The cosmological evolution of an interactingscalar-field model in which the scalar field interacts withdark matter, radiation, and baryons via Lorentz violation isinvestigated. We propose a model of interaction through theeffective coupling, β. Using dynamical system analysis, westudy the linear dynamics of an interacting model and showthat the dynamics of critical points are completely controlledby two parameters. Some results can be mentioned as fol-lows. Firstly, the sequence of radiation, the dark matter, andthe scalar-field dark energy exist and baryons are subdomi-nant. Secondly, the model also allows for the possibility ofhaving a universe in the phantom phase with constant po-tential. Thirdly, the effective gravitational constant varieswith respect to time through β. In particular, we considerthe simple case where βhas a quadratic form and has agood agreement with the modified ACDM and quintessencemodels. Finally, we also calculate the first post-Newtonianparameters for our model.
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