Motivated by the fact that the Next-to-Minimal Supersymmetric Standard Model is one of the most plausible models that can accommodate electroweak baryogenesis, we analyze its phase structure by tracing the temperature dependence of the minima of the effective potential. Our results reveal rich patterns of phase structure that end in the observed electroweak symmetry breaking vacuum. We classify these patterns according to the first transition in their history and show the strong first-order phase transitions that may be possible in each type of pattern. These could allow for the generation of the matter-antimatter asymmetry or potentially observable gravitational waves. For a selection of benchmark points, we checked that the phase transitions completed and calculated the nucleation temperatures. We furthermore present samples that feature strong first-order phase transitions from an extensive scan of the whole parameter space. We highlight common features of our samples, including the fact that the Standard Model like Higgs is often not the lightest Higgs in the model.

In the Minimal Supersymmetric Standard Model light neutralinos can satisfy the dark matter (DM) abundance constraint by resonant annihilation via a Z or a light Higgs (h) boson. In this work we study the current and future status of this scenario by investigating relevant experimental constraints, including DM direct detection, measurements of Z and Higgs invisible decays, and direct searches at the Large Hadron Collider (LHC). To take full advantage of the LHC data, we combine the results of all relevant electroweakino searches performed by the Compact Muon Solenoid (CMS) Collaboration. Such combination increases the bound on the Higgsino mass parameter to |µ| > 390 GeV, which is about 80 GeV stricter than the bound obtained from individual analyses. In a simplified model we find that the Z funnel region is on the brink of exclusion, the h funnel for µ < 0 only survives if tan β < 7.4, and the h funnel for µ > 0 is the main surviving region. Future DM direct detection experiments, such as LUX and ZEPLIN, can explore the whole region, while the high luminosity LHC can exclude tan β > 8 for µ > 0 and tan β > 5.5 for µ < 0. After applying the muon anomalous magnetic moment constraint only a tiny part of the Z/h funnel region survives which will soon be probed by ongoing experiments. *

We improve upon the simple model studied by Casadio and Orlandi [JHEP 08 (2013) 025] for a black hole as a condensate of gravitons. Instead of the harmonic oscillator potential, the Pöschl-Teller potential is used, which allows for a continuum of scattering states. The quantum mechanical model is embedded into a relativistic wave equation for a complex Klein-Gordon field, and the charge of the field is interpreted as the gravitational charge (mass) carried by the graviton condensate.