Power Spectrum Of Gravitational Waves Research Articles

Transition rate and gravitational wave spectrum from first-order QCD phase transitions

We investigate the gravitational wave spectrum induced by first-order quantum chromodynamics (QCD) phase transitions, e.g., the confinement-deconfinement phase transition of the pure gluon system and the chiral phase transitions in the quark-meson model and Polyakov quark-meson model. The gravitational wave power spectra are sensitive to the phase transition rate β/H. All QCD models predict a relatively large phase transition rate in the order of β/H∼104 at high temperature region, and the produced gravitational waves lie in the peak frequency region of 10−4–0.01 Hz, corresponding to an energy spectrum in the range of 10−8–10−7, which can be detected by LISA and Taiji. If a high baryon density region is generated through Affleck-Dine baryogenesis or other mechanisms, the baryon chemical potential significantly reduces the phase transition rate, which will drop to the order of β/H∼101, thus leading to the production of nanohertz gravitational waves. Furthermore, there exists a critical quark chemical potential with zero phase transition rate β/H=0, indicating that the false vacuum will not decay, which supports the formation of primordial quark nuggets in the early Universe. Published by the American Physical Society 2025

Signatures of the speed of sound on the gravitational wave power spectrum from sound waves

Future space-based interferometers offer an unprecedented opportunity to detect signals from the stochastic gravitational wave background originating from a first-order phase transition at the electroweak scale. The phase transition is accompanied by a change of the equation of state from that of pure radiation. In this work we study the effect of this change on the power spectrum of gravitational waves generated by the sound waves in the plasma during the acoustic phase of the transition. We carry out an analytic calculation assuming that the sound speed and the fluid shear-stress that sources tensor perturbations remain approximately constant during the acoustic phase. The effect of a softer equation of state is twofold:(i) a scale-independent suppression of the power spectrum at all scales, due to the modified propagation of both sound and gravitational waves and(ii) the peak of the spectrum moves to smaller frequencies as the equation of state becomes softer.The power-law indices of the spectrum at small and large scales are unaffected by the softening of the equation of state. Our work improves the current estimation of the gravitational waves power spectrum from first order phase transitions and expands the possible scenarios of transitions that can be tested by gravitational wave detectors.

Domain wall networks from first-order phase transitions and gravitational waves

In the first-order phase transitions (PTs) colliding bubble is an important gravitational wave (GW) source. Following bubble collision, domain walls can be formed when degenerate vacua occur as a result of the spontaneous breaking of a discrete symmetry relevant to new physics at electroweak or higher scales. Using lattice simulations, we study the dynamical evolution of domain walls and find that the networks of the domain wall are formed around the completion of PTs and quickly collapse before entering into the scaling regime provide that the degeneracy of true vacua is broken. Our numerical results indicate that domain wall networks continue to produce GWs in the aftermath of PTs, leading to dramatically changing the spectral shape and enhancing the magnitude by about one order. The resulting GW power spectra are peaked at kR*≃π as predicted by the envelop approximation model, above the peak wave number it has a decaying power law close to k−1.2 followed by a slowly decreasing plateau with the UV cutoff at kR*∼O(102). Published by the American Physical Society 2024

The effect of quantum decoherence on inflationary gravitational waves

The theory of inflation provides a mechanism to explain the structures we observe today in the Universe, starting from quantum-mechanically generated fluctuations. However, this leaves the question of: how did the quantum-to-classical transition, occur? During inflation, tensor perturbations interact (at least gravitationally) with other fields, meaning that we need to view these perturbations as an open system that interacts with an environment. In this paper, the evolution of the system is described using a Lindblad equation, which describes the quantum decoherence of the system. This is a possible mechanism for explaining the quantum-to-classical transition. We show that this quantum decoherence during a de Sitter phase leads to a scale-dependent increase of the gravitational wave power spectrum, depending on the strength and time dependence of the interaction between the system and the environment. By using current upper bounds on the gravitational wave power spectrum from inflation, obtained from CMB and the LIGO-Virgo-KAGRA constraints, we find an upper bound on the interaction strength. Furthermore, we compute the decoherence criterion, which indicates the minimal interaction strength needed for a specific scale to have successfully decohered by the end of inflation. Assuming that the CMB modes have completely decohered, we indicate a lower bound on the interaction strength. In addition, this decoherence criterion allows us to look at which scales might not have fully decohered and could still show some relic quantum signatures. Lastly, we use sensitivity forecasts to study how future gravitational-wave detectors, such as LISA and ET, could constrain the decoherence parameter space. Due to the scale-dependence of the power spectrum, LISA could only have a very small impact. However, ET will be able to significantly improve our current constraints for specific decoherence scenarios.

Higher-order-operator corrections to phase-transition parameters in dimensional reduction

The dynamics of phase transitions (PT) in quantum field theories at finite temperature is most accurately described within the framework of dimensional reduction. In this framework, thermodynamic quantities are computed within the 3-dimensional effective field theory (EFT) that results from integrating out the high-temperature Matsubara modes. However, strong-enough PTs, observable in gravitational wave (GW) detectors, occur often nearby the limit of validity of the EFT, where effective operators can no longer be neglected. Here, we perform a quantitative analysis of the impact of these interactions on the determination of PT parameters. We find that they allow for strong PTs in a wider region of parameter space, and that both the peak frequency and the amplitude of the resulting GW power spectrum can change by more than one order of magnitude when they are included. As a byproduct of this work, we derive equations for computing the bounce solution in the presence of higher-derivative terms, consistently with the EFT power counting.

Climbing over the potential barrier during inflation via null energy condition violation

The violation of the null energy condition (NEC) may play a crucial role in enabling a scalar field to climb over high potential barriers, potentially significant in the very early universe. We propose a single-field model where the universe sequentially undergoes a first stage of slow-roll inflation, NEC violation, and a second stage of slow-roll inflation. Through the NEC violation, the scalar field climbs over high potential barriers, leaving unique characteristics on the primordial gravitational wave power spectrum, including a blue-tilted nature in the middle-frequency range and diminishing oscillation amplitudes at higher frequencies. Additionally, the power spectrum exhibits nearly scale-invariant behavior on both large and small scales.

Cosmologically consistent analysis of gravitational waves from hidden sectors

Production of gravitational waves in the early Universe is discussed in a cosmologically consistent analysis within a first-order phase transition involving a hidden sector feebly coupled with the visible sector. Each sector resides in its own heat bath leading to a potential dependent on two temperatures and on two fields: one a standard model Higgs field and the other a scalar arising from a hidden sector U(1) gauge theory. A synchronous evolution of the hidden and visible sector temperatures is carried out from the reheat temperature down to the electroweak scale. The hydrodynamics of two-field phase transitions, one for the visible and the other for the hidden is discussed, which leads to separate tunneling temperatures and different sound speeds for the two sectors. Gravitational waves emerging from the two sectors are computed and their imprint on the measured gravitational wave power spectrum vs frequency is analyzed in terms of bubble nucleation signature, i.e., detonation, deflagration, and hybrid. It is shown that the two-field model predicts gravitational waves accessible at several proposed gravitational wave detectors: LISA, DECIGO, BBO, and Taiji, and their discovery would probe specific regions of the hidden sector parameter space and may also shed light on the nature of bubble nucleation in the early Universe. The analysis presented here indicates that the cosmologically preferred models are those where the tunneling in the visible sector precedes the tunneling in the hidden sector and the sound speed cs lies below its maximum, i.e., cs2<13. It is of interest to investigate if these features are universal and applicable to a wider class of cosmologically consistent models. Published by the American Physical Society 2024

Signature of nonminimal scalar-gravity coupling with an early matter domination on the power spectrum of gravitational waves

The signal strength of primordial gravitational waves experiencing an epoch of early scalar domination, due to an oscillating scalar field, is reduced with respect to radiation domination. In this paper, we demonstrate that the specific pattern of this reduction is sensitive to the coupling between the dominant field and gravity. When this coupling is zero, the impact of early-matter domination on gravitational waves is solely attributed to the alteration of the Hubble parameter and the scale factor. In the presence of nonzero couplings, on the other hand, the evolution of primordial gravitational waves is directly affected as well, resulting in a distinct steplike feature in the power spectrum of the gravitational wave as a function of frequency. This feature serves as a smoking gun signature of this model. Although the aforementioned results are obtained numerically, we also provide an analytical expression of the power spectrum to illustrate its dependence on the model parameters and initial conditions. Furthermore, we provide analytical relations that specify the frequency interval in which the step occurs. We compare the analytical estimates with numerical analysis and show they match well. Published by the American Physical Society 2024

A-B Transition in Superfluid 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He and Cosmological Phase Transitions

First-order phase transitions in the very early universe are a prediction of many extensions of the Standard Model of particle physics and could provide the departure from equilibrium needed for a dynamical explanation of the baryon asymmetry of the Universe. They could also produce gravitational waves of a frequency observable by future space-based detectors such as the Laser Interferometer Space Antenna. All calculations of the gravitational wave power spectrum rely on a relativistic version of the classical nucleation theory of Cahn-Hilliard and Langer, due to Coleman and Linde. The high purity and precise control of pressure and temperature achievable in the laboratory made the first-order A to B transition of superfluid 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He ideal for test of classical nucleation theory. As Leggett and others have noted, the theory fails dramatically. The lifetime of the metastable A phase is measurable, typically of order minutes to hours, far faster than classical nucleation theory predicts. If the nucleation of B phase from the supercooled A phase is due to a new, rapid intrinsic mechanism that would have implications for first-order cosmological phase transitions as well as predictions for gravitational wave production in the early universe. Here we discuss studies of the A-B phase transition dynamics in 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He, both experimental and theoretical, and show how the computational technology for cosmological phase transition can be used to simulate the dynamics of the A-B transition, support the experimental investigations of the A-B transition in the QUEST-DMC collaboration with the goal of identifying and quantifying the mechanism(s) responsible for nucleation of stable phases in ultra-pure metastable quantum phases.

Primordial non-Gaussianity f NL and anisotropies in scalar-induced gravitational waves

Primordial non-Gaussianity encodes vital information of the physics of the early universe, particularly during the inflationary epoch. To explore the local-type primordial non-Gaussianity f NL, we study the anisotropies in gravitational wave background induced by the linear cosmological scalar perturbations during radiation domination in the early universe. We provide the first complete analysis to the angular power spectrum of such scalar-induced gravitational waves. The spectrum is expressed in terms of the initial inhomogeneities, the Sachs-Wolfe effect, and their crossing. It is anticipated to have frequency dependence and multipole dependence, i.e., Cℓ (ν) ∝ [ℓ(ℓ+1)]-1 with ν being a frequency and ℓ referring to the ℓ-th spherical harmonic multipole. In particular, the initial inhomogeneites in this background depend on gravitational-wave frequency. These properties are potentially useful for the component separation, foreground removal, and breaking degeneracies in model parameters, making the non-Gaussian parameter f NL measurable. Further, theoretical expectations may be tested by space-borne gravitational-wave detectors in future.

Role of spatial curvature in the primordial gravitational wave power spectrum

Role of spatial curvature in the primordial gravitational wave power spectrum

Bubble nucleation and gravitational waves from holography in the probe approximation

We investigate the bounce solution in the holographic dark-QCD and electroweak models with first-order phase transition. The strength parameter α, inverse duration time β/H and bubble wall velocity vw in the gravitational wave power spectra are calculated by holographic bounce solution. We find the parameter α is about \U0001d4aa(1) and β/H is about 104, which implies that the phase transition is fast and strong. The critical temperature, nucleation temperature and the temperature at the beginning time of the phase transition are close to each other in the holographic model. In addition, the velocity vw is found to be less than the sound speed of the plasma {c}_s=1/sqrt{3} , which corresponds to the deflagration scenario. The gravitational wave signal from phase transitions is difficult to detect since the factor ϒ suppresses the gravitational wave power spectrum. The GW signal can be detected only when the model is in the period of electroweak phase transition and with suitable parameters. Moreover, the primordial black hole is not favorable for formation due to the large parameter β/H and small velocity vw.

The effect of non-minimally coupled scalar field on gravitational waves from first-order vacuum phase transitions

We investigate first-order vacuum phase transitions in the presence of a non-minimally coupled scalar field starting with the coupling effect on the initial dynamics of phase transitions by defining an effective potential for the scalar field and then performing three dimensional numerical simulations to observe any possible distinction in gravitational wave power spectrum. Although we give a description of the model with the expanding background, in this particular paper, we exclude the scale factor contribution since we primarily focus on the immediate impact of the non-minimal coupling at initial phases of the transition. Even in this case we found that this modification has discernible effect on the power spectrum of the gravitational wave energy density.

A peak in the power spectrum of primordial gravitational waves induced by primordial dark magnetic fields

Dark gauge fields have been discussed as candidates for dark matter recently. If they existed, primordial dark magnetic fields during inflation would have existed. It is believed that primordial gravitational waves (PGWs) arise out of quantum fluctuations during inflation. We study the graviton-dark photon conversion process in the presence of background primordial dark magnetic fields and find that the process induces the tachyonic instability of the PGWs. As a consequence, a peak appears in the power spectrum of PGWs. It turns out that the peak height depends on the direction of observation. The peak frequency could be in the range from 10-5 to 103 Hertz for GUT scale inflation. Hence, the observation of PGWs could provide a new window for probing primordial dark magnetic fields.

Reconstructing physical parameters from template gravitational wave spectra at LISA: first order phase transitions

A gravitational wave background from a first order phase transition in the early universe may be observable at millihertz gravitational wave (GW) detectors such as the Laser Interferometer Space Antenna (LISA). In this paper we introduce and test a method for investigating LISA's sensitivity to gravitational waves from a first order phase transition using parametrised templates as an approximation to a more complete physical model. The motivation for developing the method is to provide a less computationally intensive way to perform Markov Chain Monte Carlo (MCMC) inference on the thermodynamic parameters of a first order phase transition, or on generally computationally intensive models. Starting from a map between the physical parameters and the parameters of an empirical template, we first construct a prior on the empirical parameters that contains the necessary information about the physical parameters; we then use the inverse mapping to reconstruct approximate posteriors on the physical parameters from a fast MCMC on the empirical template. We test the method on a double broken power law approximation to spectra in the sound shell model. The reconstruction method substantially reduces the proposal evaluation time, and despite requiring some precomputing of the mapping, this method is still cost-effective overall. In two test cases, with signal-to-noise ∼ 40, the method recovers the physical parameters and the spectrum of the injected gravitational wave power spectrum to 95% confidence. In previous Fisher matrix analysis we found the phase boundary speed v w was expected to be the best constrained of the thermodynamic parameters. In this work, for an injected phase transition GW power spectrum with v w = 0.55, with a direct sample on the thermodynamic parameters we recover 0.630+0.17 -0.059 and for our reconstructed sample 0.646+0.098 -0.075.

Probing parity-odd bispectra with anisotropies of GW V modes

It is well known that non-trivial squeezed tensor bispectra can lead to anisotropies in the inflationary stochastic gravitational wave (GW) background, providing us with an alternative and complementary window to primordial non-Gaussianities (NGs) with respect to the CMB. Previous works have highlighted the detection prospects of parity-even tensor NGs via the GW I-mode anisotropies. In this work we extend this by analysing for the first time the additional information carried by GW V-mode anisotropies due to squeezed NGs. We show that GW V modes allow us to probe parity-odd squeezed 〈 tts 〉 and 〈 ttt 〉 bispectra. These bispectra break parity at the non-linear level and can be introduced by allowing alternative symmetry breaking patterns during inflation, like those comprised in solid inflation. Considering a BBO-like experiment, we find that a non-zero detection of squeezed 〈 tts 〉 parity-odd bispectra in the V modes dipole is possible without requiring any short-scale enhancement of the GW power spectrum amplitude over the constraints set by the CMB. We also briefly discuss the role of V-CMB cross-correlations. Our work can be extended in several directions and motivates a systematic search for polarized GW anisotropies in the next generations of GW experiments.

Droplet collapse during strongly supercooled transitions

We simulate the decay of isolated, spherically symmetric droplets in a cosmological phase transition. It has long been posited that such heated droplets of the metastable state could form, and they have recently been observed in 3D multi-bubble simulations. In those simulations, the droplets were associated with a reduction in the wall velocity and a decrease in the kinetic energy of the fluid, with a consequent suppression in the gravitational wave power spectrum. In the present work, we track the wall speed and kinetic energy production in isolated droplets and compare them to those found in multi-bubble collisions. The late-time wall velocities that we observe match those of the 3D simulations, though we find that the spherical simulations are a poor predictor of the kinetic energy production. This implies that spherically symmetric simulations could be used to refine baryogenesis predictions due to the formation of droplets, but not to estimate any accompanying suppression of the gravitational wave signal.

Quantum gravitational signatures in next-generation gravitational wave detectors

A recent study established a correspondence between the Generalized Uncertainty Principle (GUP) and Modified theories of gravity, particularly Stelle gravity. We investigate the consequences of this correspondence for inflation and cosmological observables by evaluating the power spectrum of the scalar and tensor perturbations using two distinct methods. First, we employ PLANCK observations to determine the GUP parameter $\gamma_0$. Then, we use the value of $\gamma_0$ to investigate the implications of quantum gravity on the power spectrum of primordial gravitational waves and their possible detectability in the next-generation detectors, like Einstein Telescope and Cosmic explorer.

Decay of acoustic turbulence in two dimensions and implications for cosmological gravitational waves

Gravitational waves from a phase transition associated with the generation of the masses of elementary particles are within the reach of future space-based detectors such as LISA. A key determinant of the resulting power spectrum, not previously studied, is the lifetime of the acoustic turbulence which follows. We study decaying acoustic turbulence using numerical simulations of a relativistic fluid in two dimensions. Working in the limit of non-relativistic bulk velocities, with an ultra-relativistic equation of state, we find that the energy spectrum evolves towards a self-similar broken power law, with a high-wavenumber behaviour of $k^{-2.08 \pm 0.08}$, cut off at very high $k$ by the inverse width of the shock waves. Our model for the decay of acoustic turbulence can be extended to three dimensions using the universality of the high-$k$ power law and the evolution laws for the kinetic energy and the integral length scale. It is used to build an estimate for the gravitational wave power spectrum resulting from a collection of shock waves, as might be found in the aftermath of a strong first order phase transition in the early universe. The power spectrum has a peak wavenumber set by the initial length scale of the acoustic waves, and a new secondary scale at a lower wavenumber set by the integral scale after a Hubble time. Between these scales a distinctive new power law appears. Our results allow more accurate predictions of the gravitational wave power spectrum for a wide range of early universe phase transition scenarios.

Thermal suppression of bubble nucleation at first-order phase transitions in the early Universe

One of the key observables in a gravitational wave power spectrum from a first order phase transition in the early Universe is the mean bubble spacing, which depends on the rate of nucleation of bubbles of the stable phase, as well as the bubble wall speed. When the bubbles expand as deflagrations, it is expected that the heating of the fluid in front of the phase boundary suppresses the nucleation rate. We quantify the effect, showing that it increases the mean bubble separation, and acts to enhance the gravitational wave signal by a factor of up to order 10. The effect is largest for small wall speeds and strong transitions.