  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.
