In the ΛCDM 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.

Abstract. We study the late-time evolution of the Universe where dark energy (DE) is presented by a barotropic fluid on top of cold dark matter (CDM). We also take into account the radiation content of the Universe. Here by the late stage of the evolution we refer to the epoch where CDM is already clustered into inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Under this condition the mechanical approach is an adequate tool to study the Universe deep inside the cell of uniformity. More precisely, we study scalar perturbations of the FLRW metric due to inhomogeneities of CDM as well as fluctuations of radiation and DE. For an arbitrary equation of state for DE we obtain a system of equations for the scalar perturbations within the mechanical approach. First, in the case of a constant DE equation of state parameter w, we demonstrate that our method singles out the cosmological constant as the only viable dark energy candidate. Then, we apply our approach to variable equation of state parameters in the form of three different linear parametrizations of w, e.g., the Chevallier-Polarski-Linder perfect fluid model. We conclude that all these models are incompatible with the theory of scalar perturbations in the late Universe.-1 -

We make a generalization of a self-consistent first-order perturbation scheme, being suitable for all (sub-horizon and super-horizon) scales, which has been recently constructed for the concordance cosmological model and discrete presentation of matter sources, to the case of extended models with extra perfect fluids and continuous presentation. Namely, we derive a single equation determining the scalar perturbation and covering the whole space as well as define the corresponding universal Yukawa interaction range. We also demonstrate explicitly that the structure growth is suppressed at distances exceeding this fundamental range.