Asymmetric Swiss-cheese brane-worlds

Abstract

We study a brane-world cosmological scenario with local inhomogeneities represented byblack holes. The brane is asymmetrically embedded into the bulk. The black strings/cigarspenetrating the Friedmann brane generate a Swiss-cheese-type structure. This universeforever expands and decelerates, as its general relativistic analogue. The evolution of thecosmological fluid, however, can proceed along four branches, two allowed to have positiveenergy density, and one of them having the symmetric embedding limit. On this branch afuture pressure singularity can arise for either (a) a difference in the cosmologicalconstants of the cosmological and black hole brane regions or (b) a differencein the left and right bulk cosmological constants. While behaviour (a) can beavoided by a redefinition of the fluid variables, (b) establishes a critical valueof the asymmetry over which the pressure singularity occurs. We introduce thepressure singularity censorship which bounds the degree of asymmetry in the bulkcosmological constant. We also show as a model-independent generic feature thatthe asymmetry source term due to the bulk cosmological constant increases inthe early universe. In order to obey the nucleosynthesis constraints, the branetension should be constrained therefore both from below and from above. With themaximal degree of asymmetry obeying the pressure singularity censorship, thehigher limit is ten times the lower limit. The degree of asymmetry allowed bypresent cosmological observations is, however, much less, pushing the upper limit toinfinity.