In this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Supposing that the Universe contains also the cosmological constant and a perfect fluid with a negative constant equation of state (EoS) parameter (e.g., quintessence, phantom or frustrated network of topological defects), we investigate scalar perturbations of the Friedmann–Robertson–Walker metrics due to inhomogeneities. Our analysis shows that, to be compatible with the theory of scalar perturbations, this perfect fluid, first, should be clustered and, second, should have the EoS parameter . In particular, this value corresponds to the frustrated network of cosmic strings. Therefore, the frustrated network of domain walls with is ruled out. A perfect fluid with neither accelerates nor decelerates the Universe. We also obtain the equation for the nonrelativistic gravitational potential created by a system of inhomogeneities. Due to the perfect fluid with , the physically reasonable solutions take place for flat, open and closed Universes. This perfect fluid is concentrated around the inhomogeneities and results in screening of the gravitational potential.

Abstract. In this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, we consider the Universe to be filled with dustlike matter in the form of discretely distributed galaxies, a minimally coupled scalar field and radiation as matter sources. We investigate such a Universe in the mechanical approach. This means that the peculiar velocities of the inhomogeneities (in the form of galaxies) as well as fluctuations of other perfect fluids are non-relativistic. Such fluids are designated as coupled because they are concentrated around inhomogeneities. In the present paper we investigate the conditions under which a scalar field can become coupled, and show that, at the background level, such coupled scalar field behaves as a two component perfect fluid: a network of frustrated cosmic strings with EoS parameter w = −1/3 and a cosmological constant. The potential of this scalar field is very flat at the present time. Hence, the coupled scalar field can provide the late cosmic acceleration. The fluctuations of the energy density and pressure of this field are concentrated around the galaxies screening their gravitational potentials. Therefore, such scalar fields can be regarded as coupled to the inhomogeneities.

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