Stochastic Gravitational Wave Background Signal Research Articles

Phases of Pseudo-Nambu-Goldstone bosons

We study the vacuum dynamics of pseudo-Nambu-Goldstone bosons (pNGBs) for SO(N + 1) → SO(N) spontaneous and explicit symmetry breaking. We determine the magnitude of explicit symmetry breaking consistent with an EFT description of the effective potential at zero and finite temperatures. We expose and clarify novel additional vacuum transitions that can arise for generic pNGBs below the initial scale of SO(N + 1) → SO(N) spontaneous symmetry breaking, which may have phenomenological relevance. In this respect, two phenomenological scenarios are analyzed: thermal and supercooled dark sector pNGBs. In the thermal scenario the vacuum transition is first-order but very weak. For a supercooled dark sector we find that, depending on the sign of the explicit symmetry breaking, one can have a symmetry-restoring vacuum transition SO(N – 1) → SO(N) which can be strongly first-order, with a detectable stochastic gravitational wave background signal.

Non-stationary astrophysical stochastic gravitational-wave background: a new probe to the high-redshift population of binary black holes

ABSTRACT The astrophysical stochastic gravitational-wave background (SGWB) originates from the mergers of compact binary objects that are otherwise undetected as individual events, along with other sources such as supernovae, magnetars, etc. The individual gravitational-wave (GW) signal is time-varying over a time-scale that depends on the chirp mass of the coalescing binaries. Another time-scale that plays a role is the time-scale at which the sources repeat, which depends on the merger rate. The combined effect of these two leads to a breakdown of the time translation symmetry of the observed SGWB and a correlation between different frequency modes in the signal covariance matrix of the SGWB. Using an ensemble of SGWB due to binary black hole coalescence, calculated using simulations of different black hole mass distributions and merger rates, we show how the structure of the signal covariance matrix varies. This structure in the signal covariance matrix brings additional information about the sources on top of the power spectrum. We show that there is a significant improvement in the figure of merit by using this additional information in comparison to only power spectrum estimation for the LIGO–Virgo–KAGRA (LVK) network of detectors with the design sensitivity noise with 2 yr of observation. The inclusion of the off-diagonal correlation in the covariance of the SGWB in the data analysis pipelines will be beneficial in the quest for the SGWB signal in LVK frequency bands as well as in lower frequencies and in getting an insight into its origin.

Pulsar timing array observations as possible hints for nonsingular cosmology

Recent pulsar timing array (PTA) experiments have reported strong evidence of the stochastic gravitational wave background (SGWB). If interpreted as primordial gravitational waves (GWs), the signal favors a strongly blue-tilted spectrum. Consequently, the nonsingular cosmology, which is able to predict a strongly blue-tilted GW spectrum with n_T simeq 2 on certain scales, offers a potential explanation for the observed SGWB signal. In this paper, we present a Genesis-inflation model capable of explaining the SGWB signal observed by the PTA collaborations while also overcoming the initial singularity problem associated with the inflationary cosmology. Furthermore, our model predicts distinctive features in the SGWB spectrum, which might be examined by forthcoming space-based gravitational wave experiments.

Inflationary interpretation of the stochastic gravitational wave background signal detected by pulsar timing array experiments

Various pulsar timing array (PTA) experiments (NANOGrav, EPTA, PPTA, CPTA, including data from InPTA) very recently reported evidence for excess red common-spectrum signals in their latest datasets, with inter-pulsar correlations following the Hellings-Downs pattern, pointing to a stochastic gravitational wave background (SGWB) origin. Focusing for concreteness on the NANOGrav signal (given that all signals are in good agreement between each other), I inspect whether it supports an inflationary SGWB explanation, finding that such an interpretation calls for an extremely blue tensor spectrum, with spectral index nT≃1.8±0.3, while Big Bang Nucleosynthesis limits require a very low reheating scale, Trh≲10GeV. While not impossible, an inflationary origin for the PTA signal is barely tenable: within well-motivated inflationary models it is hard to achieve such a blue tilt, whereas models who do tend to predict sizeable non-Gaussianities, excluded by observations. Intriguingly, ekpyrotic models naturally predict a SGWB with spectral index nT=2, although with an amplitude too suppressed to be able to explain the signal detected by PTA experiments. Finally, I provide explicit expressions for a bivariate Gaussian approximation to the joint posterior distribution for the intrinsic-noise amplitude and spectral index of the NANOGrav signal, which can facilitate extending similar analyses to different theoretical signals.

Probing ensemble properties of vortex-avalanche pulsar glitches with a stochastic gravitational-wave background search

A stochastic gravitational-wave background (SGWB) is expected to be produced by the superposition of individually undetectable, unresolved gravitational-wave (GW) signals from cosmological and astrophysical sources. Such a signal can be searched with dedicated techniques using the data acquired by a network of ground-based GW detectors. In this work, we consider the astrophysical SGWB resulting from pulsar glitches, which are sudden increases in the rotational pulsar frequency, within our Galaxy. More specifically, we assume glitches to be associated with quantized, superfluid, vortex avalanches in the pulsars, and we model the SGWB from the superposition of GW bursts emitted during the glitching phase. We perform a cross-correlation search for this SGWB-like signal employing the data from the first three observation runs of Advanced LIGO and Virgo. Not having found any evidence for a SGWB signal, we set upper limits on the dimensionless energy density parameter ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{gw}}(f)$ for two different power-law SGWBs, corresponding to two different glitch regimes. We obtain ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{gw}}(f)\ensuremath{\le}7.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ at 25 Hz for a spectral index $5/2$, and ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{gw}}(f)\ensuremath{\le}5.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ at 25 Hz for a spectral index $17/2$. We then use these results to set constraints on the average glitch duration and the average radial motion of the vortices during the glitches for the population of the glitching Galactic pulsars, as a function of the Galactic glitch rate.

Gravitational wave stochastic background in reduced Horndeski theories

We generalize to reduced Horndeski theories of gravity, where gravitational waves (GWs) travel at the speed of light, the expression of a statistically homogeneous and unpolarized stochastic gravitational wave background (SGWB) signal measured as the correlation between the individual signals detected by two interferometers in arbitrary configurations. We also discuss some results found in the literature regarding cosmological distances in modified theories, namely, the simultaneous validity of a duality distance relation for GW signals and of the coincidence between the gravitational wave luminosity distance, based on the energy flux, and the distance inferred from the wave amplitude. This discussion allows us to conclude that the spectral energy density per unit solid angle of an astrophysical SGWB signal has the same functional dependency with the luminosity of each emitting source as in General Relativity (GR). Using the generalized expression of the GW energy-momentum tensor and the modified propagation law for the tensor modes, we conclude that the energy density of a SGWB maintains the same functional relation with the scale factor as in GR, provided that the modified theory coincides with GR in a given hypersurface of constant time. However, the relation between the detected signal and the spectral energy density is changed by the global factor $G_4(\varphi(t_0))$, thus potentially serving as a probe for modified gravity theories.

NANOGrav signal from the end of inflation and the LIGO mass and heavier primordial black holes

Releasing the 12.5-year pulsar timing array data, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported the evidence for a stochastic common-spectrum which would herald the detection of a stochastic gravitational wave background (SGWB) for the first time. We investigate if the signal could be generated from the end of a ∼10 MeV but still phenomenologically viable double-field inflation when the field configuration settles to its true vacuum. During the double-field inflation at such scales, bubbles of true vacuum that can collapse to LIGO mass, and heavier primordial black holes form. We show that only when this process happens with a first-order phase transition, the produced gravitational wave spectrum can match with the NANOGrav acclaimed SGWB signal. We show that the produced gravitational wave spectrum matches the NANOGrav SGWB signal only when this process happens through a first-order phase transition. Using LATTICEEASY, we also examine the previous observation in the literature that by lowering the scale of preheating, despite the shift of the peak frequency of the gravitational wave profile to smaller values, the amplitude of the SGWB could be kept almost constant. We notice that this observation breaks down at the preheating scale, M≲10−14mPl.

Targeted search for the stochastic gravitational-wave background from the galactic millisecond pulsar population

The millisecond pulsars, old-recycled objects spinning with high frequency $\mathcal{O}$ (kHz) sustaining the deformation from their spherical shape, may emit gravitational waves (GW). These are one of the potential candidates contributing to the anisotropic stochastic gravitational-wave background (SGWB) observable in the ground-based GW detectors. Here, we present the results from a likelihood-based targeted search for the SGWB due to millisecond pulsars in the Milky Way, by analyzing the data from the first three observing runs of Advanced LIGO and Advanced Virgo detector. We assume that the shape of SGWB power spectra and the sky distribution is known a priori from the population synthesis model. The information of the ensemble source properties, i.e., the in-band number of pulsars, ${N}_{\mathrm{obs}}$ and the averaged ellipticity, ${\ensuremath{\mu}}_{\ensuremath{\epsilon}}$ is encoded in the maximum likelihood statistic. We do not find significant evidence for the SGWB signal from the considered source population. The best Bayesian upper limit with 95% confidence for the parameters are ${N}_{\mathrm{obs}}\ensuremath{\le}8.8\ifmmode\times\else\texttimes\fi{}{10}^{4}$ and ${\ensuremath{\mu}}_{ϵ}\ensuremath{\le}1.4\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}6}$, which is comparable to the bounds on mean ellipticity with the GW observations of the individual pulsars. Finally, we show that for the plausible case of ${N}_{\mathrm{obs}}=40000$, with the one year of observations, the one-sigma sensitivity on ${\ensuremath{\mu}}_{\ensuremath{\epsilon}}$ might reach $1.5\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}7}$ and $4.1\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$ for the second-generation detector network having $\mathrm{A}+$ sensitivity and third-generation detector network, respectively.

Gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band

The NANOGrav, Parkes, European, and International Pulsar Timing Array (PTA) Collaborations have reported evidence for a common-spectrum process that can potentially correspond to a stochastic gravitational wave background (SGWB) in the 1--100 nHz frequency range. We consider the scenario in which this signal is produced by magnetohydrodynamic (MHD) turbulence in the early Universe, induced by a nonhelical primordial magnetic field at the energy scale corresponding to the quark confinement phase transition. We perform MHD simulations to study the dynamical evolution of the magnetic field and compute the resulting SGWB. We show that the SGWB output from the simulations can be very well approximated by assuming that the magnetic anisotropic stress is constant in time, over a time interval related to the eddy turnover time. The analytical spectrum that we derive under this assumption features a change of slope at a frequency corresponding to the GW source duration that we confirm with the numerical simulations. We compare the SGWB signal with the PTA data to constrain the temperature scale at which the SGWB is sourced, as well as the amplitude and characteristic scale of the initial magnetic field. We find that the generation temperature is constrained to be in the 1--200 MeV range, the magnetic field amplitude must be $>1$\% of the radiation energy density at that time, and the magnetic field characteristic scale is constrained to be $>10$\% of the horizon scale. We show that the turbulent decay of this magnetic field will lead to a field at recombination that can help to alleviate the Hubble tension and can be tested by measurements in the voids of the Large Scale Structure with gamma-ray telescopes like the Cherenkov Telescope Array.

Gravitational wave nonlinearities and pulsar-timing array angular correlations

Several pulsar-timing array (PTA) collaborations are finding tantalizing hints for a stochastic gravitational wave background signal in the nano-Hertz regime. So far, though, no convincing evidence for the expected Hellings-Downs quadrupolar correlations has been found. While this issue might get fixed at the light of more accurate, forthcoming data, it is important to keep an eye open on different possibilities and explore scenarios able to produce different types of PTA angular correlations. We point out that a stationary non-Gaussian component to the gravitational wave background can modulate the two-point PTA overlap reduction function, adding contributions that can help in fitting the angular distribution of PTA data. We discuss possible sources for such non-Gaussian signal in terms of cosmological processes occurring after inflation ends, and we investigate further tests for this idea.

Stochastic gravitational-wave background searches and constraints on neutron-star ellipticity

ABSTRACTRotating neutron stars (NSs) are promising sources of gravitational waves (GWs) in the frequency band of ground-based detectors. They are expected to emit quasi-monochromatic, long-duration GW signals, called continuous waves (CWs), due to their deviations from spherical symmetry. The degree of such deformations, and hence the information about the internal structure of an NS, is encoded in a dimension-less parameter ε called ellipticity. Searches for CW signals from isolated Galactic NSs have shown to be sensitive to ellipticities as low as $\varepsilon \sim \mathcal {O}(10^{-9})$. These searches are optimal for detecting and characterizing GWs from individual NSs, but they are not designed to measure the properties of NSs as population, such as the average ellipticity εav. These ensemble properties can be determined by the measurement of the stochastic gravitational-wave background (SGWB) arising from the superposition of GW signals from individually undetectable NSs. In this work, we perform a cross-correlation search for such a SGWB using the data from the first three observation runs of Advanced LIGO and Virgo. Finding no evidence for an SGWB signal, we set upper limits on the dimension-less energy density parameter Ωgw(f). Using these results, we also constrain the average ellipticity of Galactic NSs and five NS ‘hotspots’, as a function of the number of NSs emitting GWs within the frequency band of the search Nband. We find $\varepsilon _{\mathrm{av}} \lesssim 1.8 \times 10^{-8}$, with Nband = 1.6 × 107, for Galactic NSs, and $\varepsilon _{\mathrm{av}} \lesssim [3.5-11.8]\times 10^{-7}$, with Nband = 1.6 × 1010, for NS hotspots.

Inferring the lensing rate of LIGO–Virgo sources from the stochastic gravitational wave background

ABSTRACT Strong lensing of gravitational waves (GWs) is more likely for distant sources but predicted event rates are highly uncertain with many astrophysical origins proposed. Here, we open a new avenue to estimate the event rate of strongly lensed systems by exploring the amplitude of the stochastic gravitational wave background (SGWB). This method can provide a direct upper bound on the high-redshift binary coalescing rates, which can be translated into an upper bound on the expected rate of strongly lensed systems. We show that from the ongoing analysis of the Laser Interferometer Gravitational-wave Observatory (LIGO)-Virgo and in the future from the LIGO–Virgo design sensitivity stringent bounds on the lensing event rate can be imposed using the SGWB signal. Combining measurements of loud GW events with an unresolved stochastic background detection will improve estimates of the numbers of lensed events at high redshift. The proposed method is going to play a crucial in understanding the population of lensed and unlensed systems from GW observations.

Detecting a stochastic gravitational-wave background in the presence of correlated magnetic noise

A detection of the stochastic gravitational-wave background (SGWB) from unresolved compact binary coalescences could be made by Advanced LIGO and Advanced Virgo at their design sensitivities. However, it is possible for magnetic noise that is correlated between spatially separated ground-based detectors to mimic a SGWB signal. In this paper we propose a new method for detecting correlated magnetic noise and separating it from a true SGWB signal. A commonly discussed method for addressing correlated magnetic noise is coherent subtraction in the raw data using Wiener filtering. The method proposed here uses a parameterized model of the magnetometer-to-strain coupling functions, along with measurements from local magnetometers, to estimate the contribution of correlated noise to the traditional SGWB detection statistic. We then use Bayesian model selection to distinguish between models that include correlated magnetic noise and those with a SGWB. Realistic simulations are used to show that this method prevents a false SGWB detection due to correlated magnetic noise. We also demonstrate that it can be used for a detection of a SGWB in the presence of strong correlated magnetic noise, albeit with reduced significance compared to the case with no correlated noise. Finally, we discuss the advantages of using a global three-detector network for both identifying and characterizing correlated magnetic noise.

Assessing the detectability of a stochastic gravitational wave background with LISA, using an excess of power approach

The laser interferometer space antenna will be the first gravitational wave observatory in space. It is scheduled to fly in the early 2030’s. LISA design predicts sensitivity levels that potentially enable the detection a stochastic gravitational wave background signal. This stochastic type of signal is a superposition of signatures from sources that cannot be resolved individually and which are of various types, each one contributing with a different spectral shape. In this work we present a fast methodology to assess the detectability of a stationary, Gaussian, and isotropic stochastic signal in a set of frequency bins, combining information from the available data channels. We derive an analytic expression of the Bayes factor between the instrumental noise-only and the signal plus instrumental noise models, that allows us to compute the detectability bounds of a given signal, as a function of frequency and prior knowledge on the instrumental noise spectrum.

Detecting circular polarisation in the stochastic gravitational-wave background from a first-order cosmological phase transition

We discuss the observability of circular polarisation of the stochastic gravitational-wave background (SGWB) generated by helical turbulence following a first-order cosmological phase transition, using a model that incorporates the effects of both direct and inverse energy cascades. We explore the strength of the gravitational-wave signal and the dependence of its polarisation on the helicity fraction, ζ*, the strength of the transition, α, the bubble size, R*, and the temperature, T*, at which the transition finishes. We calculate the prospective signal-to-noise ratios of the SGWB strength and polarisation signals in the LISA experiment, exploring the parameter space in a way that is minimally sensitive to the underlying particle physics model. We find that discovery of SGWB polarisation is generally more challenging than measuring the total SGWB signal, but would be possible for appropriately strong transitions with large bubble sizes and a substantial polarisation fraction.

Time-dependence of the astrophysical stochastic gravitational wave background

Abstract The astrophysical stochastic gravitational wave background (SGWB) is mostly produced from unresolved stellar binary mergers, and the number of events at any moment of time is expected to be Poisson-distributed. The event rate is governed by several astrophysical processes. The Poisson nature leads to variation in the number of sources and this causes temporal variations in the SGWB. The intrinsic temporal fluctuations of the SGWB are a rich source of astrophysical information that can be explored via ongoing and future gravitational wave experiments to classify the sources of the SGWB signal. Along with several other methods to estimate the GW event rates from individual sources, the study of the temporal variations of the SGWB signal provides an independent method for estimating the event rates of the GW sources that contribute to the SGWB. Along with direct estimates of event rates, this approach can also distinguish between different sources contributing to the SGWB signal and will be a useful probe of its evolution over a vast cosmic volume. On averaging over observation times, the SGWB will be statistically invariant under time translation. Statistical time translation symmetry of the SGWB is expected due to the negligible evolution of the relevant cosmological and astrophysical phenomena over the observation time-scales over which the data is collected.

THE FEASIBILITY OF USING BLACK WIDOW PULSARS IN PULSAR TIMING ARRAYS FOR GRAVITATIONAL WAVE DETECTION

In the past five years, approximately one third of the 65 pulsars discovered by radio observations of Fermi unassociated sources are black widow pulsars (BWPs). BWPs are binary millisecond pulsars with companion masses ranging from 0.01-0.1 solar masses which often exhibit radio eclipses. The bloated companions in BWP systems exert small torques on the system causing the orbit to change on small but measurable time scales. Because adding parameters to a timing model reduces sensitivity to a gravitational wave (GW) signal, the need to fit many orbital frequency derivatives to the timing data is potentially problematic for using BWPs to detect GWs with pulsar timing arrays. Using simulated data with up to four orbital frequency derivatives, we show that fitting for orbital frequency derivatives absorbs less than 5% of the low frequency spectrum expected from a stochastic gravitational wave background signal. Furthermore, this result does not change with orbital period. Therefore, we suggest that if timing systematics can be accounted for by modeling orbital frequency derivatives and is not caused by spin frequency noise, pulsar timing array experiments should include BWPs in their arrays.

Parameter Estimation in Searches for the Stochastic Gravitational-Wave Background

The stochastic gravitational-wave background (SGWB) is expected to arise from the superposition of many independent and unresolved gravitational-wave signals of either cosmological or astrophysical origin. The spectral content of the SGWB carries signatures of the physics that generated it. We present a Bayesian framework for estimating the parameters associated with different SGWB models using data from gravitational-wave detectors. We apply this technique to recent results from LIGO to produce the first simultaneous 95% confidence level limits on multiple parameters in generic power-law SGWB models and in SGWB models of compact binary coalescences. We also estimate the sensitivity of the upcoming second-generation detectors such as Advanced LIGO or Virgo to these models and demonstrate how SGWB measurements can be combined and compared with observations of individual compact binary coalescences in order to build confidence in the origin of an observed SGWB signal. In doing so, we demonstrate a novel means of differentiating between different sources of the SGWB.