We investigate the potential for observing gravitational waves from cosmological phase transitions with LISA in light of recent theoretical and experimental developments. Our analysis is based on current state-of-the-art simulations of sound waves in the cosmic fluid after the phase transition completes. We discuss the various sources of gravitational radiation, the underlying parameters describing the phase transition and a variety of viable particle physics models in this context, clarifying common misconceptions that appear in the literature and identifying open questions requiring future study. We also present a web-based tool, PTPlot, that allows users to obtain up-to-date detection prospects for a given set of phase transition parameters at LISA.

We review in detail recent advances in our understanding of the phase structure and the phase transitions of hadronic matter in strong magnetic fields B and zero quark chemical potentials µ f . Many aspects of QCD are described using low-energy effective theories and models such as the MIT bag model, the hadron resonance gas model, chiral perturbation theory, the Nambu-Jona-Lasinio (NJL) model, the quark-meson (QM) model and Polyakov-loop extended versions of the NJL and QM models. We critically examine their properties and applications. This includes mean-field calculations as well as approaches beyond the mean-field approximation such as the functional renormalization group (FRG). Renormalization issues are discussed and the influence of the vacuum fluctuations on the chiral phase transition is pointed out. Magnetic catalysis at T = 0 is covered as well. We discuss recent lattice results for the thermodynamics of nonabelian gauge theories with emphasis on SU (2)c and SU (3)c. In particular, we focus on inverse magnetic catalysis around the transition temperature Tc as a competition between contributions from valence quarks and sea quarks resulting in a decrease of Tc as a function of B. Finally, we discuss recent efforts to modify models in order to reproduce the behavior observed on the lattice. A. B-dependent transition temperature T0 51 B. B-dependent coupling constant 52 XI. Anisotropic pressure and magnetization 55 XII. Conclusions and outlook 57 Acknowledgments 59 A. Notation and conventions 59 B. Sum-integrals 59 C. Small and large-B expansions 61 D. Propagators in a magnetic background 61References 63 1 Another common choice is the symmetric gauge, Aµ = 1 2 (0, By, −Bx, 0).

We use large-scale lattice simulations to compute the rate of baryon number violating processes (the sphaleron rate), the Higgs field expectation value, and the critical temperature in the Standard Model across the electroweak phase transition temperature. While there is no true phase transition between the high-temperature symmetric phase and the low-temperature broken phase, the crossover is sharply defined at Tc = (159 ± 1) GeV. The sphaleron rate in the symmetric phase (T > Tc) is Γ/T 4 = (18 ± 3)α 5 W , and in the broken phase in the physically interesting temperature range 130 GeV < T < Tc it can be parametrized as log(Γ/T 4 ) = (0.83 ± 0.01)T /GeV − (147.7 ± 1.9). The freeze-out temperature in the early Universe, where the Hubble rate wins over the baryon number violation rate, is T * = (131.7 ± 2.3) GeV. These values, beyond being intrinsic properties of the Standard Model, are relevant for e.g. low-scale leptogenesis scenarios. Introduction:The current results from the LHC are in complete agreement with the Standard Model of particle physics: a Higgs boson with the mass of 125 -126 GeV has been discovered [1], and no evidence of exotic physics has been observed. If the Standard Model is indeed the complete description of the physics at the electroweak scale, the electroweak symmetry breaking transition in the early Universe was a smooth cross-over from the symmetric phase at T > T c , where the (expectation value of the) Higgs field was approximately zero, to the broken phase at T < T c GeV where it is finite, reaching the experimentally determined value |φ| ≃ 246/ √ 2 GeV at zero temperature. The cross-over temperature T c is somewhat larger than the Higgs mass. The nature of the transition was settled already in 1995-98 using lattice simulations [2][3][4][5], which indicate a first-order phase transition at Higgs masses < ∼ 72 GeV, and a cross-over otherwise.A smooth cross-over means that the standard electroweak baryogenesis scenarios [6,7] are ineffective. These scenarios produce the matter-antimatter asymmetry of the Universe through electroweak physics only, and they require a strong first-order phase transition, with supercooling and associated out-of-equilibrium dynamics. Thus, the origin of the baryon asymmetry must rely on physics beyond the Standard Model.Baryogenesis at the electroweak scale is possible in the first place through the existence of the chiral anomaly relating the baryon number of fermions to the topological Chern-Simons number N cs of the electroweak SU(2) gauge fields

We consider a scenario in which the baryon asymmetry was created in the early universe during a cold electroweak transition. The spinodal instability of the Higgs field caused by a rapid change of sign of its effective mass-squared parameter induces tachyonic preheating. We study the development of Chern-Simons number in this transition by numerical lattice simulations of the SU(2)-Higgs model with an added effective CPviolating term. A net asymmetry is produced, and we study its dependence on the size of CP violation and the ratio of Higgs to W mass.

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