$K$-essence model from the mechanical approach point of view: coupled scalar field and the late cosmic acceleration

TL;DR

This paper explores how a general $K$-essence scalar field can be coupled to matter in the late universe, demonstrating that such coupling can produce cosmic acceleration compatible with the mechanical approach.

Contribution

It identifies conditions for coupling in $K$-essence models and shows they can act as multicomponent fluids driving late-time acceleration.

Findings

Coupled $K$-essence models can be represented as multicomponent perfect fluids.

Such models can produce late-time cosmic acceleration.

Coupled models are compatible with the mechanical approach constraints.

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 can consider the Universe to be filled with dust-like matter in the form of discretely distributed galaxies, a $K$-essence scalar field, playing the role of dark energy, 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 the fluctuations of the other perfect fluids are non-relativistic. Such fluids are designated as coupled because they are concentrated around the inhomogeneities. In the present paper, we investigate 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: (i) the pure kinetic $K$-essence field, (ii) a $K$-essence with a constant speed of sound and (iii) the $K$-essence model with the Lagrangian $bX+cX^2-V(\phi)$. 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.