# Analytic expressions for the second-order scalar perturbations in the $\Lambda$CDM Universe within the cosmic screening approach

## TL;DR

This paper derives analytic expressions for second-order scalar perturbations in the $$CDM universe using the cosmic screening approach, highlighting the Yukawa screening effect and its implications for precision cosmology.

## Contribution

It provides the first analytic formulas for second-order scalar perturbations in $$CDM within the cosmic screening framework, including velocity-dependent effects.

## Key findings

- Yukawa screening effect appears in second-order perturbations.
- Formulas reduce to post-Newtonian expressions at small distances.
- Second-order corrections impact interpretation of cosmological observations.

## Abstract

We study the second-order scalar perturbations in the conventional $\Lambda$CDM Universe within the cosmic screening approach. The analytic expressions for both the velocity-independent and velocity-dependent second-order scalar perturbations are derived. We demonstrate how the Yukawa screening effect, which is inherent in the first-order metric corrections, manifests itself in the second-order ones. It is shown that the obtained formulas for the second-order perturbations are reduced to the known post-Newtonian expressions at distances much smaller than the Yukawa screening length. In the era of precision cosmology, these analytic formulas play an important role since the second-order metric corrections may affect the interpretation of observational data (e.g., the luminosity-redshift relation, gravitational lensing, baryon acoustic oscillations).