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Finding a stochastic gravitational-wave background (SGWB) of astrophysical or primordial origin is one of the quests of current and future gravitational-wave observatories. While detector networks such as LIGO-Virgo-Kagra or pulsar timing arrays can use cross-correlations to tell instrumental noise and SGWB apart, LISA is likely to be the only flying detector of its kind in 2035. This particularity poses a challenge for data analysis. To tackle it, we present a strategy based on Bayesian model selection. We use a flexible noise power spectral density~(PSD) model and the knowledge of noise and signal transfer functions to allow SGWBs detection when the noise PSD is unknown. With this technique, we then probe the parameter space accessible by LISA for power-law SGWB shapes., 5 pages, 1 figure, contribution to the 2023 Gravitation session of the 57th Rencontres de Moriond

In recent years, the field of Gravitational Wave Astronomy has flourished. With the advent of more sophisticated ground-based detectors and space-based observatories, it is anticipated that Gravitational Wave events will be detected at a much higher rate in the near future. One of the future data analysis challenges, is performing robust statistical inference in the presence of detector noise transients or non-stationarities, as well as in the presence of stochastic Gravitational Wave signals of possible astrophysical origin. The incomplete knowledge of instrumental noise can introduce bias in parameter estimation of detected sources. Here, we propose a heavier-tailed likelihood filter based on the Generalized Hyperbolic distribution. With the Hyperbolic likelihood we obtain a robust data analysis framework against data outliers, noise non-stationarities, and possible inaccurate modeling of the noise power spectral density. We apply this methodology to examples drawn from gravitational wave astronomy, and in particular using synthetic data sets from the planned LISA mission, demonstrating its effectiveness in improving parameter estimation accuracy. Our findings suggest that the use of heavier-tailed likelihoods can significantly improve the robustness of statistical inference in Gravitational Wave Astronomy., 16 pages, 6 figures

We use the latest constraints on the population of stellar origin binary black holes (SOBBH) from LIGO/Virgo/KAGRA (LVK) observations, to estimate the stochastic gravitational wave background (SGWB) they generate in the frequency band of LISA. We account for the faint and distant binaries, which contribute the most to the SGWB, by extending the merger rate at high redshift assuming it tracks the star formation rate. We adopt different methods to compute the SGWB signal: an analytical evaluation, Monte Carlo sums over SOBBH population realisations, and a method that accounts for the role of the detector by simulating LISA data and iteratively removing resolvable signals until only the confusion noise is left, allowing for the extraction of both the expected SGWB and the number of resolvable SOBBHs. Since the latter are few for SNR thresholds larger than five, we confirm that the spectral shape of the SGWB in the LISA band follows the analytical prediction of a power law. We infer the probability distribution of the SGWB amplitude from the LVK GWTC-3 posterior of the binary population model; its interquartile range of $h^2\Omega_\mathrm{GW}(f=3\times10^{-3}\,\mathrm{Hz}) \in [5.65,\,11.5]\times10^{-13}$ is in agreement with most previous estimates. We perform a MC analysis to assess LISA's capability to detect and characterise this signal. Accounting for both the instrumental noise and the galactic binaries foreground, with four years of data, LISA will be able to detect the SOBBH SGWB with percent accuracy, narrowing down the uncertainty on the amplitude by one order of magnitude with respect to the range of possible amplitudes inferred from the population model. A measurement of this signal by LISA will help to break the degeneracy among some of the population parameters, and provide interesting constraints, in particular on the redshift evolution of the SOBBH merger rate., Comment: 39 pages, 15 figures. Prepared for submission to JCAP

International audience; Extreme mass ratio inspirals (EMRIs) are among the primary targets for the Laser Interferometer Space Antenna (LISA). The extreme mass ratios of these systems result in relatively weak GW signals, that can be individually resolved only for cosmologically nearby sources (up to $z\approx2$). The incoherent piling up of the signal emitted by unresolved EMRIs generate a confusion noise, that can be formally treated as a stochastic GW background (GWB). In this paper, we estimate the level of this background considering a collection of astrophysically motivated EMRI models, spanning the range of uncertainties affecting EMRI formation. To this end, we employed the innovative Augmented Analytic Kludge waveforms and used the full LISA response function. For each model, we compute the GWB SNR and the number of resolvable sources. Compared to simplified computations of the EMRI signals from the literature, we find that for a given model the GWB SNR is lower by a factor of $\approx 2$ whereas the number of resolvable sources drops by a factor 3-to-5. Nonetheless, the vast majority of the models result in potentially detectable GWB which can also significantly contribute to the overall LISA noise budget in the 1-10 mHz frequency range.

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case. Bayesian inference has been very successful because this technique provides a representation of the parameters as a posterior probability distribution, with uncertainties informed by the precision of the experimental measurements. During the last couple of decades, many specific advances have been proposed and employed in order to solve a large variety of different problems. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm that integrates many of those concepts into a single MCMC package. For this purpose, we have built {\tt Eryn}, a user-friendly and multipurpose toolbox for Bayesian inference, which can be utilized for solving parameter estimation and model selection problems, ranging from simple inference questions, to those with large-scale model variation requiring trans-dimensional MCMC methods, like the LISA global fit problem. In this paper, we describe this sampler package and illustrate its capabilities on a variety of use cases., Comment: 21 pages, 7 figures

Detecting stochastic background radiation of cosmological origin is an exciting possibility for current and future gravitational-wave (GW) detectors. However, distinguishing it from other stochastic processes, such as instrumental noise and astrophysical backgrounds, is challenging. It is even more delicate for the space-based GW observatory LISA since it cannot correlate its observations with other detectors, unlike today's terrestrial network. Nonetheless, with multiple measurements across the constellation and high accuracy in the noise level, detection is still possible. In the context of GW background detection, previous studies have assumed that instrumental noise has a known, possibly parameterized, spectral shape. To make our analysis robust against imperfect knowledge of the instrumental noise, we challenge this crucial assumption and assume that the single-link interferometric noises have an arbitrary and unknown spectrum. We investigate possible ways of separating instrumental and GW contributions by using realistic LISA data simulations with time-varying arms and second-generation time-delay interferometry. By fitting a generic spline model to the interferometer noise and a power-law template to the signal, we can detect GW stochastic backgrounds up to energy density levels comparable with fixed-shape models. We also demonstrate that we can probe a region of the GW background parameter space that today's detectors cannot access., Comment: 15 pages, 10 figures. Added references and minor changes

Gravitational-wave science is rapidly growing in maturity as a research area; in May 2021 the next generation of gravitational-wave scientists gathered together to create a vision of the future of the field. Non

et al., The science objectives of the LISA mission have been defined under the implicit assumption of a 4-years continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of ≈0.75 , which would reduce the effective span of usable data to 3 years. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 years of mission operations is recommended., C.P.L. Berry is supported by the CIERA Board of Visitors Professorship. E. Berti is supported by NSF Grants No. PHY-1912550 and AST-2006538, NASA ATP Grants No. 17-ATP17-0225 and 19-ATP19-0051, NSF-XSEDE Grant No. PHY-090003, and NSF Grant PHY-20043. D. Blas acknowledges support from the Fundación Jesus Serra and the Instituto de Astrofísica de Canarias under the Visiting Researcher Programme 2021 agreed between both institutions. T. Bogdanović acknowledges the support by the National Aeronautics and Space Administration (NASA) under award No. 80NSSC19K0319 and by the National Science Foundation (NSF) under Award No. 1908042. V. Cardoso acknowledges financial support provided under the European Union’s H2020 ERC Consolidator Grant “Matter and strong-field gravity: New frontiers in Einstein’s theory” Grant Agreement No. MaGRaTh–646597. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101007855. We thank FCT for financial support through Projects No. UIDB/00099/2020 and through grants PTDC/MAT-APL/30043/2017 and PTDC/FIS-AST/7002/2020. H.-Y. Chen is supported by NASA through NASA Hubble Fellowship Grants No. HST-HF2-51452.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. Z. Haiman acknowledges support by NASA Grant NNX15AB19G and NSF Grants AST-2006176 and AST-1715661. G. Nardini is partly supported by the ROMFORSK Grant Project. No. 302640 “Gravitational Wave Signals From Early Universe Phase Transitions”. P. Pani acknowledges financial support provided under the European Union’s H2020 ERC, Starting Grant Agreement No. DarkGRA–757480. He also acknowledges support under the MIUR PRIN and FARE programmes (GW-NEXT, CUP: B84I20000100001), and by the Amaldi Research Center funded by the MIUR program “Dipartimento di Eccellenza” (CUP: B81I18001170001). A. Sesana acknowledges financial support provided under the European Union’s H2020 ERC Consolidator Grant “Binary Massive Black Hole Astrophysics” (B Massive, Grant Agreement: 818691). K. Yagi acknowledges support from NSF Grant PHY-1806776, NASA Grant 80NSSC20K0523, a Sloan Foundation Research Fellowship and the Owens Family Foundation. D. J. Weir was supported by a Science and Technology Facilities Council Ernest Rutherford Fellowship, Grant no. ST/R003904/1, and by the Academy of Finland, Grants 324882 and 328958. A. Zimmerman is supported by NSF Grant No. PHY-1912578. The authors would like to acknowledge networking support by the GWverse COST Action CA16104, “Black holes, gravitational waves and fundamental physics.” The Flatiron Institute is supported by the Simons Foundation. This research has made use of data, software and web tools obtained from the Gravitational Wave Open Science Center (www.gw-openscience.org/), a service of LIGO Laboratory, the LIGO Scientific Collaboration and the Virgo Collaboration. LIGO Laboratory and Advanced LIGO are funded by the United States National Science Foundation (NSF) as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. Virgo is funded, through the European Gravitational Observatory (EGO), by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain.

Gravitational wave science is a dynamical, fast-expanding research field founded on results, tools and methodologies drawn from different research areas and communities. Early career scientists entering this field must learn and combine knowledge and techniques from a range of disciplines. The Workshop on Gravitational-Wave Astrophysics for Early Career Scientists (GWAECS), held virtually in May 2021, planted the seeds of an interdisciplinary, well-connected and all-inclusive community of early career scientists working on gravitational waves, able to exchange relevant information and ideas, build a healthy professional and international environment, share and learn valuable skills, and ensure that ongoing research efforts are perpetuated and expanded in order to attain the main scientific goals envisioned by the whole community. GWAECS was the first event unifying early career scientists belonging to different communities, historically associated with different large-scale gravitational wave experiments. It provided a broad perspective on the future of gravitational waves, offered training on soft and transferable skills and allowed ample time for informal discussions between early career scientists and well-known research experts. The essence of those activities is summarised and collected in the present document, which presents a recap of each session of the workshop and aims to provide all early career scientists with a long-lasting, useful reference which constitutes the legacy of all the ideas that circulated at GWAECS., Comment: 60 pages, 12 figures; Legacy document of the Workshop on Gravitational Wave Astrophysics for Early Career Scientists (GW{\AE}CS), Lorentz Center Workshop, online, 3-7 May 2021

The Laser Interferometer Space Antenna will be the first Gravitational Wave observatory in space developed by the European Space Agency. It is scheduled to fly in the early 2030's. LISA design predicts sensitivity levels that 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 obtain the posterior probability to measure this signal in a set of frequency bins, combining information from all the available data channels. We use this methodology in order to obtain an efficient and computationally cheap first assessment of the stochastic gravitational wave backgrounds, but also generate sensible prior densities for more computationally expensive template-based searches. We also derive useful detectability bounds as a function of frequency and prior knowledge on the instrumental noise spectrum.

A statistical procedure for the analysis of time-frequency noise maps is presented and applied to LISA Pathfinder mission synthetic data. The procedure is based on the Kolmogorov-Smirnov like test that is applied to the analysis of time-frequency noise maps produced with the spectrogram technique. The influence of the finite size windowing on the statistic of the test is calculated with a Monte Carlo simulation for 4 different windows type. Such calculation demonstrate that the test statistic is modified by the correlations introduced in the spectrum by the finite size of the window and by the correlations between different time bins originated by overlapping between windowed segments. The application of the test procedure to LISA Pathfinder data demonstrates the test capability of detecting non-stationary features in a noise time series that is simulating low frequency non-stationary noise in the system., Experimental Astronomy, 39 (1), ISSN:0922-6435, ISSN:1572-9508

Les ones gravitatòries són una predicció de la teoria de la Relativitat General d’Einstein, la detecció i anàlisi de les quals obrirà una nova àrea en el nostre coneixement de l’Univers. En efecte, aquestes ones porten informació de sistemes amb gravetat molt forta i que són molt difícils d’observar amb instruments convencionals, basats en la detecció de llum, per a qual cosa el nostre coneixement actual només en pot ser parcial. Avui en dia tenim evidències experimentals de l’existència de les ones gravitatòries, com la variació del període orbital del pulsar binari PSRB1913+16 (Premi Nobel 1993). Tot i això, encara no se n’ha pogut obtenir una detecció. La comunitat científica té doncs un gran interès en assolir aquesta detecció com es demostra per la quantitat d’observatoris repartits arreu del món: LIGO (Estats Units), VIRGO (Italia, França), GEO600 (Alemanya, Regne Unit), LCGT (Japó), etc. La missió LISA (Laser Interferomer Space Antenna) és una proposta per posar un d’aquests observatoris en òrbita heliocèntrica mitjançant tres satèl.lits que contindrien masses en caiguda lliure la distància entre les quals es mesuraria mitjançant interferometria laser. El link laser connectaria els diferents satèl.lits que es trobarien separats 1 mil.lió de quilòmetres, conseguint una configuració triangular que seguiria la Terra en la seva òrbita. Aquesta proposta ha estat acceptada per l’Agència Espacia Europea l’any 2013 en el seu pla científic, com el tema d’una missió que seria llançada en la decàda del 2030. Aquesta tesis s’emmarca dins la missió LISA Pathfinder, que és la missió precursora de LISA i que té data de llançament el 2015. Aquesta missió posarà a proba la tecnologia que requereix la futura missió LISA i per això conté els principals elements (laser, massa de test, etc.) però en una versió reduïda i en un únic satèl.lit. L’objectiu científic principal és aconseguir mesurar l’acceleració relativa entre dues masses en caiguda lliure fins a nivells de 10^(-14) m / s^2 / Hz ^(1/2) en la banda de molt baixa freqüència, és a dir 1mHz. La tesis desenvolupa els mètodes coneguts com a Markov Chain Monte Carlo (MCMC), els quals s’utilitzen, entre d’altres, per a l’estimació de paràmetres. Aquestes tècniques han estat posades a proba en els darrers anys mitjançant diferents campanyes amb dades simulades i actualment formen part del LTPDA, una toolbox de MATLAB desenvolupada per la col.laboració per a l’anàlisis de les dades de la missió. El treball en aquesta tesis descriu en detall l’aplicació d’aquests tècniques a per a l’estimació dels paràmetres que descriuen la dinàmica de la massa de test a l’interior del satèl.lit. De la mateixa manera, s’han desenvolupat tècniques estadístiques més enllà de l’estimació de paràmetres per tal d’aplicar-les al que es coneix com a selecció del models, és a dir, l’evaluació estadistíca de diferents models per determinar quin és el que permet una millor descripció de les dades. En aquest aspecte s’han evaluat les diferents opcions existents en la literatura i, en particular, s’ha establert el Reversible Jump Markov Chain Monte Carlo (RJMCMC) com una eina per a poder a duu a terme aquests estudis. Aquesta tècnica permet la comparació de models de diferent dimensionalitat, representat una generalització dels mètodes MCMC. Les tècniques i resultats obtinguts en aquesta tesis es posaran en pràctica durant les operacions de la missió LISA Pathfinder, la qual obrirà el camí cap a la futura detecció d’ones gravitatòries a l’espai., Gravitational waves are a prediction of Einstein's General Relativity, the detection and analysis of which will open a new area in our understanding of the Universe. Indeed, these waves carry information from systems with strong gravity and are very difficult to observe with conventional instruments, which are based on the detection of light. Today, we have experimental evidence of the existence of gravitational waves, as the variation of the orbital period of the binary pulsar PSRB1913 + 16 (Nobel Prize 1993). However, there has been no detection. The scientific community is pursuing this detection with several observatories spread around the world: LIGO (USA), VIRGO (Italy, France), GEO600 (Germany, UK), LCGT (Japan ), etc. LISA (Laser Interferomer Space Antenna) is a proposal to put one of these observatories in heliocentric orbit using three satellites that contain masses in free fall. A laser interferometer is used to measure the distance between them. The satellites will be separated 1 Mkm, resulting in a triangular configuration that follows the Earth in its orbit. This proposal was accepted by the European Agency Espacia in 2013, as the subject of a mission to be launched in the early 2030's. This thesis is part of the LISA Pathfinder mission, which is the precursor mission of LISA and has a release date in 2015. This mission will test the technology required for the future LISA mission and therefore contains the main elements (laser, test mass, etc.) but in a smaller version and in a single satellite. The main scientific objective is to measure the relative acceleration between two masses in free fall to levels down to 10^(-14) m / s^2 / Hz ^(1/2) in the low frequency band, i.e. 1mHz. This thesis develops the methods known as Markov Chain Monte Carlo (MCMC), which are used, among others, for the estimation of parameters. These techniques have been put to the test in recent years through various campaigns with simulated data and are currently part of the LTPDA, a MATLAB toolbox developed by the collaboration for the analysis of data from the mission. The work in this thesis describes in detail the application of these techniques to estimate the parameters that describe the dynamics of the test mass inside the satellite. Similarly, we have developed statistical techniques beyond the estimation of parameters in order to apply them to what is known as model selection, i.e. the evaluation of different statistical models to determine which one allows a better description of the data. In this respect, we have evaluated the different options available in the literature and, in particular, we have established the Reversible Jump Markov Chain Monte Carlo (RJMCMC) as a tool to carry out these studies during operations. This technique allows the comparison of models of different dimensionality, which represents a generalization of the MCMC methods. The techniques and results obtained in this thesis will be used during the operations of the LISA Pathfinder mission, which will open the way for future detection of gravitational waves in space.

The thermal experiments to be carried out onboard LISA Pathfinder (LPF) will provide essential information of the dependences of the instrument with respect to temperature variations. These thermal experiments must be modelled and simulated both to be validated for mission operations purposes and also to develop a data analysis tool able to characterise the temperature noise contribution to the instrument performance. Here we will present the models developed and the simulated signals for some of the experiments together with the corresponding interferometer readouts, the latter being computed by combining the thermal models with the global LTP (LISA Technology Package) simulator of the LTP Data Analysis team., Submitted to ASP Conference Series for the Proceedings of the 9th International LISA Symposium, 21-25 May 2012, Paris

The STOC (Science and Technology Operations Centre) simulator of the LPF (LISA PathFinder) mission is intended to provide a validation tool for the mission operations tele-commanding chain, as well as for a deeper understanding of the underlying physical processes happening in the LTP (LISA Technology Package). Amongst the different physical effects that will appear onboard, temperature fluctuations in the Electrode Housing (EH) could generate disturbances on the interferometer (IFO) readouts, therefore they must be known and controlled. In this article we report on the latest progress in the analysis at IEEC of the LTP response to thermal signals injected by means of heaters. More specifically, we determine the transfer functions relating heat input signals to forces on the Test Masses (TMs) in the LTP frequency band, from 1 mHz to 30 mHz. A complete thermal model of the entire LPF spacecraft plus payload, elaborated and maintained at European Space Technology Center (ESTEC), was used to obtain temperature distributions in response to heat inputs at prescribed spots (heaters), which are later processed to calculate the associated dynamical effects on the Test Masses., Comment: Submitted to JPCS for the Proceedings of the 8th LISA Symposium (2011)

International audience; The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.