Brane-world Cosmologies with non-local bulk effects

It is very common to ignore the non-local bulk effects in the study of brane-world cosmologies using the brane-world approach. However, we shall illustrate through the use of three different scenarios, that the non-local bulk-effect ${\mathcal{P}}_{\mu \nu }$ does indeed have significant impact on both the initial and future behaviour of brane-world cosmologies.