Energy Spectrum Of Gravitational Waves Research Articles

A single-bubble source for gravitational waves in a cosmological phase transition

Abstract We show that quantum fluctuations of an expanding phase transition bubble give rise to gravitational wave (GW) emission, even when considering a single bubble, without bubble collisions or plasma effects. The ratio of GW energy to the total bubble energy reservoir increases with time as ∝ t. If the bubble expands for long enough before percolation destroys it, back-reaction due to the GW emission becomes important after t br ~ (16π5)m pl 2 R 0 3, where R 0 is the bubble nucleation radius and m pl is the reduced Planck mass. As seen by experiments today, the GW energy spectrum would appear blue. However, simple estimates suggest that the signal falls short of detection by even ambitious future experiments.

Gravitational wave production after inflation for a hybrid inflationary model

We discuss a cosmological scenario with a stochastic background of gravitational waves sourced by the tensor perturbation due to a hybrid inflationary model with cubic potential. The tensor-to-scalar ratio for the present hybrid inflationary model is obtained as [Formula: see text]. Gravitational wave spectrum of this stochastic background, for large-scale CMB modes, [Formula: see text] to [Formula: see text] is studied. The present-day energy spectrum of gravitational waves [Formula: see text] is sensitively related to the tensor power spectrum and r which is, in turn, dependent on the unknown physics of the early cosmos. This uncertainty is characterized by two parameters: [Formula: see text] logarithmic average over the primordial tensor spectral index and [Formula: see text] logarithmic average over the effective equation-of-state parameter. Thus, exact constraints in the [Formula: see text]-[Formula: see text] plane can be obtained by comparing theoretical constraints of our model on r and [Formula: see text]. We obtain a limit on [Formula: see text] around the modes probed by CMB scales.

Constraining the gravitational-wave spectrum from cosmological first-order phase transitions using data from LIGO-Virgo first three observing runs

We search for a first-order phase transition (PT) gravitational wave (GW) signal from Advanced LIGO and Advanced Virgo's first three observing runs. Due to the large theoretical uncertainties, four shapes of GW energy spectral from bubble and sound wave collisions widely adopted in literature are investigated, separately. Our results indicate that there is no evidence for the existence of such GW signals, and therefore we give the upper limits on the amplitude of GW energy spectrum Ωpt(f *) in the peak frequency range of f * ∈ [5,500] Hz for these four theoretical models, separately. We find that Ωpt(f * ≃ 40 Hz) < 1.3 × 10-8 at 95% credible level, and roughly H */β ≲ 0.1 and α ≲ 1 at 68% credible level in the peak frequency range of 20 ≲ f * ≲ 100 Hz corresponding to the mostsensitive frequency band of Advanced LIGO and Advanced Virgo's first three observing runs, where H * is the Hubble parameter when PT happens, β is the bubble nucleation rate and α is the normalized latent heat.

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.

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).

Effects of the axion through the Higgs portal on primordial gravitational waves during the electroweak breaking

We investigate the effects of short axion kination eras on the energy spectrum of the primordial gravitational waves corresponding to modes that reenter the Hubble horizon at the postelectroweak symmetry breaking epoch well within the radiation domination era. Our main assumption is the existence of an extremely weakly coupled hidden sector between the Higgs and the axion, materialized by higher order nonrenormalizable dimension six and dimension eight operators, active at a scale $M$ of the order 20--100 TeV. This new physics scale $M$, which is way higher than the electroweak scale, is motivated by the lack of new particle observations in the large hadron collider to date beyond the electroweak scale. Once the electroweak symmetry breaking occurs at $T\ensuremath{\sim}100\text{ }\text{ }\mathrm{GeV}$, the axion potential acquires a new minimum due to the new terms generated by the electroweak breaking, and the axion oscillations at the origin are destabilized. In effect after some considerable amount of time, the axion rolls swiftly to its new minimum, experiencing a short kination epoch, where its energy density redshifts as ${\ensuremath{\rho}}_{a}\ensuremath{\sim}{a}^{\ensuremath{-}6}$. After it reaches the new minimum, since the latter is energetically less favorable that the Higgs minimum, it decays to the Higgs minimum and the Universe is described again by the Higgs minimum. The axion returns to the origin and commences again oscillations initiated by quantum fluctuations, redshifts as dark matter, and the same procedure is repeated perpetually. These short axion kination eras may disturb the background total equation of state parameter during the radiation domination era, changing it from that of radiation $w=1/3$ to some value closer to the kination value $w=1$. We examined the effect of a value $w=1/2$ on the energy density of the primordial gravitational waves. As we show, the energy spectrum of the gravitational waves mainly depends on how many times the short axion kination epochs occur, on the inflationary theory, on the actual value of the background equation of state parameter during the short kination eras, and finally on the reheating temperature. Our findings indicate a characteristic shape in the energy spectrum that can be observed in future gravitational wave experiments. We however disregarded the contribution of the electroweak phase transition on the gravitational waves for simplicity and transparency of our results.

Gravitational waves from bubble collisions in FLRW spacetime

Stochastic gravitational wave background (SGWB) is a promising tool to probe the very early universe where the standard model of particle physics and cosmology are connected closely. As a possible component of SGWB, gravitational waves (GW) from bubble collisions during the first order cosmological phase transitions deserve comprehensive analyses. In 2017, Ryusuke Jinno and Masahiro Takimoto proposed an elegant analysis approach to derive the analytical expressions of energy spectra of GW from bubble collisions in Minkowski spacetime avoiding large-scale numerical simulations for the first time [26]. However, they neglect the expansion of the universe and regard the duration of phase transitions as infinity in their derivation which could deviate their estimations from true values. For these two reasons, we give a new expression of GW spectra by adopting their method, switching spacetime background to FLRW spacetime, and considering a finite duration of phase transitions. By denoting σ as the fraction of the speed of phase transitions to the expansion speed of the universe, we find when σ is around mathcal{O} (10), the maxima of estimated GW energy spectra drop by around 1 order of magnitude than the results given by their previous work. Even when σ = 100, the maximum of GW energy spectrum is only 65% of their previous estimation. Such a significant decrease may bring about new challenges for the detectability of GW from bubble collisions. Luckily, by comparing new spectra with PLI (power-law integrated) sensitivity curves of GW detectors, we find that the detection prospect for GW from bubble collisions is still promising for DECIGO, BBO, LISA, and TianQin in the foreseeable future.

Resonance instability of primordial gravitational waves during inflation in Chern\u2013Simons gravity

We investigate axion inflation where the gravitational Chern–Simons term is coupled to a periodic function of the inflaton. We find that tensor perturbations with different polarizations are amplified in different ways by the Chern–Simons coupling. Depending on the model parameters, the resonance amplification results in a parity-violating peak or a board plateau in the energy spectrum of gravitational waves, and the sharp cutoff in the infrared region constitutes a characteristic distinguishable from stochastic gravitational wave backgrounds produced by matter fields in Einstein gravity.

Sound Speed Resonance of the Stochastic Gravitational-Wave Background.

We propose a novel mechanism to test time variation of the propagation speed of gravitational waves (GWs) in light of GWs astronomy. As the stochastic GWs experience the whole history of cosmic expansion, they encode potential observational evidence of such variation. We report that, one feature of a varying GWs speed is that the energy spectrum of GWs will present resonantly enhanced peaks if the GWs speed oscillates in time at high-energy scales. Such oscillatory behavior arises in a wide class of modified gravity theories. The amplitude of these peaks can be at reach by current and forthcoming GWs instruments, hence making the underlying theories falsifiable. This mechanism reveals that probing the variation of GWs speed can be a promising way to search for new physics beyond general relativity.

Analytical approximation of the scalar spectrum in the ultraslow-roll inflationary models

The ultra-slow-roll (USR) inflationary models predict large-amplitude scalar perturbations at small scales which can lead to the primordial black hole production and scalar-induced gravitational waves. In general scalar perturbations in the USR models can only be obtained using numerical method because the usual slow-roll approximation breaks. In this work, we propose an analytical approach to estimate the scalar spectrum which is consistent with the numerical result. We find that the USR inflationary models predict a peak with power-law slopes in the scalar spectrum and energy spectrum of gravitational waves, and we derive the expression of the spectral indexes in terms of the inflationary potential. In turn, the inflationary potential near the USR regime can be reconstructed from the negative spectral index of the gravitational wave energy spectrum.

Constraints on the reheating parameters after Gauss-Bonnet inflation from primordial gravitational waves

We study the effects of the Gauss-Bonnet term on the energy spectrum of inflationary gravitational waves. The models of inflation are classified into two types based on their predictions for the tensor power spectrum: red-tilted ($n_T<0$) and blue-tilted spectra ($n_T>0$), respectively, and then the energy spectra of the gravitational waves are calculated for each type of model. We find that the gravitational wave spectra are enhanced depending on the model parameter if the predicted inflationary tensor spectra have a blue tilt, whereas they are suppressed for the spectra that have a red tilt. Moreover, we perform the analyses on the reheating parameters involving the temperature, the equation-of-state parameter, and the number of $e$-folds using the gravitational wave spectrum. Our results imply that the Gauss-Bonnet term plays an important role not only during inflation but also during reheating whether the process is instantaneous or lasts for a certain number of $e$-folds until it thermalizes and eventually completes.

Domain walls in the extensions of the Standard Model

Our main interest is the evolution of domain walls of the Higgs field in the early Universe. The aim of this paper is to understand how dynamics of Higgs domain walls could be influenced by yet unknown interactions from beyond the Standard Model. We assume that the Standard Model is valid up to certain, high, energy scale Λ and use the framework of the effective field theory to describe physics below that scale. Performing numerical simulations with different values of the scale Λ we are able to extend our previous analysis [1]. Our recent numerical simulations show that evolution of Higgs domain walls is rather insensitive to interactions beyond the Standard Model as long as masses of new particles are grater than 1012 GeV. For lower values of Λ the RG improved effective potential is strongly modified at field strengths crucial to the evolution of domain walls. However, we find that even for low values of Λ, Higgs domain walls decayed shortly after their formation for generic initial conditions. On the other hand, in simulations with specifically chosen initial conditions Higgs domain walls can live longer and enter the scaling regime. We also determine the energy spectrum of gravitational waves produced by decaying domain walls of the Higgs field. For generic initial field configurations the amplitude of the signal is too small to be observed in planned detectors.

Gravitational Waves from Oscillons with Cuspy Potentials.

We study the production of gravitational waves during oscillations of the inflaton around the minimum of a cuspy potential after inflation. We find that a cusp in the potential can trigger copious oscillon formation, which sources a characteristic energy spectrum of gravitational waves with double peaks. The discovery of such a double-peak spectrum could test the underlying inflationary physics.

Primordial gravitational waves from the space-condensate inflation model

We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for the full frequency range with the assumption that the phase transition between two consecutive regimes is abrupt during the evolution of the Universe. The suppression of the energy spectrum is found in our model for the decreasing frequency of gravitational waves depending on the model parameter. To realize the suppression of the energy spectrum of the primordial gravitational waves, we study the existence of the early phase transition during inflation for the space-condensate inflation model.

Suppression of the Primordial Gravitational Waves

We study the primordial gravitational waves induced by space-space condensate inflation model. For modes that cross the comoving horizon during matter dominated era, we calculate the energy spectrum of gravitational waves. The energy spectrum of gravitational waves for our model has significantly suppressed in the low frequency range. The suppression occurs due to the phase transition during the early evolution of the Universe and depends on model parameter.

Energy spectrum of gravitational waves in a loop quantum cosmological model

We explore the consequences of loop quantum cosmology (inverse-volume corrections) in the spectrum of the gravitational waves using the method of the Bogoliubov coefficients. These corrections are taken into account at the background level of the theory as well as at the first order in the perturbations theory framework. We show that these corrections lead to an intense graviton production during the loop super-inflationary phase prior to the standard slow-roll era, which leave their imprints through new features on the energy spectrum of the gravitational waves as would be measured today, including a new maximum on the low frequency end of the spectrum.

Gravitational wave energy spectrum of a parabolic encounter

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (~10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ~10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of rp > 20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by LISA.

Parametric resonance and cosmological gravitational waves

We investigate the production of gravitational waves due to quantum fluctuations of the vacuum during the transition from the inflationary to the radiation-dominated eras of the universe, assuming this transition to be dominated by the phenomenon of parametric resonance. The energy spectrum of the gravitational waves is calculated using the method of continuous Bogoliubov coefficients, which avoids the problem of overproduction of gravitons at large frequencies. We found, on the sole basis of the mechanism of quantum fluctuations, that the resonance field leaves no explicit and distinctive imprint on the gravitational-wave energy spectrum, apart from an overall upward or downward translation. Therefore, the main features in the spectrum are due to the inflaton field, which leaves a characteristic imprint at frequencies of the order of MHz/GHz.

Gravitational Waves from Relativistic Neutron-Star Mergers with Microphysical Equations of State

The gravitational wave (GW) emission from a set of relativistic neutron-star (NS) merger simulations is analyzed and characteristic signal features are identified. The distinct peak in the GW energy spectrum that is associated with the formation of a hypermassive merger remnant has a frequency that depends strongly on the properties of the nuclear equation of state (EOS) and on the total mass of the binary system, whereas the mass ratio and the NS spins have a weak influence. If the total mass can be determined from the inspiral chirp signal, the peak frequency of the post-merger signal is a sensitive indicator of the EOS.

Confusion noise from LISA capture sources

Captures of compact objects (COs) by massive black holes (MBHs) in galactic nuclei will be an important source for LISA, the space-based gravitational-wave (GW) detector. However, a large fraction of captures will not be individually resolvable--either because they are too distant, have unfavorable orientation, or have too many years to go before final plunge--and so will constitute a source of ``confusion noise,'' obscuring other types of sources. Here we estimate the shape and overall magnitude of the spectrum of confusion noise from CO captures. The overall magnitude depends on the capture rates, which are rather uncertain, so we present results for a plausible range of rates. We show that the impact of capture confusion noise on the total LISA noise curve ranges from insignificant to modest, depending on these rates. Capture rates at the high end of estimated ranges would raise LISA's overall (effective) noise level by at most a factor \sim 2. While this slightly elevated noise level would somewhat decrease LISA's sensitivity to other classes of sources, overall, this would be a pleasant problem for LISA to have: It would also imply that detection rates for CO captures were at nearly their maximum possible levels (given LISA's baseline design). This paper includes several other results that should be useful in further studies of LISA capture sources, including (i) a calculation of the total GW energy output from generic inspirals into Kerr MBHs, and (ii) an approximate GW energy spectrum for a typical capture.