Abstract
In this paper, we study the possibility of obtaining a stable flat dark energy-dominated universe in a good agreement with observations in the framework of Swiss-cheese brane-world cosmology. Two different brane-world cosmologies with black strings have been introduced for any cosmological constant A using two empirical forms of the scale factor. In both models, we have performed a fine-tuning between the brane tension and the cosmological constant so that the Equation of state (EoS) parameter omega(t) -> -1 for the current epoch, where the redshift z similar or equal to 0. We then used these fine-tuned values to calculate and plot all parameters and energy conditions. The deceleration-acceleration cosmic transition is allowed in both models, and the jerk parameter j -> 1 at late- times. Both solutions predict a future dark energy-dominated universe in which omega = -1 with no crossing to the phantom divide line. While the pressure in the first solution is always negative, the second solution predicts a better behavior of cosmic pressure where the pressure is negative only in the late-time accelerating era but positive in the early-time decelerating era. Such a positive-to-negative transition in the evolution of pressure helps to explain the cosmic deceleration-acceleration transition. Since black strings have been proved to be unstable by some authors, this instability can actually reflect doubts on the stability of cosmological models with black strings (Swiss-cheese type brane-worlds cosmological models). For this reason, we have carefully investigated the stability through energy conditions and sound speed. Because of the presence of quadratic energy terms in Swiss-cheese type brane-world cosmology, we have tested the new nonlinear energy conditions in addition to the classical energy conditions. We have also found that. a negative tension brane is not allowed in both models of the current work as the energy density will no longer be well defined.