Cosmological evolution of interacting dark energy in Lorentz violation

The cosmological evolution of an interacting scalar-field model in which the scalar field interacts with dark matter, radiation, and baryons via Lorentz violation is investigated. We propose a model of interaction through the effective coupling, [`(b)]\bar{\beta} . Using dynamical system analysis, we study the linear dynamics of an interacting model and show that the dynamics of critical points are completely controlled by two parameters. Some results can be mentioned as follows. Firstly, the sequence of radiation, the dark matter, and the scalar-field dark energy exist and baryons are subdominant. Secondly, the model also allows for the possibility of having a universe in the phantom phase with constant potential. Thirdly, the effective gravitational constant varies with respect to time through [`(b)]\bar{\beta} . In particular, we consider the simple case where [`(b)]\bar{\beta} has a quadratic form and has a good agreement with the modified ΛCDM and quintessence models. Finally, we also calculate the first post-Newtonian parameters for our model.     

Modified gravitational equations on braneworld with Lorentz invariant violation

The modified gravitational equations to describe a four-dimensional braneworld in the case with the Lorentz invariant violation in a bulk spacetime is presented. It contains a trace part of the brane energy-momentum tensor and the coefficients of all terms describe the Lorentz violation effects from the bulk spacetime. As an application, we apply this formalism to study cosmology. In respect to standard effective Friedmann equations on the brane, Lorentz invariance violation in the bulk causes a modification of this equations that can lead to significant physical consequences. In particular, the effective Friedmann equation on the brane explicitly depends on the equation of state of the brane matter and the Lorentz violating parameters. We show that the components of five-dimensional Weyl curvature are related to the matter on brane even at low energies. We also find that the constraints on the theory parameters are depend on the equation of state of the energy components of the brane matter. Finally, the stability of the model depend on the specific choices of initial conditions and the parameters β _i .