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Assurance cases offer a structured way to present arguments and evidence for certification of systems where safety and security are critical. However, creating and evaluating these assurance cases can be complex and challenging, even for systems of moderate complexity. Therefore, there is a growing need to develop new automation methods for these tasks. While most existing assurance case tools focus on automating structural aspects, they lack the ability to fully assess the semantic coherence and correctness of the assurance arguments. In prior work, we introduced the Assurance 2.0 framework that prioritizes the reasoning process, evidence utilization, and explicit delineation of counter-claims (defeaters) and counter-evidence. In this paper, we present our approach to enhancing Assurance 2.0 with semantic rule-based analysis capabilities using common-sense reasoning and answer set programming solvers, specifically s(CASP). By employing these analysis techniques, we examine the unique semantic aspects of assurance cases, such as logical consistency, adequacy, indefeasibility, etc. The application of these analyses provides both system developers and evaluators with increased confidence about the assurance case.

Building upon the statistical formulation for parameter estimation in the presence of correlated noise proposed by Cireddu et al., we present an initial study to incorporate the effects of correlated noise into the analyses of various detector designs' performance. We consider a two L-shaped detector configuration located in the European Union, and compare the expectation of parameter estimation between the non-colocated and a hypothetical colocated configurations. In our study, we posit the existence of low-frequency correlated noise within the $5\text{ Hz}$ to $10\text{ Hz}$ range for the colocated detector configuration, with a varying degree of correlation. In this specific detector setup, our observations indicate an enhancement in the precision of intrinsic parameter measurements as the degree of correlation increases. This trend suggests that higher degrees of noise correlation may beneficially influence the accuracy of parameter estimation. In particular, when the noise is highly correlated, the uncertainty on chirp mass decreases by up to $30\%$. The absence of an inter-European baseline does hinder the estimation of the extrinsic parameters. However, given a realistic global network with the additional detector located in the United States, the uncertainty of extrinsic parameters is significantly reduced. This reduction is further amplified as the degree of noise correlation increases. When noise correlation exceeds a certain level, the colocated configuration outperforms the non-colocated one, reducing the $90\%$ credible area of sky location by up to $10\%$. We conclude that noise correlation significantly impacts detector performance, potentially altering both quantitative and qualitative outcomes. Thus, we recommend including noise correlation in comprehensive assessments of third-generation gravitational wave detector designs., Comment: 10 pages, 2 figures

The Einstein Telescope faces a critical data analysis challenge with correlated noise, often overlooked in current parameter estimation analyses. We address this issue by presenting the statistical formulation of the likelihood function that includes correlated noise for the Einstein Telescope or any detector network. Neglecting these correlations may significantly reduce parameter estimation accuracy, even leading to the failure to reconstruct otherwise resolvable signals. This emphasizes how critical a proper treatment of correlated noise is, as presented in this work, to unlocking the wealth of results promised by the Einstein Telescope., Comment: 7 pages, 3 figures

Since the first detection of gravitational waves in 2015, gravitational-wave astronomy has emerged as a rapidly advancing field that holds great potential for studying the cosmos, from probing the properties of black holes to testing the limits of our current understanding of gravity. One important aspect of gravitational-wave astronomy is the phenomenon of gravitational lensing, where massive intervening objects can bend and magnify gravitational waves, providing a unique way to probe the distribution of matter in the universe, as well as finding applications to fundamental physics, astrophysics, and cosmology. However, current models for gravitational-wave millilensing - a specific form of lensing where small-scale astrophysical objects can split a gravitational wave signal into multiple copies - are often limited to simple isolated lenses, which is not realistic for complex lensing scenarios. In this paper, we present a novel phenomenological approach to incorporate millilensing in data analysis in a model-independent fashion. Our approach enables the recovery of arbitrary lens configurations without the need for extensive computational lens modeling, making it a more accurate and computationally efficient tool for studying the distribution of matter in the universe using gravitational-wave signals. When gravitational-wave lensing observations become possible, our method can provide a powerful tool for studying complex lens configurations, including dark matter subhalos and MACHOs., Comment: 12 pages, 8 figures

We present the first systematic search for exotic compact mergers in Advanced LIGO and Virgo events. We compare the short gravitational-wave signals GW190521, GW190426$\_$190642, GW200220$\_$061928 and the trigger 200114$\_$020818 (or S200114f) to a new catalogue of 759 numerical simulations of head-on mergers of horizonless exotic compact objects known as Proca stars, interpreted as self-gravitating lumps of (fuzzy) dark matter sourced by an ultralight (vector) bosonic particle. The Proca-star merger hypothesis is strongly rejected with respect to the black hole merger one by GW190426, weakly rejected by GW200220 and weakly favoured by GW190521 and S200114f. GW190521 and GW200220 yield highly consistent boson masses of $\mu_{\rm B} = 8.69^{+0.61}_{-0.75}\times10^{-13}$ eV and $\mu_{\rm B} = 9.13^{+1.18}_{-1.30}\times10^{-13}$ eV at the $90\%$ credible level. We conduct a preliminary population study of the compact binaries behind these events. Excluding (including) S200114f as a real event, and ignoring boson-mass consistencies across events, we estimate a fraction of Proca-star mergers of $\zeta = 0.27^{+0.43}_{-0.25} \ (0.39^{+0.38}_{-0.33})$. We discuss the impact of boson-mass consistency across events in such estimates. Our results maintain GW190521 as a Proca-star merger candidate and pave the way towards population studies considering exotic compact objects., Comment: Version accepted in Phys.Rev.D. 27 pages, 16 Figures, 4 Appendixes

Detection and parameter inference of gravitational-wave signals \ncor{from compact mergers} rely on the comparison of the incoming detector strain data $d(t)$ to waveform templates for the gravitational-wave strain $h(t)$ that ultimately rely on the resolution of Einstein's equations via numerical relativity simulations. These, however, commonly output a quantity known as the Newman-Penrose scalar $\psi_4(t)$ which, under the Bondi gauge, is related to the gravitational-wave strain by $\psi_4(t)=\mathrm{d}^2h(t) / \mathrm{d}t^2$. Therefore, obtaining strain templates involves an integration process that introduces artefacts that need to be treated in a rather manual way. By taking second-order finite differences on the detector data and inferring the corresponding background noise distribution, we develop a framework to perform gravitational-wave data analysis directly using $\psi_4(t)$ templates. We first demonstrate this formalism, and the impact of integration artefacts in strain templates, through the recovery of numerically simulated signals from head-on collisions of Proca stars injected in Advanced LIGO noise. Next, we re-analyse the event GW190521 under the hypothesis of a Proca-star merger, obtaining results equivalent to those in Ref.[1], where we used the classical strain framework. We find, however, that integration errors would strongly impact our analysis if GW190521 was four times louder. Finally, we show that our framework fixes significant biases in the interpretation of the high-mass GW trigger S200114f arising from the usage of strain templates. We remove the need to obtain strain waveforms from numerical relativity simulations, avoiding the associated systematic errors., Comment: Version accepted for publication in Physical Review X. 27 pages, 11 Figures, 3 Appendixes

When a gravitational wave passes by a massive object, its trajectory gets curved which can result in multiple images separated by a time delay, a phenomenon known as strong lensing. Although gravitational wave lensing has not been observed yet, it is currently predicted that it will be possible to detect with third-generation detectors. Moreover, the future detectors are expected to significantly increase the gravitational-wave detection rate up to $O(10^5 - 10^6)$ $\mathrm{yr}^{-1}$ which could also increase the chance of observing gravitational wave lensing. Therefore, it is necessary to develop accurate and efficient tools to filter potentially lensed gravitational-wave signal pairs. In the study, we propose three statistics to analyze the overlap of two sky localization probability maps, which could provide a quick preliminary lensing analysis of two gravitational-wave signals within 3 seconds. We simulate 200 lensed pairs of gravitational-wave signals for 5 signal-to-noise ratios to investigate the performance of the search methodology. By setting up a threshold with a specific false positive rate $\mathrm{FPR} = 10^{-2}$ for the three overlap statistics, we conclude that it is possible to filter out more than $99\%$ of the non-lensed event pairs while keeping all lensed event pairs., Comment: 8 pages, 3 figures, 2 tables

The proposed third-generation gravitational-wave detectors Einstein Telescope will have a triangular design that consists of three colocated interferometers. Summing the strain outputs from the three interferometers will cancel any gravitational-wave signal and the resultant signal-free stream is known as null stream. The null stream is in a fixed subspace of the observation space of Einstein telescope where no gravitational-wave signal can exist. In this paper, we establish the decomposition of the observation space of Einstein Telescope into the signal space that contains all possible gravitational-wave signals and the null space that contains the null stream. We show that the results of Bayesian parameter estimation and model selection using the strain data in the signal space are identical to that using the full set of strain data. This implies that one could use a fraction of the strain data to extract all information of the source which reduces the memory usage and speeds up the likelihood evaluation. We also discuss the existence of a fixed null space in Einstein Telescope allows the unbiased estimation of the noise properties in the signal-free subspace., Comment: 9 pages

We present a null-stream-based Bayesian unmodeled framework to probe generic gravitational-wave polarizations. Generic metric theories allow six gravitational-wave polarization states, but general relativity only permits the existence of two of them namely the tensorial polarizations. The strain signal measured by an interferometer is a linear combination of the polarization modes and such a linear combination depends on the geometry of the detector and the source location. The detector network of Advanced LIGO and Advanced Virgo allows us to measure different linear combinations of the polarization modes and therefore we can constrain the polarization content by analyzing how the polarization modes are linearly combined. We propose the basis formulation to construct a null stream along the polarization basis modes without requiring modeling the basis explicitly. We conduct a mock data study and we show that the framework is capable of probing pure and mixed polarizations in the Advanced LIGO-Advanced Virgo 3-detector network without knowing the sky location of the source from electromagnetic counterparts. We also discuss the effect of the presence of the uncaptured orthogonal polarization component in the framework, and we propose using the plug-in method to test the existence of the orthogonal polarizations., Comment: 26 pages, 20 figures

The detection of gravitational wave signals by Advanced LIGO and Advanced Virgo enables us to probe the polarization content of gravitational waves. In general relativity, only tensor modes are present, while in a variety of alternative theories one can also have vector or scalar modes. Recently test were performed which compared Bayesian evidences for the hypotheses that either purely tensor, purely vector, or purely scalar polarizations were present. Indeed, with only three detectors in a network and allowing for mixtures of tensor polarizations and alternative polarization states, it is not possible to identify precisely which non-standard polarizations might be in the signal and by what amounts. However, we demonstrate that one can still infer whether, in addition to tensor polarizations, alternative polarizations are present in the first place, irrespective of the detailed polarization content. We develop two methods to do this for sources with electromagnetic counterparts, both based on the so-called null stream. Apart from being able to detect mixtures of tensor and alternative polarizations, these have the added advantage that no waveform models are needed, and signals from any kind of transient source with known sky position can be used. Both formalisms allow us to combine information from multiple sources so as to arrive at increasingly more stringent bounds. For now we apply these on the binary neutron star signal GW170817, showing consistency with the tensor-only hypothesis with p-values of 0.315 and 0.790 for the two methods., Comment: 8 pages, 3 figures