Numerical calculation of second order perturbations

TL;DR

This paper presents a numerical method for solving second order cosmological perturbations in single scalar field models, enabling analysis beyond analytical solutions and aiding in non-Gaussianity studies.

Contribution

It introduces a detailed numerical approach for second order perturbations in cosmology, extendable to full equations, and validated against known analytic results.

Findings

Results agree with previous analytic calculations where available.

Method allows evolution of second order perturbations without analytical solutions.

Enables calculation of non-linearity parameter f_NL in complex models.

Abstract

We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source term and argue that our method is extendable to the full equation. We consider two standard single field models and find that the results agree with previous calculations using analytic methods, where comparison is possible. Our procedure allows the evolution of second order perturbations in general and the calculation of the non-linearity parameter f_NL to be examined in cases where there is no analytical solution available.