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

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