic context. In addition, we demonstrate how the full primordial and CMB bispectrum can be extracted from observational maps using these mode expansions, irrespective of the theoretical model under study. We also propose a universal definition of the bispectrum parameter

Combining power spectrum and bispectrum measurements to detect oscillatory features

{F}_{mathrm{NL}}

Probing inflation with CMB polarization

, so that the integrated bispectrum on the observational domain can be more consistently compared between theoretical models. We obtain WMAP5 estimates of