In searching for continuous gravitational waves over very many ($\approx 10^{17}$) templates , clustering is a powerful tool which increases the search sensitivity by identifying and bundling together candidates that are due to the same root cause. We implement a deep learning network that identifies clusters of signal candidates in the output of continuous gravitational wave searches and assess its performance. For loud signals our network achieves a detection efficiency higher than 97\% with a very low false alarm rate, and maintains a reasonable detection efficiency for signals with lower amplitudes, i.e. at $\lesssim$ current upper limit values.
Gravitational-wave bursts are observable as bright clusters of pixels in spectrograms of strain power. Clustering algorithms can be used to identify candidate gravitational-wave events. Clusters are often identified by grouping together seed pixels in which the power exceeds some threshold. If the gravitational-wave signal is long-lived, however, the excess power may be spread out over many pixels, none of which are bright enough to become seeds. Without seeds, the problem of detection through clustering becomes more complicated. In this paper we investigate seedless clustering algorithms in s…
Searches for continuous gravitational waves target nearly monochromatic gravitational wave emission from e.g. non-axysmmetric fast-spinning neutron stars. Broad surveys often require to explicitly search for a very large number of different waveforms, easily exceeding $\sim10^{17}$ templates. In such cases, for practical reasons, only the top, say $\sim10^{10}$, results are saved and followed-up through a hierarchy of stages. Most of these candidates are not completely independent of neighbouring ones, but arise due to some common cause: a fluctuation, a signal or a disturbance. By judiciously…
Compact binary coalescences are a promising source of gravitational waves for second-generation interferometric gravitational-wave detectors. Although matched filtering is the optimal search method for well-modeled systems, alternative detection strategies can be used to guard against theoretical errors (e.g., involving new physics and/or assumptions about spin/eccentricity) while providing a measure of redundancy. In previous work, we showed how "seedless clustering" can be used to detect long-lived gravitational-wave transients in both targeted and all-sky searches. In this paper, we apply s…
We have developed a method 'time-frequency (TF) clustering' to find the burst gravitational waves for TAMA data analysis. TF clustering method on sonogram (spectrogram) shows some characteristics of short duration signal. Using parameters which represent the cluster shape, we can efficiently identify some predicted gravitational wave forms and can exclude typical unstable spike like noises due to detector instruments. The requirement of some parameters of cluster achieved roughly 50% average efficiency for injected DFM waveforms of $h_{rss}\sim 2 \times 10^{-19}$ for type I burst. Also the red…
We show that the effect of initial non-Gaussian clustering can significantly enhance the event rate for primordial black hole (PBH) coalescence. The impact of such clustering is studied in a specific scenario of multi-stream inflation. Initial clustering enables the possibility of detecting massive PBH coalescence by space-based gravitational wave interferometers such as LISA and DECIGO/BBO. The parameter regime for the ground-based detectors to detect PBH coalescence is also extended.
Observed angular positions and redshifts of large-scale structure tracers such as galaxies are affected by gravitational waves through volume distortion and magnification effects. Thus, a gravitational wave background can in principle be probed through clustering statistics of large-scale structure. We calculate the observed angular clustering of galaxies in the presence of a gravitational wave background at linear order including all relativistic effects. For a scale-invariant spectrum of gravitational waves, the effects are most significant at the smallest multipoles (2 <= l <= 5), but typic…
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（阿尔伯特·爱因斯坦研究所））；Leibniz Universität Hannover（莱布尼茨汉诺威大学）；University of Wisconsin Milwaukee（威斯康星大学密尔沃基分校）
Broad searches for continuous gravitational wave signals rely on hierarchies of follow-up stages for candidates above a given significance threshold. An important step to simplify these follow-ups and reduce the computational cost is to bundle together in a single follow-up nearby candidates. This step is called clustering and we investigate carrying it out with a deep learning network. In our first paper [1], we implemented a deep learning clustering network capable of correctly identifying clusters due to large signals. In this paper, a network is implemented that can detect clusters due to …
We investigate the formation, gravitational clustering and interactions of solitons in a self-interacting, non-relativistic scalar field in an expanding universe. Rapid formation of large number of solitons is driven by attractive self-interactions of the field, whereas the slower clustering of solitons is driven by gravitational forces. Driven closer together by gravity, we see a rich plethora of dynamics in the soliton "gas" including mergers, scatterings and formation of soliton binaries. The numerical simulations are complemented by analytic calculations and estimates of (i) the relevant i…
In hierarchical searches for continuous gravitational waves, clustering of candidates is an important postprocessing step because it reduces the number of noise candidates that are followed-up at successive stages [1][7][12]. Previous clustering procedures bundled together nearby candidates ascribing them to the same root cause (be it a signal or a disturbance), based on a predefined cluster volume. In this paper, we present a procedure that adapts the cluster volume to the data itself and checks for consistency of such volume with what is expected from a signal. This significantly improves th…
In recent years there has been a developing realization that the interesting large--scale structure of voids, ``pancakes", and filaments in the Universe is a consequence of the efficacy of an approximation scheme for cosmological gravitation clustering proposal by Zel'dovich in 1970. However, this scheme was only supposed to apply to smoothed initial conditions, and its efficacy for hierarchical clustering has not been justified. We show that this is explained by the fact that the gravitationally evolved potential from N--body simulations closely resembles the smoothed potential of the initial…
We derive the time evolution of the density contrast to all orders of perturbation theory, by solving the Einstein equation for scale-invariant fluctuations. These fluctuations are represented by an infinite series in inverse powers of the radial parameter. In addition to the standard growing modes, we find infinitely many more new growing modes for open and closed universes.
The rapid release of accurate sky localization for gravitational-wave candidates is crucial for multi-messenger observations. During the third observing run of Advanced LIGO and Advanced Virgo, automated gravitational-wave alerts were publicly released within minutes of detection. Subsequent inspection and analysis resulted in the eventual retraction of a fraction of the candidates. Updates could be delayed by up to several days, sometimes issued during or after exhaustive multi-messenger followup campaigns. We introduce GWSkyNet, a real-time framework to distinguish between astrophysical even…
LIGO Laboratory（LIGO实验室）；California Institute of Technology（加州理工学院）
One class of gravitational wave signals LIGO is searching for consists of short duration bursts of unknown waveforms. Potential sources include core collapse supernovae, gamma ray burst progenitors, and mergers of binary black holes or neutron stars. We present a density-based clustering algorithm to improve the performance of time-frequency searches for such gravitational-wave bursts when they are extended in time and/or frequency, and not sufficiently well known to permit matched filtering. We have implemented this algorithm as an extension to the QPipeline, a gravitational-wave data analysi…
Advanced LIGO data contains numerous noise transients, or "glitches", that have been shown to reduce the sensitivity of matched filter searches for gravitational waves from compact binaries by increasing the rate at which random coincidences occur. The presence of these transients has precipitated extensive work to establish that observed gravitational wave events are astrophysical in nature. We discuss the response of the PyCBC search for gravitational waves from stellar mass binaries to various common glitches that were observed during Advanced LIGO's first and second observing runs. We show…
We estimate galaxy clustering under a modified gravitational potential. In particular, the modifications in gravitational potential energy occur due to a power-law and cosmological constant terms. We derive a canonical partition function for the system of galaxies interacting under such a modified gravitational potential. Moreover, we compute various thermodynamical equation of states for the system. We do comparative analysis in order to emphasize the effect of corrections on thermodynamics of the system. Interestingly, the modifications in thermodynamical quantities are embedded in clusterin…
Observations with interferometric gravitational-wave detectors result in probability sky maps that are multimodal and spread over 10-100 deg^2. We present a scheme for maximizing the probability of imaging optical counterparts to gravitational-wave transients given limited observing resources. Our framework is capable of coordinating many telescopes with different fields of view and limiting magnitudes. We present a case study comparing three different planning algorithms. We find that, with the network of telescopes that was used in the most recent joint LIGO-Virgo science run, a relatively s…
We investigate the correlation between the distribution of galaxies and the predicted gravitational-wave background of astrophysical origin. We show that the large angular scale anisotropies of this background are dominated by nearby non-linear structure, which depends on the notoriously hard to model galaxy power spectrum at small scales. In contrast, we report that the cross-correlation of this signal with galaxy catalogues depends only on linear scales and can be used to constrain the average contribution to the gravitational-wave background as a function of time. Using mock data based on a…
This article addresses some issues related to statistical description of gravitating systems in an expanding backgrounds. In particular, I describe (a) how the non linear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale and (b) what are the asymptotic characteristics of gravitational clustering that are independent of the initial conditions. The analysis uses a new approach based on an integro-differential equation for the evolution of the gravitational potential in the Fourier space. I show how t…
We explore the possibility of improving the $Λ$CDM model at megaparsec scales by introducing a scalar interaction which increases the mutual gravitational attraction of dark matter particles. Using N-body simulations, we study the spatial distribution of dark matter particles and halos. We measure the effect of modifications in the Newton's gravity on properties of the two-point correlation function, the dark matter power spectrum, the cumulative halo mass function and density probability distribution functions. The results look promising: the scalar interactions produce desirable features at …
We study the thermodynamics of galactic clustering under the higher-order corrected Newtonian dynamics. The clustering of galaxies is considered as a gravitational phase transition. In order to study the effects of higher-order correction to the thermodynamics of gravitational system, we compute more exact equations of state. Moreover, we investigate the corrected probability distribution function for such gravitating system. A relation between order parameter and the critical temperature is also established.
The potential is a constant to linear order in cosmological gravitational clustering. In this Letter we present results of testing the conjecture, proposed by Pauls and Melott (1995), that the effect of nonlinear evolution on the potential can be better described by smoothing it on the scale of nonlinearity. We show two-dimensional simulations consisting of an N-body code in which particles are accelerated not by their mutual attraction, but by the gradient of the initial potential smoothed on the current scale of nonlinearity. This approximation produces results considerably improved over usi…
Astrophysical or Terrestrial: Machine learning classification of gravitational-wave candidates using multiple-search information
University of Minnesota（明尼苏达大学）；The University of British Columbia（不列颠哥伦比亚大学）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；Joint Space-Science Institute, University of Maryland（马里兰大学联合空间科学研究所）
Bayesian Framework to Follow-up Continuous Gravitational Wave Candidates from Deep Surveys
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Departament de Física, Universitat de les Illes Balears, IAC3 – IEEC（巴利阿里群岛大学物理系，IAC3-IEEC）
The connection between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime is studied. Under a scaling hypothesis, we find that the three-point correlation function, $ζ$, obeys the scaling law $ζ\propto ξ^{\frac{3m+4w-2ε}{2m+2w}}$ in the nonlinear regime, where $ξ$, $m$, $w$, and $ε$ are the two-point correlation function, the power index of the power spectrum in the nonlinear regime, the number of spatial dimensions, and the power index of the phase correlations, respectively. The new formula reveals the origin of the power index of the th…
Large-scale structure formation can be modeled as a nonlinear process that transfers energy from the largest scales to successively smaller scales until it is dissipated, in analogy with Kolmogorov's cascade model of incompressible turbulence. However, cosmic turbulence is very compressible, and vorticity plays a secondary role in it. The simplest model of cosmic turbulence is the adhesion model, which can be studied perturbatively or adapting to it Kolmogorov's non-perturbative approach to incompressible turbulence. This approach leads to observationally testable predictions, e.g., to the pow…
We describe a general approach to detection of transient gravitational-wave signals in the presence of non-Gaussian background noise. We prove that under quite general conditions, the ratio of the likelihood of observed data to contain a signal to the likelihood of it being a noise fluctuation provides optimal ranking for the candidate events found in an experiment. The likelihood-ratio ranking allows us to combine different kinds of data into a single analysis. We apply the general framework to the problem of unifying the results of independent experiments and the problem of accounting for no…
Based on thermodynamics, we study the galactic clustering of an expanding Universe by considering the logarithmic and volume (quantum) corrections to Newton's law along with the repulsive effect of a harmonic force induced by the cosmological constant ($Λ$) in the formation of the large scale structure of the Universe. We derive the $N$-body partition function for extended-mass galaxies (galaxies with halos) analytically. For this partition function, we compute the exact equations of states, which exhibit the logarithmic, volume and cosmological constant corrections. In this setting, a modifie…
In this paper, leveraging the capabilities of neural networks for modeling the non-linearities that exist in the data, we propose several models that can project data into a low dimensional, discriminative, and smooth manifold. The proposed models can transfer knowledge from the domain of known classes to a new domain where the classes are unknown. A clustering algorithm is further applied in the new domain to find potentially new classes from the pool of unlabeled data. The research problem and data for this paper originated from the Gravity Spy project which is a side project of Advanced Las…
We present a formulation of observed number density fluctuations of gravitational-wave (GW) sources in a three dimensional space. In GW observations, redshift identification for each GW source is a challenging issue, in particular, for high redshift sources. The use of observed luminosity distance as a distance indicator will be a simple yet optimal way for measuring the clustering signal. We derive the density fluctuations of GW sources estimated from observed luminosity distance and sky position of each source. The density fluctuations are distorted as similar to the so-called redshift space…
Non-linear gravitational clustering in a universe dominated by dark energy, modelled by a `quintessence' scalar field, and cold dark matter with space-time varying mass is studied. Models of this type, where the variable mass is induced by dependence on the scalar field, as suggested by string theory or extra-dimensions, have been proposed as a viable solution of the coincidence problem. A general framework for the study of the non-linear phases of structure formation in scalar field cosmologies is provided, starting from a general relativistic treatment of the combined dark matter-dark energy…
We derive two different methods to compute the minimal required integration time of a fully coherent follow-up of candidates produced in wide parameter space semi-coherent searches, such as global correlation StackSlide searches using Einstein@Home. We numerically compare these methods in terms of integration duration and computing cost. In a Monte Carlo study we confirm that we can achieve the required detection probability.
Breaking binary formation mechanism degeneracies with gravitational wave clustering
Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INAF - Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；Scuola Internazionale Superiore di Studi Avanzati（国际高等研究院）；University of Trento（特伦托大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Universität Heidelberg（海德堡大学）
The search for continuous gravitational waves from unknown isolated sources is computationally limited due to the enormous parameter space that needs to be covered and the weakness of the expected signals. Therefore semi-coherent search strategies have been developed and applied in distributed computing environments such as Einstein@Home, in order to narrow down the parameter space and identify interesting candidates. However, in order to optimally confirm or dismiss a candidate as a possible gravitational-wave signal, a fully-coherent follow-up using all the available data is required. We pre…
The first discovery of the gravitational wave (GW) event, GW150914, suggests a higher merger rate of black-hole (BH) binaries. If this is true, a number of BH binaries will be observed via the second-generation GW detectors, and the statistical properties of the observed BH binaries can be scrutinized. A naive but important question to ask is whether the spatial distribution of BH binaries faithfully traces the matter inhomogeneities in the Universe or not. Although the BH binaries are thought to be formed inside the galaxies in most of the scenarios, there is no observational evidence to conf…
In modern cosmology, an important task is investigating whether there exists a signal of modified gravity in the universe. Due to the limited resolutions and sensitivities of facilities, current observations can not detect any signal of modified gravity. As a consequence, it is urgent to predict the constraining power of future cosmological surveys on modified gravity. We constrain the Hu-Sawicki $f(R)$ gravity with eight future mainstream probes encompassing 21 cm intensity mapping, HI galaxy, cosmic microwave background, optical galaxy, weak lensing, galaxy clustering, type Ia supernovae and…
It has been recently recognized that the observational relativistic effects, mainly arising from the light propagation in an inhomogeneous universe, induce the dipole asymmetry in the cross-correlation function of galaxies. In particular, the dipole asymmetry at small scales is shown to be dominated by the gravitational redshift effects. In this paper, we exploit a simple analytical description for the dipole asymmetry in the cross-correlation function valid at quasi-linear regime. In contrast to the previous model, a new prescription involves only one dimensional integrals, providing a faster…
The formation of primordial black holes in the early universe in the Brans-Dicke scalar-tensor theory of gravity is investigated. Corrections to the threshold value of density perturbations are found. Above the threshold, the gravitational collapse occurs after the cosmological horizon crossing. The corrections depend in a certain way on the evolving scalar field. They affect the probability of primordial black holes formation, and can lead to their clustering at large scales if the scalar field is inhomogeneous. The formation of the clusters, in turn, increases the probability of black holes …
Bayesian model selection provides a powerful and mathematically transparent framework to tackle hypothesis testing, such as detection tests of gravitational waves emitted during the coalescence of binary systems using ground-based laser interferometers. Although its implementation is computationally intensive, we have developed an efficient probabilistic algorithm based on a technique known as nested sampling that makes Bayesian model selection applicable to follow-up studies of candidate signals produced by on-going searches of inspiralling compact binaries. We discuss the performance of this…
Ground-based gravitational wave laser interferometers (LIGO, GEO-600, Virgo and Tama-300) have now reached high sensitivity and duty cycle. We present a Bayesian evidence-based approach to the search for gravitational waves, in particular aimed at the followup of candidate events generated by the analysis pipeline. We introduce and demonstrate an efficient method to compute the evidence and odds ratio between different models, and illustrate this approach using the specific case of the gravitational wave signal generated during the inspiral phase of binary systems, modelled at the leading quad…
In this paper, we will study the large scale structure formation using the gravitational partition function. We will assertively argue that the system of gravitating galaxies can be analyzed using the Tsallis statistical mechanics. The divergences in the Tsallis gravitational partition function can be removed using the mathematical riches of the generalization of the dimensional regularization (GDR). The finite gravitational partition function thus obtained will be used to evaluate the thermodynamics of the system of galaxies and thus, to understand the clustering of galaxies in the universe. …
The growth of density perturbations in an expanding universe in the non-linear regime is investigated. The underlying equations of motion are cast in a suggestive form, and motivate a conjecture that the scaled pair velocity, $h(a,x)\equiv -[v/(\dot{a}x)]$ depends on the expansion factor $a$ and comoving coordinate $x$ only through the density contrast $σ(a,x)$. This leads to the result that the true, non-linear, density contrast $<(δρ/ρ)^{2}_{x}>^{1/2}=σ(a,x)$ is a universal function of the density contrast $σ_L(a,l)$, computed in the linear theory and evaluated at a scale $l$ where $l=x(1+σ^…
We present a search for binary neutron star mergers that produced gravitational-waves during the first observing run of Advanced LIGO and gamma-ray emission seen by either \textit{Swift}-BAT or Fermi-GBM, similar to GW170817 and GRB 170817A. We introduce a new method using a combined ranking statistic to detect sources that do not produce significant gravitational-wave or gamma-ray burst candidates individually. The current version of this search can increase by 70% the detections of joint gravitational-wave and gamma-ray signals. We find one possible candidate observed by LIGO and Fermi-GBM, …
To explain the rich structure of voids, clusters, sheets, and filaments apparent in the Universe, we present evidence for the convergence of the two classic approaches to gravitational clustering, the ``pancake'' and ``hierarchical'' pictures. We compare these two models by looking at agreement between individual structures -- the ``pancakes'' which are characteristic of the Zel'dovich Approximation (ZA) and also appear in hierarchical N-body simulations. We find that we can predict the orientation and position of N-body simulation objects rather well, with decreasing accuracy for increasing l…
Large redshift surveys of galaxies and clusters are providing the first opportunities to search for distortions in the observed pattern of large-scale structure due to such effects as gravitational redshift. We focus on non-linear scales and apply a quasi-Newtonian approach using N-body simulations to predict the small asymmetries in the cross-correlation function of two galaxy different populations. Following recent work by Bonvin et al., Zhao and Peacock and Kaiser on galaxy clusters, we include effects which enter at the same order as gravitational redshift: the transverse Doppler effect, l…
The black hole merging rates inferred after the gravitational-wave detection by Advanced LIGO/VIRGO and the relatively high mass of the progenitors are consistent with models of dark matter made of massive primordial black holes (PBH). PBH binaries emit gravitational waves in a broad range of frequencies that will be probed by future space interferometers (LISA) and pulsar timing arrays (PTA). The amplitude of the stochastic gravitational-wave background expected for PBH dark matter is calculated taking into account various effects such as initial eccentricity of binaries, PBH velocities, mass…
GW number count can be used as a novel tracer of the large scale structure (LSS) in the luminosity distance space (LDS), just like galaxies in the redshift space. It is possible to obtain the $D_L-D_A$ duality relation with clustering effect. However, several LSS induced errors will contaminate the GW luminosity distance measurement, such as the peculiar velocity dispersion error of the host galaxy as well as the foreground lensing magnification. The distance uncertainties induced from these effects will degrade the GW clustering from a spectroscopic-like data down to a photometric-like data. …
