  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).
