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 ∆β (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

15 We define the differential operator L i ≡ 1 2 ǫ ijk L jk . Then, noting that L = x × P , it follows that L · P = 0. Hence, J · P = ( L + S) · P = S · P .

The peculiar value of θ is a challenge to the notion of an anthropic landscape. We briefly review the possibility that a suitable axion might arise from an anthropic requirement of dark matter. We then consider an alternative suggestion of Kaloper and Terning that θ might be correlated with the cosmological constant. We note that in a landscape one expects that θ is determined by the expectation value of one or more axions. We discuss how a discretuum of values of θ might arise with an energy distribution dominated by QCD, and find the requirements to be quite stringent. Given such a discretuum, we find no circumstances where small θ might be selected by anthropic requirements on the cosmological constant.