PhaseTracer2: from the effective potential to gravitational waves

We calculate the gravitational wave spectrum generated by sound waves during a cosmological phase transition, incorporating several advancements beyond the current state-of-the-art. Rather than relying on the bag model or similar approximations, we derive the equation of state directly from the effective potential. This approach enables us to accurately determine the hydrodynamic quantities, which serve as initial conditions in a generalised hybrid simulation. This simulation tracks the fluid evolution after bubble collisions, leading to the generation of gravitational waves. Our work thus provides a self-consistent numerical calculation of gravitational waves for the real singlet extension of the standard model. Our computational method is adaptable to any particle physics model, offering a fast and reliable way to calculate gravitational waves generated by sound waves. With fewer approximations, our approach provides a robust foundation for precise gravitational wave calculations and allows for the exploration of model-independent features of gravitational waves from phase transitions.

In the singlet Majoron model, we study cosmological phase transitions (PTs) and their resulting gravitational waves (GWs), in the two-field phase space, without freezing any of the field directions. We first calculate the effective potential, at one loop and at finite temperature, of the Standard Model Higgs doublet together with one extra Higgs singlet. We make use of the public available Python package ‘CosmoTransitions’ to simulate the two-dimensional (2D) cosmological PTs and evaluate the gravitational waves generated by first-order PTs. With the full 2D simulation, we are able not only to confirm the PTs’ properties previously discussed in the literature, but also we find new patterns, such as strong first-order PTs tunneling from a vacuum located on one axis to another vacuum located on the second axis. The two-field phase space analysis presents a richer panel of cosmological PT patterns compared to analysis with a single-field approximation. The PTGW amplitudes turn out to be out of the reach for the space-borne gravitational wave interferometers such as LISA, DECIGO, BBO, TAIJI and TianQin when constraints from colliders physics are taken into account.

During the past two decades, cosmologists turned to particle physics in order to explore the physics of the very early Universe. The main link between the physics of the smallest and largest structures in the Universe is the idea of spontaneous symmetry breaking, familiar from condensed matter physics. Implementing this mechanism into cosmology leads to the interesting possibility that phase transitions related to the breaking of symmetries in high energy particle physics took place during the early history of the Universe. These cosmological phase transitions may help us understand many of the challenges faced by the standard hot Big Bang model of cosmology, while offering a unique window into the very early Universe and the physics of high energy particle interactions.

Networks of cosmic domain walls can form in the early Universe as a consequence of the spontaneous breaking of discrete symmetries. We study the production of a cosmological background of gravitational waves (GWs) from such networks, when they annihilate due to a small explicit symmetry breaking term. Averaging over several 3+1-dimensional high-resolution lattice field simulations, we obtain a GW spectrum with the following characteristics: (1) a broad asymmetric peak, roughly located at frequency (at the time of emission) f ∼ 2H gw, where H gw is the Hubble rate at the end of GW production, shortly after annihilation, (2) a doubly broken power law spectrum ∝ k-n , with initial slope n ∼ 0.5 after the main peak and n ∼ 1.8 at high f, while the low frequency region f < fp agrees with the causality behavior ∼ k 3. Additionally, extending previous results, we find that GW production continues to be efficient until a value of the Hubble scale H gw that is roughly an order of magnitude smaller than the naive estimate σH = ΔV, where σ is the wall tension and ΔV, the size of the symmetry breaking term, thereby leading to a O(100) larger GW signal. We find such results to be robust when changing the shape of the scalar field potential or including a time-dependent symmetry breaking term. Our findings have important implications for GW searches, especially in light of the reported evidence for a stochastic GW background in Pulsar Timing Array data.

The stochastic gravitational wave (GW) background provides a fascinating window to the physics of the very early universe. Beyond the nearly scale-invariant primordial GW spectrum produced during inflation, a spectrum with a much richer structure is typically generated during the preheating phase after inflation (or after some other phase transition at lower energies). This raises the question of what one can learn from a future observation of the stochastic gravitational wave background spectrum about the underlying physics during preheating. Recently, it has been shown that during preheating non-perturbative quasi-stable objects like oscillons can act as strong sources for GW, leading to characteristic features such as distinct peaks in the spectrum. In this paper, we study the GW production from oscillons using semi-analytical techniques. In particular, we discuss how the GW spectrum is affected by the parameters that characterise a given oscillon system, e.g. by the background cosmology, the asymmetry of the oscillons and the evolution of the number density of the oscillons. We compare our semi-analytic results with numerical lattice simulations for a hilltop inflation model and a KKLT scenario, which differ strongly in some of these characteristics, and find very good agreement.

Cosmic strings are generic cosmological predictions of many extensions of the standard model of particle physics, such as a $U(1{)}^{\ensuremath{'}}$ symmetry-breaking phase transition in the early Universe or remnants of superstring theory. Unlike other topological defects, cosmic strings can reach a scaling regime that maintains a small fixed fraction of the total energy density of the Universe from a very early epoch until today. If present, they will oscillate and generate gravitational waves with a frequency spectrum that imprints the dominant sources of total cosmic energy density throughout the history of the Universe. We demonstrate that current and future gravitational wave detectors, such as LIGO and LISA, could be capable of measuring the frequency spectrum of gravitational waves from cosmic strings and discerning the energy composition of the Universe at times well before primordial nucleosynthesis and the cosmic microwave background where standard cosmology has yet to be tested. This work establishes a benchmark case that gravitational waves may provide an unprecedented, powerful tool for probing the evolutionary history of the very early Universe.

We discuss a mechanism of particle production during inflation that can result in a blue gravitational wave (GW) spectrum, compatible with the BICEP2 result and with the r < 0.11 limit on the tensor-to-scalar ratio at the Planck pivot scale. The mechanism is based on the production of vector quanta from a rolling pseudo-scalar field. Both the vector and the pseudo-scalar are only gravitationally coupled to the inflaton, to keep the production of inflaton quanta at an unobservable level (the overproduction of non-gaussian scalar perturbations is a generic difficulty for mechanisms that aim to generate a visible GW signal from particle production during inflation). This mechanism can produce a detectable amount of GWs for any inflationary energy scale. The produced GWs are chiral and non-gaussian; both these aspects can be tested with large-scale polarization data (starting from Planck). We study how to reconstruct the pseudo-scalar potential from the GW spectrum.

We estimate the gravitational wave (GW) background from Population III (Pop III) stars using the results from our hydrodynamic simulations (Suwa et al. 2007). We calculate gravitational waveforms from matter motions and anisotropic neutrino emissions for single Pop III stars. We find that the GW amplitudes from matter motions are dominant until just after bounce, but those from neutrinos dominate later on at frequencies below $\sim 10$ Hz in the GW spectrum. Computing the overall signal produced by the ensemble of such Pop III stars, we find that the resultant density parameter of the GW background peaks at the amplitude of $\Omega_\mathrm{GW}\sim 10^{-10}$ in the frequency interval $\sim 1-10$ Hz. We show that such signals, depending on the formation rate of Pop III stars, can be within the detection limits of future planned interferometers such as DECIGO and BBO in the frequency interval of $\sim 0.1-1$ Hz. Our results suggest that the detection of the GW background from Pop III stars can be an important tool to supply the information about the star formation history in the early universe.

Hydrodynamic and magnetohydrodynamic turbulence in the early Universe can drive gravitational waves (GWs) and imprint their spectrum onto that of GWs, which might still be observable today. We study the production of the GW background from freely decaying magnetohydrodynamic turbulence from helical and nonhelical initial magnetic fields. To understand the produced GW spectra, we develop a simple model on the basis of the evolution of the magnetic stress tensor. We find that the GW spectra obtained in this model reproduce those obtained in numerical simulations if we consider the detailed time evolution of the low-frequency tail of the stress spectrum from numerical simulations. We also show that the shapes of the produced GW frequency spectra are different for helical and nonhelical cases for the same initial magnetic energy spectra. Such differences can help distinguish helical and nonhelical initial magnetic fields from a polarized background of GWs -- especially when the expected circular polarization cannot be detected directly.

Primordial gravitational waves (GWs) carry the imprints of the dynamics of the universe during its earliest stages. With a variety of GW detectors being proposed to operate over a wide range of frequencies, there is great expectation that observations of primordial GWs can provide us with an unprecedented window to the physics operating during inflation and reheating. In this work, we closely examine the effects of the regime of reheating on the spectrum of primordial GWs observed today. We consider a scenario wherein the phase of reheating is described by an averaged equation of state (EoS) parameter with an abrupt transition to radiation domination as well as a scenario wherein there is a gradual change in the effective EoS parameter to that of radiation due to the perturbative decay of the inflaton. We show that the perturbative decay of the inflaton leads to oscillations in the spectrum of GWs, which, if observed, can possibly help us decipher finer aspects of the reheating mechanism. We also examine the effects of a secondary phase of reheating arising due to a brief epoch driven possibly by an exotic, noncanonical, scalar field. Interestingly, we find that, for suitable values of the EoS parameter governing the secondary phase of reheating, the GWs can be of the strength as suggested by the recent NANOGrav observations. We conclude with a discussion of the wider implications of our analysis.

We argue that the RSI model can provide a strong signature in gravitational waves. This signal is a relic stochastic background generated during the cosmological phase transition from an AdS-Schwarschild phase to the RS1 geometry that should occur at a temperature in the TeV range. We estimate the amplitude of the signal in terms of the parameters of the potential stabilizing the radion and show that over much of the parameter region in which the phase transition completes, a signal should be detectable at the planned space interferometer, LISA.

Gravitational waves (GWs) have a great potential to probe cosmology. We review early universe sources that can lead to cosmological backgrounds of GWs. We begin by presenting proper definitions of GWs in flat space-time and in a cosmological setting (section ). Following, we discuss the reasons why early universe GW backgrounds are of a stochastic nature, and describe the general properties of a stochastic background (section ). We recap current observational constraints on stochastic backgrounds, and discuss the basic characteristics of present and future GW detectors, including advanced LIGO, advanced Virgo, the Einstein telescope, KAGRA, and LISA (section ). We then review in detail early universe GW generation mechanisms, as well as the properties of the GW backgrounds they give rise to. We classify the backgrounds in five categories: GWs from quantum vacuum fluctuations during standard slow-roll inflation (section ), GWs from processes that operate within extensions of the standard inflationary paradigm (section ), GWs from post-inflationary preheating and related non-perturbative phenomena (section ), GWs from first order phase transitions related or not to the electroweak symmetry breaking (section ), and GWs from general topological defects, and from cosmic strings in particular (section ). The phenomenology of these early universe processes is extremely rich, and some of the GW backgrounds they generate can be within the reach of near-future GW detectors. A future detection of any of these backgrounds will provide crucial information on the underlying high energy theory describing the early universe, probing energy scales well beyond the reach of particle accelerators.

In many particle physics models, domain walls can form during the phase transition process after the breakdown of the discrete symmetry. Utilizing the ℤ3 symmetric complex singlet scalar extension of the Standard Model, we study the gravitational waves produced by the strongly first-order electroweak phase transition and the domain wall decay. The gravitational wave spectrum is of a typical two-peak shape. The high frequency peak corresponding to the strongly first-order electroweak phase transition is able to be probed by the future space-based interferometers, and the low frequency peak coming from the domain wall decay is far beyond the capability of the current Pulsar Timing Arrays, and future Square Kilometer Array.

Probing the Higgs potential and new physics behind the electroweak symmetry breaking is one of the most important issues of particle physics. In particular, nature of electroweak phase transition is essential for understanding physics at the early Universe, such that the strongly first order phase transition is required for a successful scenario of electroweak baryogenesis. The strongly first order phase transition is expected to be tested by precisely measuring the triple Higgs boson coupling at future colliders like the International Linear Collider. It can also be explored via the spectrum of stochastic gravitational waves to be measured at future space-based interferometers such as eLISA and DECIGO. We discuss complementarity of both the methods in testing the strongly first order phase transition of the electroweak symmetry in models with additional isospin singlet scalar fields with and without classical scale invariance. We find that they are synergetic in identifying specific models of electroweak symmetry breaking in more details.

Motivated by aLIGO's recent discovery of gravitational waves we discuss signatures of new physics that could be seen at ground and space-based interferometers. We show that a first order phase transition in a dark sector would lead to a detectable gravitational wave signal at future experiments, if the phase transition has occurred at temperatures few orders of magnitude higher than the electroweak scale. The source of gravitational waves in this case is associated with the dynamics of expanding and colliding bubbles in the early universe. At the same time we point out that topological defects, such as dark sector domain walls, may generate a detectable signal already at aLIGO. Both -- bubble and domain wall -- scenarios are sourced by semi-classical configurations of a dark new physics sector. In the first case the gravitational wave signal originates from bubble wall collisions and subsequent turbulence in hot plasma in the early universe, while the second case corresponds to domain walls passing through the interferometer at present and is not related to gravitational waves. We find that aLIGO at its current sensitivity can detect smoking-gun signatures from domain wall interactions, while future proposed experiments including the fifth phase of aLIGO at design sensitivity can probe dark sector phase transitions.