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

Abstract

We study the second-order scalar perturbations in the conventional $��$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).v2 (matching the publication in Physics of the Dark Universe) = v1 + new Section 4 + minor changes + extra discussion + new Refs.; 14 pages, no figures