Modified Gravitational Equations on Braneworld with Lorentz Invariant Violation

TL;DR

This paper develops modified gravitational equations for a braneworld scenario incorporating Lorentz invariance violation in the bulk, affecting cosmological dynamics and the effective Friedmann equations.

Contribution

It introduces a formalism for gravitational equations on the brane with Lorentz violation effects, and explores their implications for cosmology and stability.

Findings

Lorentz violation modifies the effective Friedmann equations.

The equations depend on brane matter's equation of state and Lorentz violating parameters.

Constraints on parameters are influenced by the brane matter composition.

Abstract

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 $\beta_i$.