Contributions to the Dark Matter 3-Pt Function from the Radiation Era

TL;DR

This paper analyzes how the radiation era influences the matter density three-point function, highlighting the importance of relativistic effects and nonlinear growth for accurate predictions of primordial non-Gaussianities.

Contribution

It introduces a method to numerically compute the three-point function considering radiation era effects and relativistic corrections.

Findings

Radiation era significantly modifies the three-point function for short wavelengths.

Relativistic effects become important at longer wavelengths, affecting f_NL estimates.

The proposed method solves second-order perturbation equations for accurate calculations.

Abstract

We consider the contribution to the three-point function of matter density fluctuations from nonlinear growth after modes re-enter the horizon, and discuss effects that must be included in order to predict the three-point function with an accuracy comparable to primordial nongaussianities with f_NL ~ few. In particular, we note that the shortest wavelength modes measured in galaxy surveys entered the horizon during the radiation era, and, as a result, the radiation era modifies their three-point function by a magnitude equivalent to f_NL ~ O(4). On longer wavelengths, where the radiation era is negligible, we find that the corrections to the nonlinear growth from relativistic effects become important at the level f_NL ~ few. We implement a simple method for numerically calculating the three-point function, by solving the second-order equations of motion for the perturbations with the first order perturbations providing a source.