GW170817: Implications for the Stochastic Gravitational-Wave Background from Compact Binary Coalescences

Intrinsic Limits on the Detection of the Anisotropies of the Stochastic Gravitational Wave Background

For any given network of detectors, and for any given integration time, even in the idealized limit of negligible instrumental noise, the intrinsic time variation of the isotropic component of the stochastic gravitational wave background (SGWB) induces a limit on how accurately the anisotropies in the SGWB can be measured. We show here how this sample limit can be calculated and apply this to three separate configurations of ground-based detectors placed at existing and planned sites. Our results show that in the idealized, best-case scenario, individual multipoles of the anisotropies at ℓ≤8 can only be measured to ∼10^{-5}-10^{-4} level over five years of observation as a fraction of the isotropic component. As the sensitivity improves as the square root of the observation time, this poses a very serious challenge for measuring the anisotropies of SGWB of cosmological origin, even in the case of idealized detectors with arbitrarily low instrumental noise.

Detectability of the Cross-Correlation between CMB Lensing and Stochastic GW Background from Compact Object Mergers

The anisotropies of the Stochastic Gravitational-Wave Background (SGWB), produced by merging compact binaries, constitute a possible new probe of the Large-Scale Structure (LSS). However, the significant shot noise contribution caused by the discreteness of the GW sources and the poor angular resolution of the instruments hampers the detection of the intrinsic anisotropies induced by the LSS. In this work, we investigate the potential of cross-correlating forthcoming high precision measurements of the SGWB energy density and the Cosmic Microwave Background (CMB) lensing convergence to mitigate the effect of shot noise. Combining a detailed model of stellar and galactic astrophysics with a novel framework to distribute the GW emitters in the sky, we compute the auto- and cross-correlation power spectra for the two cosmic fields, evaluate the shot noise contribution and predict the signal-to-noise ratio. The results of our analysis show that the SGWB energy density correlates significantly with the CMB lensing convergence and that the cross-correlation between these two cosmic fields reduces the impact of instrumental and shot noise. Unfortunately, the S/N is not high enough to detect the intrinsic SGWB anisotropies. Nevertheless, a network composed of both present and future generation GW interferometers, operating for at least 10 yrs, should be able to measure the shot noise contribution.

Stochastic Gravitational-Wave Backgrounds: Current Detection Efforts and Future Prospects

The collection of individually resolvable gravitational wave (GW) events makes up a tiny fraction of all GW signals that reach our detectors, while most lie below the confusion limit and are undetected. Similarly to voices in a crowded room, the collection of unresolved signals gives rise to a background that is well-described via stochastic variables and, hence, referred to as the stochastic GW background (SGWB). In this review, we provide an overview of stochastic GW signals and characterise them based on features of interest such as generation processes and observational properties. We then review the current detection strategies for stochastic backgrounds, offering a ready-to-use manual for stochastic GW searches in real data. In the process, we distinguish between interferometric measurements of GWs, either by ground-based or space-based laser interferometers, and timing-residuals analyses with pulsar timing arrays (PTAs). These detection methods have been applied to real data both by large GW collaborations and smaller research groups, and the most recent and instructive results are reported here. We close this review with an outlook on future observations with third generation detectors, space-based interferometers, and potential noninterferometric detection methods proposed in the literature.

Search for a Scalar Induced Stochastic Gravitational Wave Background in the Third LIGO-Virgo Observing Run

The formation of primordial black holes from inflationary fluctuations is accompanied by a scalar induced gravitational wave background. We perform a Bayesian search of such background in the data from Advanced LIGO and Virgo's first, second, and third observing runs, parametrizing the peak in the curvature power spectrum by a log-normal distribution. The search shows no evidence for such a background. We place 95% confidence level upper limits on the integrated power of the curvature power spectrum peak which, for a narrow width, reaches down to 0.02 at 10^{17}  Mpc^{-1}. The resulting constraints are stronger than those arising from big bang nucleosynthesis or cosmic microwave background observations. In addition, we find that the constraints from LIGO and Virgo, at their design sensitivity, and from the Einstein Telescope can compete with those related to the abundance of the formed primordial black holes.

The Quest for the Astrophysical Gravitational-Wave Background with Terrestrial Detectors

We present the gravitational-wave background and its properties focusing on the background from compact binary coalescences in terrestrial detectors. We also introduce the standard data analysis method used to search for this background and discuss its detectability with second and third generation networks of detectors. To illustrate, we first use simple models and then discuss more realistic models based on simulations.

Advanced Virgo: Status of the Detector, Latest Results and Future Prospects

The Virgo detector, based at the EGO (European Gravitational Observatory) and located in Cascina (Pisa), played a significant role in the development of the gravitational-wave astronomy. From its first scientific run in 2007, the Virgo detector has constantly been upgraded over the years; since 2017, with the Advanced Virgo project, the detector reached a high sensitivity that allowed the detection of several classes of sources and to investigate new physics. This work reports the main hardware upgrades of the detector and the main astrophysical results from the latest five years; future prospects for the Virgo detector are also presented.

Bayesian Inference for Gravitational Waves from Binary Neutron Star Mergers in Third Generation Observatories

Third generation (3G) gravitational-wave detectors will observe thousands of coalescing neutron star binaries with unprecedented fidelity. Extracting the highest precision science from these signals is expected to be challenging owing to both high signal-to-noise ratios and long-duration signals. We demonstrate that current Bayesian inference paradigms can be extended to the analysis of binary neutron star signals without breaking the computational bank. We construct reduced-order models for ∼90-min-long gravitational-wave signals covering the observing band (5-2048 Hz), speeding up inference by a factor of ∼1.3×10^{4} compared to the calculation times without reduced-order models. The reduced-order models incorporate key physics including the effects of tidal deformability, amplitude modulation due to Earth's rotation, and spin-induced orbital precession. We show how reduced-order modeling can accelerate inference on data containing multiple overlapping gravitational-wave signals, and determine the speedup as a function of the number of overlapping signals. Thus, we conclude that Bayesian inference is computationally tractable for the long-lived, overlapping, high signal-to-noise-ratio events present in 3G observatories.

Gravitational Waves from the Cosmological Quark-Hadron Phase Transition Revisited

The recent claim by the NANOGrav collaboration of a possible detection of an isotropic gravitational wave background stimulated a series of investigations searching for the origin of such a signal. The QCD phase transition appears as a natural candidate and in this paper the gravitational spectrum generated during the conversion of quarks into hadrons is calculated. Here, contrary to recent studies, equations of state for the quark-gluon plasma issued from the lattice approach were adopted. The duration of the transition, an important parameter affecting the amplitude of the gravitational wave spectrum, was estimated self-consistently with the dynamics of the universe controlled by the Einstein equations. The gravitational signal generated during the transition peaks around 0.28 μHz with amplitude of h02Ωgw≈7.6×10−11, being unable to explain the claimed NANOGrav signal. However, the expected QCD gravitational wave background could be detected by the planned spatial interferometer Big Bang Observer in its advanced version for frequencies above 1.0 mHz. This possible detection assumes that algorithms recently proposed will be able to disentangle the cosmological signal from that expected for the astrophysical background generated by black hole binaries.

Constraints on Cosmic Strings Using Data from the Third Advanced LIGO-Virgo Observing Run

We search for gravitational-wave signals produced by cosmic strings in the Advanced LIGO and Virgo full O3 dataset. Search results are presented for gravitational waves produced by cosmic string loop features such as cusps, kinks, and, for the first time, kink-kink collisions. A template-based search for short-duration transient signals does not yield a detection. We also use the stochastic gravitational-wave background energy density upper limits derived from the O3 data to constrain the cosmic string tension Gμ as a function of the number of kinks, or the number of cusps, for two cosmic string loop distribution models. Additionally, we develop and test a third model that interpolates between these two models. Our results improve upon the previous LIGO-Virgo constraints on Gμ by 1 to 2 orders of magnitude depending on the model that is tested. In particular, for the one-loop distribution model, we set the most competitive constraints to date: Gμ≲4×10^{-15}. In the case of cosmic strings formed at the end of inflation in the context of grand unified theories, these results challenge simple inflationary models.

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 25 Hz 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 25 Hz 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.

Inference of the Neutron Star Equation of State from Cosmological Distances

Finite-size effects on the gravitational wave signal from a neutron star merger typically manifest at high frequencies where detector sensitivity decreases. Proposed sensitivity improvements can give us access both to stronger signals and to a myriad of weak signals from cosmological distances. The latter will outnumber the former and the relevant part of the signal will be redshifted towards the detector's most sensitive band. We study the redshift dependence of information about neutron star matter and find that single-scale properties, such as the star radius or the postmerger frequency, are better measured from the distant weak sources from z∼1.

Measuring the Primordial Gravitational-Wave Background in the Presence of Astrophysical Foregrounds

Primordial gravitational waves are expected to create a stochastic background encoding information about the early Universe that may not be accessible by other means. However, the primordial background is obscured by an astrophysical foreground consisting of gravitational waves from compact binaries. We demonstrate a Bayesian method for estimating the primordial background in the presence of an astrophysical foreground. Since the background and foreground signal parameters are estimated simultaneously, there is no subtraction step, and therefore we avoid astrophysical contamination of the primordial measurement, sometimes referred to as "residuals." Additionally, since we include the non-Gaussianity of the astrophysical foreground in our model, this method represents the statistically optimal approach to the simultaneous detection of a multicomponent stochastic background.

Constraining the Lensing of Binary Black Holes from Their Stochastic Background

Gravitational waves (GWs) are subject to gravitational lensing in the same way as electromagnetic radiation. However, to date, no unequivocal observation of a lensed GW transient has been reported. Independently, GW observatories continue to search for the stochastic GW signal that is produced by many transient events at high redshift. We exploit a surprising connection between the lensing of individual transients and limits to the background radiation produced by the unresolved population of binary back hole mergers: we show that it constrains the fraction of individually resolvable lensed binary black holes to less than ∼4×10^{-5} at present sensitivity. We clarify the interpretation of existing, low redshift GW observations (obtained assuming no lensing) in terms of their apparent lensed redshifts and masses and explore constraints from GW observatories at future sensitivity. Based on our results, recent claims of observations of lensed events are statistically disfavored.

Anisotropies in the Astrophysical Gravitational-Wave Background: The Impact of Black Hole Distributions

We use population inference to explore the impact that uncertainties in the distribution of binary black holes (BBH) have on the astrophysical gravitational-wave background (AGWB). Our results show that the AGWB monopole is sensitive to the nature of the BBH population (particularly the local merger rate), while the anisotropic C_{ℓ} spectrum is only modified to within a few percent, at a level which is insignificant compared to other sources of uncertainty (such as cosmic variance). This is very promising news for future observational studies of the AGWB, as it shows that (i) the monopole can be used as a new probe of the population of compact objects throughout cosmic history, complementary to direct observations by LIGO and Virgo and (ii) we are able to make surprisingly robust predictions for the C_{ℓ} spectrum, even with only very approximate knowledge of the black hole population. As a result, the AGWB anisotropies have enormous potential as a new probe of the large-scale structure of the Universe, and of late-Universe cosmology in general.

Stochastic gravitational wave backgrounds

A stochastic background of gravitational waves could be created by the superposition of a large number of independent sources. The physical processes occurring at the earliest moments of the universe certainly created a stochastic background that exists, at some level, today. This is analogous to the cosmic microwave background, which is an electromagnetic record of the early universe. The recent observations of gravitational waves by the Advanced LIGO and Advanced Virgo detectors imply that there is also a stochastic background that has been created by binary black hole and binary neutron star mergers over the history of the universe. Whether the stochastic background is observed directly, or upper limits placed on it in specific frequency bands, important astrophysical and cosmological statements about it can be made. This review will summarize the current state of research of the stochastic background, from the sources of these gravitational waves to the current methods used to observe them.

Searching for Near-Horizon Quantum Structures in the Binary Black-Hole Stochastic Gravitational-Wave Background

Quantum gravity corrections have been speculated to lead to modifications to space-time geometry near black-hole horizons. Such structures may reflect gravitational waves, causing echoes that follow the main gravitational waves from binary black-hole coalescence. By studying two phenomenological models of the near-horizon structures under the Schwarzschild approximation, we show that such echoes, if they exist, will give rise to a stochastic gravitational-wave background, which is very substantial if the near-horizon structure has a near-unity reflectivity for gravitational waves, readily detectable by Advanced LIGO. In case the reflectivity is much less than unity, the background will mainly be arising from the first echo, with a level proportional to the power reflectivity of the near-horizon structure, but robust against uncertainties in the location and the shape of the structure-as long as it is localized and close to the horizon. Sensitivity of third-generation detectors allows the detection of a background that corresponds to power reflectivity ∼3×10^{-3}, if uncertainties in the binary black-hole merger rate can be removed. We note that the echoes do alter the f^{2/3} power law of the background spectra at low frequencies, which is rather robust against uncertainties.

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω_{0}^{T}<5.58×10^{-8}, Ω_{0}^{V}<6.35×10^{-8}, and Ω_{0}^{S}<1.08×10^{-7} at a reference frequency f_{0}=25  Hz.