The Ph.D. thesis is devoted to investigations of cosmological models with perfect fluids and scalar fields at the background and perturbed levels. The theory of scalar perturbations is a powerful tool to investigate cosmological models, allowing us to consider such perturbation at any stage of the Universe evolution. It was studied the scalar perturbations of Friedmann–Robertson–Walker metrics of the Universe deep inside the cell of uniformity at the late stage of its evolution, using the mechanical approach, which works for the models where the peculiar velocities of the inhomogeneities (galaxies, groups, and clusters of galaxies) could be considered as negligibly small (as compared to the speed of light), and on scales smaller than the cell of uniformity. Thus, on the one hand, the peculiar velocities in this approach do not affect the gravitational potential. On the other hand, the energy density of those perfect fluids are concentrated around the dust-like matter (in the form of galaxies). In this meaning, they could be considered as coupled. We have investigated the Universe filled with inhomogeneously distributed structures (galaxies, groups and clusters of galaxies), cosmological constant and perfect fluid with the negative constant parameter of the state equation. Within the mechanical approach, those perfect fluids with the constant negative parameter of the equation of state are compatible with the theory of scalar perturbations as long as they are inhomogeneous (clustered) and have the parameter of the equation of state ω = −1/3 (for example, the frustrated network of cosmic strings could fit all the requirements for a role of that perfect fluid, but frustrated domain walls are ruled out within the mechanical approach because they have ω = −2/3). Then, it was shown that the physically reasonable solutions of the equation for non-relativistic gravitational potential take place for flat, open, and close Universe topology. For the cosmological models of the Universe filled with the dust-like matter, radiation and scalar fields, minimally coupled to the gravitation, the coupled scalar field within the mechanical approach behaves as a two-component perfect fluid (cosmological constant and the frustrated network of cosmic strings), and the potential for that scalar field at the current time is very flat. Also, the scalar field’s energy density and pressure were investigated that with the mechanical approach, and they fluctuate as a result of the gravitational potential and background scalar field interaction, and the energy density fluctuations of the scalar field are concentrated around galaxies and screen their gravitational potentials. In the cosmic screening approach (where the peculiar velocities of inhomogeneities are not neglected and early Universe can be investigated as well), we have studied how the peculiar velocities affect the gravitational potential for the Universe filled with the perfect fluid with a constant parameter of the equation of state, e.g. radiation. For the radiation, it was obtained the expression for the gravitational potential in the integral form. It was also demonstrated the gravitational potential modulation by acoustic oscillations (numerical calculations). Besides that, it was shown that the peculiar velocities affect the gravitational potential in the case of the frustrated network of cosmic strings with ω = −1/3.
