Geometrical measures of non-Gaussianity generated from single field inflationary models

Abstract

We calculate the third-order moments of scalar curvature perturbations in configuration space for different inflationary models. We develop a robust numerical technique to compute the bispectrum for different models that have some features in the inflationary potential. From the bispectrum we evaluate moments analytically in the slow-roll regime while we devise a numerical mechanism to calculated these moments for non-slow-roll single-field inflationary models with a standard kinetic term that are minimally coupled to gravity. With the help of these third-order moments one can directly predict many non-Gaussian and geometrical measures of cosmic microwave background distributions in the configuration space. Thus, we devise a framework to calculate different thirdorder moments and geometrical measures, e.g. Minkowski functionals or the skeleton statistic, generated by different single-field models of inflation.

Inflationary study of non-Gaussianity using two-dimensional geometrical measures of CMB temperature maps

“…16. The results show that our numerics match the analytical results with the error bar below 1% for slow-roll models of inflation [39]. The generalised f N L is plotted in Fig.…”

“…Analysis of these moments provides a robust measure of non-Gaussianity and has also become an important field of investigation [53? ]. In this paper we will extend our previous work on 3D calculation of moments [39]. These 2D moments will provide important information on the geometrical properties of the CMB temperature fluctuations map, and give us 2D non-Gaussianity observables such as extrema counts, genus and skeleton [29].…”

“…This Fig 2 describe two different integration regimes BHC τ < τ * and AHC τ > τ * . In BHC regime, we integrate in the backward direction from the horizon crossing point τ * using the extended Cesaro Integral [39]. Our technique converges very quickly as can be seen that the integral plateaus as we go 5-6 e-folds left of the horizon crossing points.…”

“…We previously worked out the Minkowski functionals for 3D perturbation field ζ at the end of inflation in single-field models of inflation [39]. In this paper we have developed a robust mechanism to compute theoretical predictions for third-order moments such as ζ 3 , ζ 2 ∆ζ and (∇ζ) 2 ∆ζ on 2D CMB maps that are generated from these inflationary initial conditions.…”

A Study on the Baryon Acoustic Oscillation with Topological Data Analysis

“…Since basically the smoothed random field contains the whole information on the infinitely high-order moments of the field, in principle the Minkowski Functionals can specify the galaxy density field completely. Indeed this method has been applied very extensively to the analysis of the cosmic density field [e.g., 9,12,13,14,15,16,17], as well as redshift distortion [e.g., 18], weak lensing cosmology [e.g., 19,20,21], cosmic reionization [22,23,24,25], test of cosmological/gravity theories [26,27,28,29], and the cosmic microwave background (CMB: e.g., [30,31,32,33,34,35]).…”