Stochastic gravitational wave backgrounds

The muon Smasher's guide

We lay out a comprehensive physics case for a future high-energy muon collider, exploring a range of collision energies (from 1 to 100 TeV) and luminosities. We highlight the advantages of such a collider over proposed alternatives. We show how one can leverage both the point-like nature of the muons themselves as well as the cloud of electroweak radiation that surrounds the beam to blur the dichotomy between energy and precision in the search for new physics. The physics case is buttressed by a range of studies with applications to electroweak symmetry breaking, dark matter, and the naturalness of the weak scale. Furthermore, we make sharp connections with complementary experiments that are probing new physics effects using electric dipole moments, flavor violation, and gravitational waves. An extensive appendix provides cross section predictions as a function of the center-of-mass energy for many canonical simplified models.

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.

Scalar Induced Gravitational Waves Review

We provide a review on the state-of-the-art of gravitational waves induced by primordial fluctuations, so-called induced gravitational waves. We present the intuitive physics behind induced gravitational waves and we revisit and unify the general analytical formulation. We then present general formulas in a compact form, ready to be applied. This review places emphasis on the open possibility that the primordial universe experienced a different expansion history than the often assumed radiation dominated cosmology. We hope that anyone interested in the topic will become aware of current advances in the cosmology of induced gravitational waves, as well as becoming familiar with the calculations behind.

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.

Bremsstrahlung of Light through Spontaneous Emission of Gravitational Waves

Zero-point fluctuations are a universal consequence of quantum theory. Vacuum fluctuations of electromagnetic field have provided crucial evidence and guidance for QED as a successful quantum field theory with a defining gauge symmetry through the Lamb shift, Casimir effect, and spontaneous emission. In an accelerated frame, the thermalisation of the zero-point electromagnetic field gives rise to the Unruh effect linked to the Hawking effect of a black hole via the equivalence principle. This principle is the basis of general covariance, the symmetry of general relativity as the classical theory of gravity. If quantum gravity exists, the quantum vacuum fluctuations of the gravitational field should also lead to the quantum decoherence and dissertation of general forms of energy and matter. Here we present a novel theoretical effect involving the spontaneous emission of soft gravitons by photons as they bend around a heavy mass and discuss its observational prospects. Our analytic and numerical investigations suggest that the gravitational bending of starlight predicted by classical general relativity should also be accompanied by the emission of gravitational waves. This in turn redshifts the light causing a loss of its energy somewhat analogous to the bremsstrahlung of electrons by a heavier charged particle. It is suggested that this new effect may be important for a combined astronomical source of intense gravity and high-frequency radiation such as X-ray binaries and that the proposed LISA mission may be potentially sensitive to the resulting sub-Hz stochastic gravitational waves.

Has NANOGrav Found First Evidence for Cosmic Strings?

The North American Nanohertz Observatory for Gravitational Waves has recently reported strong evidence for a stochastic common-spectrum process affecting the pulsar timing residuals in its 12.5-year data set. We demonstrate that this process admits an interpretation in terms of a stochastic gravitational-wave background emitted by a cosmic-string network in the early Universe. We study stable Nambu-Goto strings in dependence of their tension Gμ and loop size α and show that the entire viable parameter space will be probed by an array of future experiments.

Implications of the NANOGrav results for inflation

The NANOGrav pulsar timing array experiment reported evidence for a stochastic common-spectrum process affecting pulsar timing residuals in its 12.5-yr data set, which might be interpreted as the first detection of a stochastic gravitational wave background (SGWB). I examine whether the NANOGrav signal might be explained by an inflationary SGWB, focusing on the implications for the tensor spectral index nT and the tensor-to-scalar ratio r. Explaining NANOGrav while complying with upper limits on r from BICEP2/Keck Array and Planck requires $r \gtrsim {\cal O}(10^{-6})$ in conjunction with an extremely blue tensor spectrum, 0.7 ≲ nT ≲ 1.3. After discussing models, which can realize such a blue spectrum, I show that this region of parameter space can be brought in agreement with big bang nucleosynthesis constraints for a sufficiently low reheating scale, $T_{\rm rh} \lesssim 100\, {\rm GeV} \!-\! 1\, {\rm TeV}$. With the important caveat of having assumed a power-law parametrization for the primordial tensor spectrum, an inflationary interpretation of the NANOGrav signal is therefore not excluded.

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.

LISA Sensitivity to Gravitational Waves from Sound Waves

Gravitational waves (GWs) produced by sound waves in the primordial plasma during a strong first-order phase transition in the early Universe are going to be a main target of the upcoming Laser Interferometer Space Antenna (LISA) experiment. In this short note, I draw a global picture of LISA’s expected sensitivity to this type of GW signal, based on the concept of peak-integrated sensitivity curves (PISCs) recently introduced in two previous papers. In particular, I use LISA’s PISC to perform a systematic comparison of several thousands of benchmark points in ten different particle physics models in a compact fashion. The presented analysis (i) retains the complete information on the optimal signal-to-noise ratio, (ii) allows for different power-law indices describing the spectral shape of the signal, (iii) accounts for galactic confusion noise from compact binaries, and (iv) exhibits the dependence of the expected sensitivity on the collected amount of data. An important outcome of this analysis is that, for the considered set of models, galactic confusion noise typically reduces the number of observable scenarios by roughly a factor of two, more or less independent of the observing time. The numerical results presented in this paper are also available in the online repository Zenodo.

Gravitational-Wave Background Sky Maps from Advanced LIGO O1 Data

We integrate the publicly available O1 LIGO time-domain data to obtain maximum-likelihood constraints on the gravitational-wave background (GWB) arising from stochastic, persistent signals. Our method produces sky maps of the strain intensity I as a function of direction on the sky at a reference frequency f_{0}. The data are integrated assuming a set of fixed power-law spectra for the signal. The maps provide upper limits on the amplitude of the GWB density Ω_{GW}(f_{0}) and any anisotropy around the background. We find 95% confidence upper limits of Ω_{GW}<4.8×10^{-7} at f_{0}=50  Hz with similar constraints on a dipole modulation for the inspiral-dominated stochastic background case.