We study the second-order scalar perturbations in the conventional ΛCDM 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). IntroductionAccording to the cosmological principle [1, 2], our Universe is isotropic and homogeneous at large enough scales. This follows from the natural assumption that the laws of physics should be the same wherever in the Universe we are. Starting from a certain scale, the distribution of inhomogeneities (e.g., galaxies and groups of galaxies) should be statistically homogeneous. As a result, such statistically homogeneous Universe has the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, and its dynamics is described by the Friedmann equations. This is the zero-order/background approach. Obviously, inhomogeneities disturb this background resulting in first-and higher-order perturbations. They play a crucial role in the investigation of the large scale structure formation. Evidently (by definition!), the average values of the first-order perturbations should be equal to zero (see, e.g., [3]). On the other hand, the average values of the second-order perturbations are different from zero and can affect the background spacetime and matter. This effect is called backreaction (see, e.g., [4,5,6,7,8,9] and references therein). It is important to determine how strong the backreaction is and to what extent we may use the standard FLRW metric as a background one. As an example, the backreaction may affect the baryon acoustic oscillations [5,10]. The second-order perturbations also contribute to the luminosity-redshift relation [11] and gravitational lensing [12,13].Within the cosmic screening approach, the theory of the first-order perturbations was developed in the papers [14,15,16,17,18]. In its framework, inhomogeneities in the Universe (e.g., galaxies and their groups) are considered as point-like gravitating masses. These masses disturb the background spacetime and matter. For example, the energy density fluctuation reads δε ≈ (c 2 /a 3 )δρ + (3ρc 2 /a 3 )Φ, where c denotes the speed of light, a is the scale factor of the Universe, and we singled out the gravitational potential Φ. Consequently, the
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