Energy Density Of Gravitational Waves Research Articles

Induced gravitational waves and baryon asymmetry fluctuations from primordial black hole formation

We consider black hole formation due to the gravitational collapse produced by large density fluctuations during an epoch of reheating with a stiff equation of state and calculate the induced gravitational wave spectrum. By considering the existing bounds on the total energy density of gravitational waves today, we find constraints on the parameter space of this scenario. We also calculate the lepton asymmetry generated by metric perturbations via the chiral gravitational anomaly present in the Standard Model and find that, once the electroweak sphaleron processes have taken place, the large spectrum of scalar perturbations responsible for black hole formation induces a peak in the baryon asymmetry fluctuations on small scales.

Gravitational Waves and gravitino mass in No-Scale Supergravity inflation with Polonyi term

We study a No-Scale supergravity inflation model which has a non-minimal deformation of the Kähler potential and a Wess-Zumino superpotential extended by the inclusion of a Polonyi mass term. The non-minimal structure of the Kähler potential is responsible for an inflexion point that can lead to the production of gravitational waves at late stages of inflation, while the Polonyi term breaks supersymmetry at the end of inflation, generating a non-vanishing gravitino mass. After a thorough parameter space scan, we identify promising points for gravitational wave production. We then study the resulting gravitational wave energy density for this set of points, and we observe that the gravitational waves should be observable in the next generation of both space-based and ground-based interferometers. Finally, we show how the presence of the Polonyi term can be used to further boost the gravitational wave energy density, which is correlated with the gravitino mass. The code used for the scan and the numerical analysis is provided at https://gitlab.com/miguel.romao/gw-and-m32-no-scale-inflation-polonyi.

Dark Energy from Cosmological Energy Conservation

The value of the gravitational wave energy density is unknown. Current progress in gravitational wave detection suggests that the energy density of the stochastic gravitational wave background (SGWB) will be estimated in the next decades. A derivation of its value is presented under the assumption that energy lost due to cosmic redshift is fully responsible for the energy gained by the cosmological constant in the expanding universe. This unknown nonlocal mechanism of energy conservation on the cosmic scale could explain dark energy and hint at a property of a theory of quantum gravity.

Primordial gravitational waves in generalized Palatini gravity

Extended Palatini gravity is the metric-affine gravity theory characterized by zero torsion, nonzero metricity and a quadratic of the antisymmetric Ricci curvature. It reduces dynamically to general relativity plus a geometric Proca field. In this work, we study imprints of the geometric Proca field on the gravitational waves. Our results show that the geometric Proca leaves significant signatures in the gravitational wave signal, and gravitational wave energy density could be large enough to be detectable by the next upgrade of the existing GW detectors. Our results, if confirmed observationally, will be an indication that the gravity could be non-Riemannian in nature.

Modified propagation of gravitational waves from the early radiation era

We study the propagation of cosmological gravitational wave (GW) backgrounds from the early radiation era until the present day in modified theories of gravity. Comparing to general relativity (GR), we study the effects that modified gravity parameters, such as the GW friction α M and the tensor speed excess α T, have on the present-day GW spectrum. We use both the WKB estimate, which provides an analytical description but fails at superhorizon scales, and numerical simulations that allow us to go beyond the WKB approximation. We show that a constant α T makes relatively insignificant changes to the GR solution, especially taking into account the constraints on its value from GW observations by the LIGO-Virgo collaboration, while α M can introduce modifications to the spectral slopes of the GW energy spectrum in the low-frequency regime depending on the considered time evolution of α M. The latter effect is additional to the damping or growth occurring equally at all scales that can be predicted by the WKB approximation. In light of the recent observations by pulsar timing array (PTA) collaborations, and the potential observations by future detectors such as SKA, LISA, DECIGO, BBO, or ET, we show that, in most of the cases, constraints cannot be placed on the effects of α M and the initial GW energy density ℰ* GW separately, but only on the combined effects of the two, unless the signal is observed at different frequency ranges. In particular, we provide some constraints on the combined effects from the reported PTA observations.

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.

Gravitational wave from graviton Bremsstrahlung during reheating

We revisit graviton production via Bremsstrahlung from the decay of the inflaton during inflationary reheating. Using two complementary computational techniques, we first show that such 3-body differential decay rates differ from previously reported results in the literature. We then compute the stochastic gravitational wave (GW) background that forms during the period of reheating, when the inflaton perturbatively decays with the radiative emission of gravitons. By computing the number of relativistic degrees of freedom in terms of Δ N eff, we constrain the resulting GW energy density from BBN and CMB. Finally, we project current and future GW detector sensitivities in probing such a stochastic GW background, which typically peaks in the GHz to THz ballpark, opening up the opportunity to be detected with microwave cavities and space-based GW detectors.

Search for stochastic gravitational-wave background from string cosmology with Advanced LIGO and Virgo's O1∼O3 data

String cosmology models predict a relic background of gravitational-wave (GW) radiation in the early universe. The GW energy spectrum of radiated power increases rapidly with the frequency, and therefore it becomes a potential and meaningful observation object for high-frequency GW detector. We focus on the stochastic background generated by superinflation in string theory and search for such signal in the observing data of Advanced LIGO and Virgo O1∼O3 runs in a Bayesian framework. We do not find the existence of the signal, and thus put constraints on the GW energy density. Our results indicate that at f = 100 Hz, the fractional energy density of GW background is less than 1.7 × 1-8 and 2.1 × 10-8 for dilaton-string and dilaton only cases respectively, and further rule out the parameter space restricted by the model itself due to the non-decreasing dilaton and stable cosmology background (β bound).

Towards a reliable calculation of relic radiation from primordial gravitational waves

ABSTRACT Inflationary gravitational waves, behaving as additional radiation in the Early Universe, can increase the effective number of relativistic species (Neff) by a further correction that depends on the integrated energy-density in gravitational waves over all scales. This effect is typically used to constrain (blue-tilted) models of inflation in light of the bounds resulting from the big bang nucleosynthesis. In this paper, we recompute this contribution, discussing some caveats of the state-of-the-art analyses. Through a parametric investigation, we first demonstrate that the calculation is dominated by the ultraviolet frequencies of the integral and therefore by the behaviour of the tensor spectrum on scales corresponding to modes that cross the horizon very close to the end of inflation, when the slow-roll dynamics breaks down and the production of gravitational waves becomes strongly model dependent. Motivated by these results, we realize a theoretical Monte Carlo and, working within the framework of the Effective Field Theory of inflation, we investigate the observable predictions of a very broad class of models. For each model, we solve a system of coupled differential equations whose solution completely specifies the evolution of the spectrum up to the end of inflation. We prove the calculation of $\Delta N_{\rm eff}^{\rm GW}$ to be remarkably model dependent and therefore conclude that accurate analyses are needed to infer reliable information on the inflationary Universe.

Implications for cosmic domain walls from the first three observing runs of LIGO-Virgo

We put constraints on the normalized energy density in gravitational waves from cosmic domain walls by searching for the stochastic gravitational-wave background in the data of Advanced LIGO and Virgo's first three observing runs. By adopting a phenomenological broken power-law model, we obtain the upper limit on the amplitude of stochastic gravitational-wave background generated by domain walls in the peak frequency band 10--200 Hz and get the most stringent limitation ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{DW}}({f}_{*}=35\text{ }\text{ }\mathrm{Hz})<1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ at 95% confidence level at the peak frequency ${f}_{*}=35\text{ }\text{ }\mathrm{Hz}$. Subsequently, we work out the constraints on the parameter space in the appealing realization of DW structure---the heavy axion model which can avoid the so-called quality problem.

Study of entropy production due to electroweak phase transition in Z2 symmetric extension of the Standard Model

In this work, we consider the simple ${Z}_{2}$ symmetric extension to the Standard Model (SM) and proceed to study the nature of electroweak phase transition (EWPT) in the early Universe. We show that the nature of the phase transition changes from a smooth crossover in the SM to a strong first order with this addition of the real scalar. Furthermore, we show that the entropy release in this scenario is higher than that of the SM. This can lead to a strong dilution of the energy density of gravitational waves, as we show in the latter part of the paper.

Gravitational wave induced baryon acoustic oscillations

We study the impact of gravitational waves originating from a first order phase transition on structure formation. To do so, we perform a second order perturbation analysis in the 1+31+3 covariant framework and derive a wave equation in which second order, adiabatic density perturbations of the photon-baryon fluid are sourced by the gravitational wave energy density during radiation domination and on sub-horizon scales. The scale on which such waves affect the energy density perturbation spectrum is found to be proportional to the horizon size at the time of the phase transition times its inverse duration. Consequently, structure of the size of galaxies and bigger can only be affected in this way by relatively late phase transitions at \ge 10^{6}\,\text{s}≥106s. Using cosmic variance as a bound we derive limits on the strength \alphaα and the relative duration (\beta/H_*)^{-1}(β/H*)−1 of phase transitions as functions of the time of their occurrence which results in a new exclusion region for the energy density in gravitational waves today. We find that the cosmic variance bound forbids only relative long lasting phase transitions, e.g. \beta/H_*\lesssim 6.8β/H*≲6.8 for t_*\approx 5\times10^{11}\,\text{s}t*≈5×1011s, which exhibit a substantial amount of supercooling \alpha>20α>20 to affect the matter power spectrum.

Gravitational waves of the QCD phase transition in a 5D soft wall model with Gauss-Bonnet correction

In this paper, we study the gravitational wave energy density spectrum of cosmological de/confinement phase transition at finite baryon chemical potential within a soft wall model of AdS/QCD with Gauss-Bonnet correction. Focusing on the approach of dilaton/radion dominance approximation, we find the dual bounce action and the duration of the phase transition at the nucleation temperature. We also consider the possibility of a supercooling period during the transition, obtain the quantities characterizing the gravitational wave spectrum through this approach, and discuss the detectability prospect of generated gravitational wave signals by gravitational wave experiments.

Gravitational waves generation in turbulent hypermagnetic fields before the electroweak phase transition

We study the production of relic gravitational waves (GWs) in turbulent hypermagnetic fields (HMFs) in the symmetric phase of the early universe before the electroweak phase transition (EWPT). The noise of HMFs is modeled by the analog of the magnetic hydrodynamics turbulence. The evolution of HMFs is driven by the analogs of the chiral magnetic effect and the Adler anomalies in the presence of the nonzero asymmetries of leptons and Higgs bosons. We track the evolution of the energy density of GWs from 10 TeV down to EWPT and analyze its dependence on the parameters of the system. We also discuss the possibility to observe the predicted GW background by the current GW detectors.

Gravitational waves of a first-order QCD phase transition at finite coupling from holography

We consider a holographic study of coupling dependent gravitational waves produced by the cosmic first-order QCD phase transition at finite baryochemical potential. In the dual description, the first-order QCD phase transition corresponds to the first-order Hawking–Page phase transition in Gauss–Bonnet gravity. At intermediate coupling, we obtain key quantities characterizing the gravitational wave energy density spectrum. We then find that the gravitational waves might be detected for sufficiently large Gauss–Bonnet coupling. We also consider a supercooling scenario during the QCD phase transition and show that the gravitational waves generated during this period can be detected by various future gravitational wave experiments.

Did Goryachev et al. detect megahertz gravitational waves?

Goryachev et al. [1] recently announced the detection of "two strongly significant events" in their Bulk Acoustic Wave High Frequency Gravitational Wave Antenna. They claim many possibilities for the cause of these events, including high-frequency megahertz gravitational waves. We demonstrate these events are not due to gravitational waves for two reasons. 1) The inferred stochastic gravitational-wave background from these events implies the gravitational-wave energy density of the Universe is $\Omega_{\rm gw}\approx 10^8$, approximately $10^8$ times the closure density of the Universe. 2) The low-frequency gravitational-wave memory signal that accompanies any high-frequency gravitational-wave source visible by the current generation of high-frequency detectors would have been visible by LIGO/Virgo as a transient burst with signal-to-noise ratio $\gtrsim10^6$. The non-detection of such loud memory bursts throughout the operation of LIGO/Virgo rules out the gravitational-wave explanation for the high-frequency events detected by Goryachev et al. We discuss broader implications of this work for the ongoing experimental search for ultra high-frequency (MHz-GHz) gravitational waves.

Oscillations in the stochastic gravitational wave background from sharp features and particle production during inflation

We identify a characteristic pattern in the scalar-induced stochastic gravitational wave background from particle production during inflation.If particle production is sufficiently efficient, the scalar power spectrum exhibits \U0001d4aa(1) oscillations periodic in k, characteristic of a sharp feature, with an exponentially enhanced envelope. We systematically study the properties of the induced spectrum of gravitational waves sourced after inflation and find that this inherits the periodic structure in k, resulting in a peak in the gravitational wave energy density spectrum with \U0001d4aa(10 %) modulations. The frequency of the oscillation in the scalar power spectrum is determined by the scale of the feature during inflation and in turn sets the frequency of modulations in the gravitational wave signal. We present an explicit realisation of this phenomenon in the framework of multifield inflation, in the form of a strong sharp turn in the inflationary trajectory. The resulting stochastic background is potentially detectable in future gravitational wave observatories, and considerations of backreaction and perturbativity can be used to constrain the parameter space from the theoretical side. Our work motivates more extensive research linking primordial features to observable properties of the stochastic background of gravitational waves, and dedicated development in data analysis for their detection.

Implications for First-Order Cosmological Phase Transitions from the Third LIGO-Virgo Observing Run.

We place constraints on the normalized energy density in gravitational waves from first-order strong phase transitions using data from Advanced LIGO and Virgo's first, second, and third observing runs. First, adopting a broken power law model, we place 95%confidence level upper limits simultaneously on the gravitational-wave energy density at 25Hz from unresolved compact binary mergers, Ω_{CBC}<6.1×10^{-9}, and strong first-order phase transitions, Ω_{BPL}<4.4×10^{-9}. The inclusion of the former is necessary since we expect this astrophysical signal to be the foreground of any detected spectrum. We then consider two more complex phenomenological models, limiting at 25Hz the gravitational-wave background due to bubble collisions to Ω_{pt}<5.0×10^{-9} and the background due to sound waves to Ω_{pt}<5.8×10^{-9} at 95%confidence level for phase transitions occurring at temperatures above 10^{8} GeV.

Potential of Radio Telescopes as High-Frequency Gravitational Wave Detectors.

In the presence of magnetic fields, gravitational waves are converted into photons and vice versa. We demonstrate that this conversion leads to a distortion of the cosmic microwave background (CMB), which can serve as a detector for MHz to GHz gravitational wave sources active before reionization. The measurements of the radio telescope EDGES can be cast as a bound on the gravitational wave amplitude, h_{c}<10^{-21}(10^{-12}) at 78MHz, for the strongest (weakest) cosmic magnetic fields allowed by current astrophysical and cosmological constraints. Similarly, the results of ARCADE 2 imply h_{c}<10^{-24}(10^{-14}) at 3-30GHz. For the strongest magnetic fields, these constraints exceed current laboratory constraints by about 7 orders of magnitude. Future advances in 21cm astronomy may conceivably push these bounds below the sensitivity of cosmological constraints on the total energy density of gravitational waves.

Constraints on primordial gravitational waves from the cosmic microwave background

Searches for primordial gravitational waves have resulted in constraints in a large frequency range from a variety of sources. The standard Cosmic Microwave Background (CMB) technique is to parameterise the tensor power spectrum in terms of the tensor-to-scalar ratio, r, and spectral index, nt, and constrain these using measurements of the temperature and polarization power spectra. Another method, applicable to modes well inside the cosmological horizon at recombination, uses the shortwave approximation, under which gravitational waves behave as an effective neutrino species. In this paper we give model-independent CMB constraints on the energy density of gravitational waves, Ωgw h2, for the entire range of observable frequencies. On large scales, f ≲ 10−16 Hz, we reconstruct the initial tensor power spectrum in logarithmic frequency bins, finding maximal sensitivity for scales close to the horizon size at recombination. On small scales, f ≳10−15 Hz, we use the shortwave approximation, finding Ωgw h2 < 1.7 ×10−6 for adiabatic initial conditions and Ωgw h2 < 2.9 ×10−7 for homogeneous initial conditions (both 2σ upper limits). For scales close to the horizon size at recombination, we use second-order perturbation theory to calculate the back-reaction from gravitational waves, finding Ωgw h2 < 8.4 ×10−7, in the absence of neutrino anisotropic stress and Ωgw h2 < 8.6 ×10−7 when including neutrino anisotropic stress. These constraints are valid for 10−15 Hz ≳ f ≳ 3 × 10−16 Hz.