Abstract:
In the limit of a high temperature T and a large quark-mass M, implying a small gauge coupling g, the heavy quark contribution to the spectral function of the electromagnetic current can be computed systematically in the weak-coupling expansion. We argue that the scale hierarchy relevant for addressing the disappearance ("melting") of the resonance peak from the spectral function reads M >> T > g^2 M > gT >> g^4 M, and review how the heavy scales can be integrated out one-by-one, to construct a set of effective field theories describing the low-energy dynamics. The parametric behaviour of the melting temperature in the weak-coupling limit is specified.

Abstract:
When considering NLO corrections to thermal particle production in the "relativistic" regime, in which the invariant mass squared of the produced particle is K^2 ~ (pi T)^2, then the production rate can be expressed as a sum of a few universal "master" spectral functions. Taking the most complicated 2-loop master as an example, a general strategy for obtaining a convergent 2-dimensional integral representation is suggested. The analysis applies both to bosonic and fermionic statistics, and shows that for this master the non-relativistic approximation is only accurate for K^2 > (8 pi T)^2, whereas the zero-momentum approximation works surprisingly well. Once the simpler masters have been similarly resolved, NLO results for quantities such as the right-handed neutrino production rate from a Standard Model plasma or the dilepton production rate from a QCD plasma can be assembled for K^2 ~ (pi T)^2.

Abstract:
By making use of the finite-temperature real-time static potential that was introduced and computed to leading non-trivial order in Hard Thermal Loop resummed perturbation theory in recent work, and solving numerically a Schr\"odinger-type equation, we estimate the quarkonium (in practice, bottomonium) contribution to the spectral function of the electromagnetic current in hot QCD. The spectral function shows a single resonance peak which becomes wider and then disappears as the temperature is increased beyond 450 MeV or so. This behaviour can be compared with recently attempted lattice reconstructions of the same quantity, based on the ``maximum entropy method'', which generically show several peaks. We also specify the dependence of our results on the spatial momentum of the electromagnetic current, as well as on the baryon chemical potential characterising the hot QCD plasma.

Abstract:
Bubble growth as a detonation is studied in the context of cosmological phase transitions. It is proved that the so called Chapman-Jouguet hypothesis, which restricts the types of detonations that can occur in spherically symmetric chemical burning, does not hold in the case of phase transitions. Therefore a much larger class of detonation solutions exists in phase transitions than in chemical burning.

Abstract:
The essential features of the high-temperature electroweak phase transition are contained in a three-dimensional super-renormalizable effective field theory. We calculate the exact counterterms needed for lattice simulations of the SU(2)-part of this theory. Scalar fields in both fundamental and adjoint representations are included. The three-dimensional U(1)+Higgs theory is also discussed.

Abstract:
The high-temperature limit of the 2-loop effective potential for the Higgs field is calculated from an effective 3d theory, in a general covariant gauge. It is shown explicitly that a gauge-independent result can be extracted for the equation of state from the gauge-dependent effective potential. The convergence of perturbation theory is estimated in the broken phase, utilizing the gauge dependence of the effective potential.

Abstract:
We compare 4d lattice results for the finite temperature phase transition in the SU(2)+Higgs model with 3d lattice results for the phase transition in the corresponding dimensionally reduced effective theory. While the large errorbars and the lack of a relation of the 4d lattice gauge coupling to continuum physics prevent rigorous conclusions, the results are nevertheless compatible. This provides a direct non-perturbative check of dimensional reduction in the present context.

Abstract:
To study the convergence of the loop expansion at the high-temperature electroweak phase transition, we calculate the 2-loop effective potential of the 3d SU(2)-Higgs model in a general covariant gauge. We find that the loop expansion definitely breaks down for large $\xi$, but converges rather well for smaller values, deep in the broken phase.

Abstract:
One of the possible explanations for the dark matter needed in the standard cosmological model is so-called warm dark matter, in the form of right-handed ("sterile") neutrinos with a mass in the keV range. I describe how various properties of QCD at temperatures of a few hundred MeV play an important role in the theoretical computations that are needed for consolidating or falsifying this scenario. In particular the points where lattice QCD could help are underlined.

Abstract:
We construct effective 3d field theories for the Minimal Supersymmetric Standard Model, relevant for the thermodynamics of the cosmological electroweak phase transition. The effective theories include a 3d theory for the bosonic sector of the original 4d theory; a 3d two Higgs doublet model; and a 3d SU(2)+Higgs model. The integrations are made at 1-loop level. In integrals related to vacuum renormalization we take into account only quarks and squarks of the third generation. Using existing non-perturbative lattice results for the 3d SU(2)+Higgs model, we then derive infrared safe upper bounds for the lightest Higgs boson mass required for successful baryogenesis at the electroweak scale. The Higgs mass bounds turn out to be close to those previously found with the effective potential, allowing baryogenesis if the right-handed stop mass parameter $m_U^2$ is small. Finally we discuss the effective theory relevant for $m_U^2$ very small, the most favourable case for baryogenesis.