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In this paper, we consider the Universe at the late stage of its evolutionand deep inside the cell of uniformity. At these scales, we consider theUniverse to be filled with dust-like matter in the form of discretelydistributed galaxies, a minimally coupled scalar field and radiation as mattersources. We investigate such a Universe in the mechanical approach. This meansthat the peculiar velocities of the inhomogeneities (in the form of galaxies)as well as fluctuations of other perfect fluids are non-relativistic. Suchfluids are designated as coupled because they are concentrated aroundinhomogeneities. In the present paper we investigate the conditions under whicha scalar field can become coupled, and show that, at the background level, suchcoupled scalar field behaves as a two component perfect fluid: a network offrustrated cosmic strings with EoS parameter $w=-1/3$ and a cosmologicalconstant. The potential of this scalar field is very flat at the present time.Hence, the coupled scalar field can provide the late cosmic acceleration. Thefluctuations of the energy density and pressure of this field are concentratedaround the galaxies screening their gravitational potentials. Therefore, suchscalar fields can be regarded as coupled to the inhomogeneities.

Coupled scalar fields in the late Universe: The mechanical approach and the late cosmic acceleration