Brane-world cosmology with black strings

We consider the simplest scenario when black strings/cigars penetrate the cosmological brane. As a result, the brane has a Swiss-cheese structure, with Schwarzschild black holes immersed in a Friedmann-Lemaitre-Robertson-Walker brane. There is no dark radiation in the model, the cosmological regions of the brane are characterized by a cosmological constant Lambda and flat spatial sections. Regardless of the value of Lambda, these brane-world universes forever expand and forever decelerate. The totality of source terms in the modified Einstein equation sum up to a dust, establishing a formal equivalence with the general relativistic Einstein-Straus model. However in this brane-world scenario with black strings the evolution of the cosmological fluid strongly depends on Lambda. For Lambda <= 0 it has positive energy density rho and negative pressure p and at late times it behaves as in the Einstein-Straus model. For (not too high) positive values of Lambda the cosmological evolution begins with positive rho and negative p, but this is followed by an epoch with both rho and p positive. Eventually, rho becomes negative, while p stays positive. A similar evolution is present for high positive values of Lambda, however in this case the evolution ends in a pressure singularity, accompanied by a regular behavior of the cosmic acceleration. This is a novel type of singularity appearing in brane-worlds.