Tests for primordial non-Gaussianity

TL;DR

The paper investigates how small primordial non-Gaussianities, parameterized by $\epsilon_{\rm A}$ and $\epsilon_{\rm B}$ in two physically motivated models, affect CMB, LSS, and the abundances of high-redshift objects and clusters. It develops an analytic framework linking primordial bispectra to observable statistics through perturbation theory and mass-function formalisms, and derives a simple ratio $R(M,z)=N_{ng}(\ge M,z)/N(\ge M,z)$ to quantify detectability. The results show that CMB maps are most sensitive to Model B-type non-Gaussianity (inflationary) while observations of rare, high-z objects can be more sensitive to Model A-type non-Gaussianity (topological defects). These findings guide observational strategies for constraining inflationary physics versus defect scenarios with upcoming data. A key contribution is translating non-Gaussian tail enhancements into measurable abundance changes and bispectrum signatures across multiple probes.

Abstract

We investigate the relative sensitivities of several tests for deviations from Gaussianity in the primordial distribution of density perturbations. We consider models for non-Gaussianity that mimic that which comes from inflation as well as that which comes from topological defects. The tests we consider involve the cosmic microwave background (CMB), large-scale structure (LSS), high-redshift galaxies, and the abundances and properties of clusters. We find that the CMB is superior at finding non-Gaussianity in the primordial gravitational potential (as inflation would produce), while observations of high-redshift galaxies are much better suited to find non-Gaussianity that resembles that expected from topological defects. We derive a simple expression that relates the abundance of high-redshift objects in non-Gaussian models to the primordial skewness.