  We study cosmological phase transitions in the Next-to-Minimal Supersymmetric
Standard Model (NMSSM) in light of the Higgs discovery. We use an effective
field theory approach to calculate the finite temperature effective potential,
focusing on regions with significant tree-level contributions to the Higgs
mass, a viable neutralino dark matter candidate, 1-2 TeV stops, and with the
remaining particle spectrum compatible with current LHC searches and results.
The phase transition structure in viable regions of parameter space exhibits a
rich phenomenology, potentially giving rise to one- or two-step first-order
phase transitions in the singlet and/or $SU(2)$ directions. We compute several
parameters pertaining to the bubble wall profile, including the bubble wall
width and $\Delta\beta$ (the variation of the ratio in Higgs vacuum expectation
values across the wall). These quantities can vary significantly across small
regions of parameter space and can be promising for successful electroweak
baryogenesis. We estimate the wall velocity microphysically, taking into
account the various sources of friction acting on the expanding bubble wall.
Ultra-relativistic solutions to the bubble wall equations of motion typically
exist when the electroweak phase transition features substantial supercooling.
For somewhat weaker transitions, the bubble wall instead tends to be
sub-luminal and, in fact, likely sub-sonic, suggesting that successful
electroweak baryogenesis may indeed occur in regions of the NMSSM compatible
with the Higgs discovery.
