# Second-order Cosmological Perturbations Engendered by Point-like Masses

## TL;DR

This paper develops a second-order cosmological perturbation theory within the $$CDM model, accounting for discrete point-like masses and nonlinear density contrasts, suitable for relativistic simulations and backreaction studies.

## Contribution

It introduces a new second-order perturbation framework for nonrelativistic matter inhomogeneities modeled as point masses, valid at arbitrary distances and nonlinear contrasts.

## Key findings

- Derived equations for second-order metric corrections including scalar, vector, and tensor modes.
- Verified Einstein equations and consistency in the weak field limit.
- Outlined potential for relativistic simulations of cosmological backreaction.

## Abstract

In the $\Lambda$CDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second-order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second-order scalar, vector and tensor metric corrections are suitable at arbitrary distances including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfilment of all Einstein equations as well as self-consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological backreaction manifestations by means of relativistic simulations are also outlined.