Scalar perturbations of Galileon cosmologies in the mechanical approach in the late Universe

We investigate the Universe at the late stage of its evolution and inside the cell of uniformity 150 - 370 MPc. We consider the Universe to be filled at these scales with dust like matter, a minimally coupled Galileon field and radiation as matter sources. We will use the mechanical approach and therefore the peculiar velocities of the inhomogeneities as well as fluctuations of other perfect fluids are nonrelativistic. Such fluids are said to be coupled, because they are concentrated around inhomogeneities. We investigate the conditions under which the Galileon field can become coupled. We know from previous work that at background level coupled scalar field behave as a two-component perfect fluid: a network of frustrated cosmic string and cosmological constant. We found a correction for the Galileon field, which behaves like matter. We investigate a similar task for K-essence models and we try to find the conditions under which the K-essence scalar field with the most general form for its action can become coupled. We investigate at the background level three particular examples of the K-essence models: (1) the pure kinetic K-essence field, (2) a K-essence with a constant speed of sound and (3) the K-essence model with the Lagrangian bX+cX2−V (φ). We demonstrate that if the K-essence is coupled, all these K-essence models take the form of multicomponent perfect fluids where one of the component is the cosmological constant. Therefore, they can provide the late-time cosmic acceleration and be simultaneously compatible with the mechanical approach