Second-order dust perturbations of the non-flat FLRW model with the positive cosmological constant

TL;DR

This paper derives a second-order perturbation solution for non-flat FLRW cosmologies with dust and a positive cosmological constant, providing a simplified inhomogeneous model to study local inhomogeneity effects.

Contribution

It presents a new second-order perturbation solution for non-flat FLRW models with dust and a positive cosmological constant, including spatial curvature effects.

Findings

Derived a simplified metric for inhomogeneous cosmological models.

Provides a flexible framework for analyzing local inhomogeneity impacts.

Enables studying inhomogeneity effects on cosmological observables.

Abstract

In this paper, a specific solution to the second-order cosmological perturbation theory is given. Perturbations are performed around any FLRW spacetime filled with dust and with a positive cosmological constant. In particular, with a possibly non-vanishing spatial curvature. The adopted symmetry condition allows us to simplify the equations, leaving us with a great deal of freedom to choose the density distribution. In the result, we get a relatively simple metric of an inhomogeneous cosmological model, which will give a perfect tool for studying the influence of the local inhomogeneities onto the cosmological observables.