The Randall-Sundrum model already has a phase transition which may be seen in 'dual' gauge theory as a deconfinement-confinement transition, or in 5d gravity as the emergence of the IR brane versus the high temperature state of a black hole in AdS space. Then the authors study the behaviour on a more realistic theory with stabilized radion and Higgs. It appears that the electroweak phase transition happens much later and much cooler than in standard 4d cosmology.In the Randall-Sundrum model where the radion is stabilized by a Goldberger-Wise (GW) potential there is a supercooled transition from a deconfined to a confined phase at temperatures orders of magnitude below the typical Standard Model critical temperature.
When the Higgs is localized at the IR brane the electroweak phase transition is delayed and becomes a strong first-order one where the Universe expands by a few e-folds.
One possible spanner in the works is described in
which I noticed a couple of weeks ago. That paper is the latest of many that look at the density in primordial black holes (4d black holes, of course, not 5d!) produced at cosmological phase transitions. One result is that the PBH's forming at strong first-order transitions overclose the Universe by an enormous factor under quite general assumptions.
However, that is a purely 4d analysis and one might have to think more carefully what could happen in a 5d model.
If RS models all have a strongly first-order phase transition then the question of PBH formation becomes rather urgent ... has anyone thought about it?