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Abstract We study in detail the viability and the patterns of a strong first-order electroweak phase transition as a prerequisite to electroweak baryogenesis in the framework of Z 3-invariant Next-to-Minimal Supersymmetric Standard Model (NMSSM), in the light of recent experimental results from the Higgs sector, dark matter (DM) searches and those from the searches of the lighter chargino and neutralinos at the Large Hadron Collider (LHC). For the latter, we undertake thorough recasts of the relevant, recent LHC analyses. With the help of a few benchmark scenarios, we demonstrate that while the LHC has started to eliminate regions of the parameter space with relatively small μ eff, that favors the coveted strong first-order phase transition, rather steadily, there remains phenomenologically much involved and compatible regions of the same which are yet not sensitive to the current LHC analyses. It is further noted that such a region could also be compatible with all pertinent theoretical and experimental constraints. We then proceed to analyze the prospects of detecting the stochastic gravitational waves, which are expected to arise from such a phase transition, at various future/proposed experiments, within the mentioned theoretical framework and find them to be somewhat ambitious under the currently projected sensitivities of those experiments.

A bstract In recent years, several pulsar timing array collaborations have reported first hints for a stochastic gravitational wave background at nano-Hertz frequencies. Here we elaborate on the possibility that this signal comes from new physics that leads to the generation of a primordial stochastic gravitational wave background. We propose a set of simple but concrete models that can serve as benchmarks for gravitational waves sourced by cosmological phase transitions, domain wall networks, cosmic strings, axion dynamics, or large scalar fluctuations. These models are then confronted with pulsar timing data and with cosmological constraints. With only a limited number of free parameters per model, we are able to identify viable regions of parameter space and also make predictions for future astrophysical and laboratory tests that can help with model identification and discrimination.

Abstract Breaking of discrete parity at high scale gives rise to Z 2-domain walls (DW). The metastability of such walls can make them relatively long lived and contradict standard cosmology. We consider two classes of theories with similar underlying feature, the left right symmetric theories and two Higgs doublet models. Both of them possess some breaking of Z 2 discrete symmetries. As a first step, domains form at a high energy scale during parity breaking. In the second step, these domains further decompose into subdomains due to Z 2 symmetry breaking in two Higgs doublet models closer to the electroweak scale. We show that after this two step formation of domains and subdomains, a QCD instanton induced energy difference can remove the domain walls as well as the subdomain walls at around the same time successfully. The removal occurs purely as the result of a chance event taking place with probability very close to 0.25, and does not require one to introduce any non-renormalisable Z 2-symmetry breaking term to the Lagrangian. We then investigate the gravitational waves arising from the collapse of such domain walls and show that the peak frequency of these waves lies in the 10 −7–10 −6 Hz band, corresponding to annihilation temperatures of 1–10 GeV. This frequency band is sensitive to pulsar timing array based experiments such as SKA and NANOGrav. The recent NANOGrav results rule out our DW collapse model for higher values of parity breaking scale above 107 GeV. Our DW collapse model with parity breaking scales below 107 GeV remains consistent with the current NANOGrav results and has a good chance of being seriously tested in future pulsar timing based experiments.

A bstract We study the formation of primordial black holes (PBHs) in strongly super-cooled first-order phase transitions. The mechanism is based on the presence of remnants dominated by the false vacuum that scale slower with the expansion of the Universe than their surroundings where this energy was already converted into radiation. We compute the PBH formation from these remnants including the contribution from the false vacuum and the bubble walls, by estimating the collapse using the hoop conjecture and by considering both regions collapsing immediately when entering the horizon and sub-horizon regions that collapse as their compactness grows. We show that for exponential bubble nucleation rate, Γ ∝ e βt , the primordial black hole formation implies β/H ≳ 3 . 8, where H denotes the Hubble rate, if the potential energy of the false vacuum is ∆ V ≲ (10 12 GeV) 4 , as otherwise a too large abundance of long-lived PBHs forms. The observed dark matter abundance can be formed in asteroid mass PBHs if β/H ≃ 3 . 8 and 10 5 GeV ≲ ∆ V 1 / 4 ≲ 10 8 GeV. Finally, we consider also the effect of the second order correction to the exponential nucleation rate showing that the PBH abundance is mainly determined by the average radius of the true vacuum bubbles.

A bstract For a discrete symmetry that is anomalous under QCD, the domain walls produced in the early universe from its spontaneous breaking can naturally annihilate due to QCD instanton effects. The gravitational waves generated from wall annihilation have their amplitude and frequency determined by both the discrete symmetry breaking scale and the QCD scale. The evidence of stochastic gravitational waves at nanohertz observed by pulsar timing array experiments suggests that the discrete-symmetry-breaking scale is around 100 TeV, assuming the domain-wall explanation. The annihilation temperature is about 100 MeV, which could naturally be below the QCD phase transition temperature. We point out that the QCD phase transition within some domains with an effective large QCD θ angle could be a first-order one. To derive the phase diagram in θ and temperature, we adopt a phenomenological linear sigma model with three quark flavors. The domain-wall explanation for the NANOGrav, EPTA, PPTA and CPTA results hints at a first-order QCD phase transition, which predicts additional gravitational waves at higher frequencies. If the initial formation of domain walls is also a first-order process, this class of domain-wall models predicts an interesting gravitational wave spectroscopy with frequencies spanning more than ten orders of magnitude, from nanohertz to 100 Hz.

A bstract First order phase transitions could play a major role in the early universe, providing important phenomenological consequences, such as the production of gravitational waves and the generation of baryon asymmetry. An important aspect that determines the properties of the phase transition is the dynamics of the true-vacuum bubbles, which is controlled by the density perturbations in the hot plasma. We study this aspect presenting, for the first time, the full solution of the linearized Boltzmann equation for the top quark species coupled to the Higgs field during a first-order electroweak phase transition. Our approach, differently from the traditional one based on the fluid approximation, does not rely on any ansatz and can fully capture the density perturbations in the plasma. We find that our results significantly differ from the ones obtained in the fluid approximation (including its extensions and modifications), both at the qualitative and quantitative level. In particular sizable differences are found for the friction acting on the bubble wall.

A bstract Supercooled first order phase transitions are typical of theories where conformal symmetry is predominantly spontaneously broken. In these theories the fate of the flat scalar direction is highly sensitive to the size and the scaling dimension of the explicit breaking deformations. For a given deformation, the coupling must lie in a particular region to realize a supercooled first order phase transition. We identify the supercooling window in weakly coupled theories and derive a fully analytical understanding of its boundaries. Mapping these boundaries allows us to identify the deformations enlarging the supercooling window and to characterize their dynamics analytically. For completeness we also discuss strongly coupled conformal field theories with an holographic dual, where the complete characterization of the supercooling window is challenged by calculability issues.

A bstract We propose a new scenario of leptogenesis, which is triggered by a first-order phase transition (FOPT). The right-handed neutrinos (RHNs) are massless in the old vacuum, while they acquire a mass in the new vacuum bubbles, and the mass gap is huge compared with the FOPT temperature. The ultra-relativistic bubble walls sweep the RHNs into the bubbles, where the RHNs experience fast decay and generate the lepton asymmetry, which is further converted to the baryon asymmetry of the Universe (BAU). Since the RHNs are out of equilibrium inside the bubble, the generated BAU does not suffer from the thermal bath washout. We first discuss the general feature of such a FOPT leptogenesis mechanism, and then realize it in an extended B − L model. The gravitational waves from U(1) B−L breaking could be detected at the future interferometers.

A bstract The recent results from the Pulsar Timing Array (PTA) collaborations show the first evidence for the detection of a stochastic background of gravitational waves at the nHz frequencies. This discovery has profound implications for the physics of both the late and the early Universe. In fact, together with the interpretation in terms of supermassive black hole binaries, many sources in the early Universe can provide viable explanations as well. In this paper, we study the gravitational wave background sourced by a network of axion-like-particle (ALP) domain walls at temperatures around the QCD crossover, where the QCD-induced potential provides the necessary bias to annihilate the network. Remarkably, this implies a peak amplitude at frequencies around the sensitivity range of PTAs. We extend previous analysis by taking into account the unavoidable friction on the network stemming from the topological coupling of the ALP to QCD in terms of gluon and pion reflection off the domain walls at high and low temperatures, respectively. We identify the regions of parameter space where the network annihilates in the scaling regime ensuring compatibility with the PTA results, as well as those where friction can be important and a more detailed study around the QCD crossover is required.

A bstract We show that primordial black holes — in the observationally allowed mass window with f PBH = 1 — formed from late nucleating patches in a first order phase transition imply upcoming gravitational wave interferometers will see a large stochastic background arising from the bubble collisions. As an example, we use a classically scale invariant B – L model, in which the right handed neutrinos explain the neutrino masses and leptogenesis, and the dark matter consists of primordial black holes. The conclusion regarding the gravitational waves is, however, expected to hold model independently for black holes coming from such late nucleating patches.