Figure 7 - available via license: Creative Commons Attribution 4.0 International
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Time evolution of the response functioñ R G LL,AA (f, t) during one year, for two specific frequencies chosen as an example. Only the real part is shown, as the imaginary part is sub-dominant. The points are the numerical values used in our analysis (taken with a time interval of one day), while the solid line is the fitting function (C.1), with A = 0.185 in both cases.
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We employ the formalism developed in [1] and [2] to study the prospect of detecting an anisotropic Stochastic Gravitational Wave Background (SGWB) with the Laser Interferometer Space Antenna (LISA) alone, and combined with the proposed space-based interferometer Taiji. Previous analyses have been performed in the frequency domain only. Here, we stu...
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... let us consider the signal from the galaxy, which, due to its angular distribution displayed in figure 6, induces a time-frequency response function (5.6) that is well fit by where G OO ′ (f ) is a function of the frequency only and A is the relative amplitude of the modulation of the galactic signal in the orbit of LISA as a function of time. Figure 7 shows the goodness of the fit for two frequencies in the A channel. We note that the modulation is the same for all frequencies (namely, A is constant, and no frequency-dependent phase is present in the argument of the cosine) as a consequence of the factorization of the angular and frequency dependencies in the galactic signal in equation (5.1). ...
Citations
... One could also think of recursive schemes by which we first fix ℓ = 0, 1 via the MCMC before fitting for ℓ = 2 only. It should be noted, however, that the correlations between the monopole and anisotropies are also partly driven by LISA's complex and non-compact sky response functions [38] (see also [69,70]). Accounting for this factor introduces an additional layer of complexity to the analysis. At this stage, we defer a deeper investigation of these issues to future work and highlight that for the model-dependent fit such complications do not arise. ...
We propose a diagnostic tool for future analyses of stochastic gravitational wave background signals of extra-galactic origin in LISA data. Next-generation gravitational wave detectors hold the capability to track unresolved gravitational waves bundled into a stochastic background. This composite background contains cosmological and astrophysical contributions, the exploration of which offers promising avenues for groundbreaking new insights into very early universe cosmology as well as late-time structure formation. In this article, we develop a full end-to-end pipeline for the extraction of extra-galactic signals, based on kinematic anisotropies arising from the galactic motion, via full-time-domain simulations of LISA's response to the gravitational wave anisotropic sky. Employing a Markov-Chain-Monte-Carlo map-making scheme, multipoles up to ℓ=2 are recovered for scale-free spectra in the case of a high signal-to-noise ratio. We demonstrate that our analysis is consistently beating sample variance and is robust against statistical and systematic errors. The impact of instrumental noise on the extraction of kinematic anisotropies is investigated, and we establish a detection threshold of Ω GW ≳ 5 × 10⁻⁸ in the presence of instrument-induced noise. Potential avenues for improvement in our methodology are highlighted.
... Similarly [24,25] used a parametric signal and noise model in a mixed time-frequency basis and modeled the confusion noise as an isotropic, intrinsically cyclo-stationary signal. The BLIP package in [26,27] models stochastic signals as intrinsically stationary but anisotropic, and recovers their sky distributions from their extrinsic nonstationarity. Both works use a fully parametrized instrument and signal model, but consider a non-parametric sky localization with a spherical harmonic basis. ...
The Laser Interferometer Space Antenna (LISA) mission poses a difficult parameter estimation challenge: the sources will be so dense in both time and frequency that they all must be fit simultaneously in a `global fit'. Successful tests of global fit efforts on synthetic datasets have been recently reported, recovering extra-galactic black hole mergers and galactic binaries, including the pipeline in arXiv:2301.03673. Injected stochastic sources, however, have so far been absent in these datasets. In this work we report our development of a stochastic search pipeline ready for inclusion in future tests of the global fit, capable of detecting or placing limits on a wide variety of possible cosmologically- and astrophysically-inspired SGWBs. The code uses short-time Fourier transforms (STFTs) to allow for inference despite the non-stationarity of the noise. We quote results using both purely synthetic confusion noise and two residuals, and quantify the impact of the residuals' non-gaussianity on injected signal recovery and on setting upper limits. We find that, if not properly mitigated, non-gaussianities can preclude setting accurate SGWB upper limits and lead to false detections. We also stress that the narrow-band non-gaussianities we find do not affect all sources equally, and many narrower-band, cosmologically-inspired SGWBs are more sensitive to non-gaussianity than others.
... As for the former, one can naturally imagine the presence of small differences among the noises in the six links. Regarding the latter, it is known that, with realistic orbits, LISA will not be perfectly equilateral with non-static arm-lengths that vary at the percent level [76] (see also Appendix A of [77]). ...
... Due to the angular dependence of the response functions and the yearly orbit of LISA, this component, dubbed Galactic foreground, is known to have an annual modulation. In principle, this feature can be used to separate the Galactic component from the other contributions considered to be stationary, e.g., by properly taking into account the variation in each chunk [29,53,77]. However, reconstruction with such a procedure is inevitably sensitive to uncertainties due to the non-stationarity of noise and data gaps. ...
... For example, this would be relevant to investigate, e.g., anisotropic SGWBs or non-stationarities in the signal or the noise. For previous studies on these topics see [55,77,[88][89][90][91][92]. Moreover, JAX compatibility allows for further code upgrades. ...
In the search for stochastic gravitational wave backgrounds (SGWB) of cosmological origin with LISA, it is crucial to account for realistic complications in the noise and astrophysical foreground modeling that may impact the signal reconstruction. To address these challenges, we updated the code to incorporate both variable noise levels across LISA arms and more complex foreground spectral shapes. Our findings suggest that, while moderate variations of the noise amplitudes have a minimal impact, poor foreground modeling (i.e., templates requiring many free parameters) significantly degrades the reconstruction of cosmological signals. This underlines the importance of accurate modeling and subtraction of the astrophysical foregrounds to characterize possible cosmological components. To perform this more challenging analysis, we have integrated the framework, which significantly improves the computational efficiency of the code, in the code, enabling faster Bayesian likelihood sampling and more effective exploration of complex SGWB signals.
... The relevance of such statistical property is twofold: it allows to better characterize the Milky Way (MW) foreground, and it facilitates the study and identification of other signals. It has been studied in previous works [16,17], although it has typically been modeled using empirical formulas. However, Ref. [18] has introduced a physically based, parameterized template that accounts for a specific distribution in the sky. ...
One of the primary sources of gravitational waves (GWs) anticipated to be detected by the Laser Interferometer Space Antenna (LISA) are Galactic double white dwarf binaries (DWDs). However, most of these binaries will be unresolved, and their GWs will overlap incoherently, creating a stochastic noise known as the Galactic foreground. Similarly, the population of unresolved systems in the Milky Way's (MW) satellites is expected to contribute to a stochastic gravitational wave background (SGWB). Due to their anisotropy and the annual motion of the LISA constellation, both the Galactic foreground and the satellite SGWB fall into the category of cyclostationary processes. Leveraging this property, we develop a purely frequency-based method to study LISA's capability to detect the MW foreground and SGWBs from the most promising MW satellites. We analyze both mock data generated by an astrophysically motivated SGWB spectrum, and realistic ones from a DWD population generated via binary population synthesis. We are able to recover or put constrains on the candidate foregrounds, reconstructing -- in the presence of noise uncertainties -- their sky distribution and spectrum. Our findings highlight the significance of the interplay between the astrophysical spectrum and LISA's sensitivity to detect the satellites' SGWB. Considering an astrophysically motivated prior on the satellite positions improves their detectability, which becomes otherwise challenging in the presence of the Galactic foreground. Furthermore, we explore the potential to observe a hypothetical satellite located behind the Galactic disk. Our results suggest that a Large Magellanic Cloud-like satellite could indeed be observable by LISA.
... This is part of the larger effort to build * riccardo.buscicchio@unimib.it a coherent, all-encompassing, data-analysis scheme for LISA data, including the estimation of individual sources, astrophysical foregrounds, and instrumental noise parameters [16][17][18][19]. Alternative approaches have been proposed to devise parametrized models for long-term periodic non-stationarities, frequently referred to as "cyclostationarities" [20][21][22]. Similarly, recent progress has been made on the development of heavy-tailed likelihoods to infer statistical properties of non-Gaussian signals [23]. ...
... In Eq. (22), the quantity ρ [x] (f ) denotes the operator mapping a realization of the process x onto its test statistics as a function of frequency. Processes whose Fourier-transform squared norm fluctuates around their mean more than the mean itself yield a test statistic larger than one. ...
... In practice, the test is carried out constructing estimators for each random quantity in Eq. (22). The denominator is evaluated via the Welch's PSD estimator [51] while the numerator is obtained through individual FFTs. ...
Upcoming space-based gravitational-wave detectors will be sensitive to millions and resolve tens of thousands of stellar-mass binary systems at mHz frequencies. The vast majority of these will be double white dwarfs in our Galaxy. The greatest part will remain unresolved, forming an incoherent stochastic foreground signal. Using state-of-the-art Galactic models for the formation and evolution of binary white dwarfs and accurate LISA simulated signals, we introduce a test for foreground Gaussianity and stationarity. We explain the former with a new analytical modulation induced by the LISA constellation motion and the intrinsic anisotropy of the source distribution. By demodulating the foreground signal, we reveal a deviation from Gaussianity in the 2-10 mHz frequency band. Our finding is crucial to design faithful data models, i.e. unbiased likelihoods for both individual sources and astrophysical foregrounds parameter estimation, and ultimately for an accurate interpretation of the LISA data.
... However, because of the better angular resolution of future interferometers, anisotropies in GW energy density could provide a new tool to distinguish among various sources of GWs in the early Universe [29,30], see e.g. [31,32] for recent applications. ...
The initial conditions on the anisotropies of the stochastic gravitational-wave background of cosmological origin (CGWB) largely depend on the mechanism that generates the gravitational waves. Since the CGWB is expected to be non-thermal, the computation of the initial conditions could be more challenging w.r.t. the Cosmic Microwave Background (CMB), whose interactions with other particles in the early Universe lead to a blackbody spectrum. In this paper, we show that the initial conditions for the cosmological background generated by quantum fluctuations of the metric during inflation deviate from adiabaticity. These primordial gravitational waves are indeed generated by quantum fluctuations of two independent degrees of freedom (the two polarization states of the gravitons). Furthermore, the CGWB plays a negligible role in the Einstein's equations, because its energy density is subdominant w.r.t. ordinary matter. Therefore, the only possible way to compute the initial conditions for inflationary gravitons is to perturb the energy-momentum tensor of the gravitational field defined in term of the small-scale tensor perturbation of the metric. This new and self-consistent approach shows that a large, non-adiabatic initial condition is present even during the single-field inflation. Such a contribution enhances the total angular power spectrum of the CGWB compared to the standard adiabatic case, increasing also the sensitivity of the anisotropies to the presence of relativistic and decoupled particles in the early Universe. In this work we have also proved that our findings are quite general and apply to both single-field inflation and other scenarios in which the CGWB is generated by the quantum fluctuations of the metric, like the curvaton.
... However, because of the better angular resolution of future interferometers, anisotropies in GW energy density could provide a new tool to distinguish among various sources of GWs in the early Universe [29,30], see e.g. [31,32] for recent applications. ...
The initial conditions on the anisotropies of the stochastic gravitational-wave background of cosmological origin (CGWB) largely depend on the mechanism that generates the gravitational waves. Since the CGWB is expected to be non-thermal, the computation of the initial conditions could be more challenging w.r.t. the Cosmic Microwave Background (CMB), whose interactions with other particles in the early Universe lead to a blackbody spectrum. In this paper, we show that the initial conditions for the cosmological background generated by quantum fluctuations of the metric during inflation deviate from adiabaticity. These primordial gravitational waves are indeed generated by quantum fluctuations of two independent degrees of freedom (the two polarization states of the gravitons). Furthermore, the CGWB plays a negligible role in the Einstein's equations, because its energy density is subdominant w.r.t. ordinary matter. Therefore, the only possible way to compute the initial conditions for inflationary gravitons is to perturb the energy-momentum tensor of the gravitational field defined in terms of the small-scale tensor perturbation of the metric. This new and self-consistent approach shows that a large, non-adiabatic initial condition is present even during the single-field inflation. Such a contribution enhances the total angular power spectrum of the CGWB compared to the standard adiabatic case, increasing also the sensitivity of the anisotropies to the presence of relativistic and decoupled particles in the early Universe. In this work we have also proved that our findings are quite general and apply to both single-field inflation and other scenarios in which the CGWB is generated by the quantum fluctuations of the metric, like the curvaton.
... For the impact of anisotropies and non-Gaussianities see, e.g., refs. [24,[153][154][155][156][157][158][159][160][161]. While most early Universe mechanisms predict stationary signals, the presence of anisotropies, projected in the data by a time-varying and sky-dependent response function, will induce time modulations in the measurements. ...
... The anisotropic nature of the galactic foreground gives rise to a time-dependent modulation of the signal, as the detector moves through space [205,206]. The improvement is however limited [160], and our analysis does not leverage this feature, opting instead for considering the average signal integrated over the mission duration. Therefore, our work may be suboptimal in this respect. ...
Various scenarios of cosmic inflation enhance the amplitude of the stochastic gravitational wave background (SGWB) at frequencies detectable by the LISA detector. We develop tools for a template-based analysis of the SGWB and introduce a template databank to describe well-motivated signals from inflation, prototype their template-based searches, and forecast their reconstruction with LISA. Specifically, we classify seven templates based on their signal frequency shape, and we identify representative fundamental physics models leading to them. By running a template-based analysis, we forecast the accuracy with which LISA can reconstruct the template parameters of representative benchmark signals, with and without galactic and extragalactic foregrounds. We identify the parameter regions that can be probed by LISA within each template. Finally, we investigate how our signal reconstructions shed light on fundamental physics models of inflation: we discuss their impact for measurements of \emph{e.g.,} ~the couplings of inflationary axions to gauge fields; the graviton mass during inflation; the fluctuation seeds of primordial black holes; the consequences of excited states during inflation, and the presence of small-scale spectral features.
Various scenarios of cosmic inflation enhance the amplitude of the stochastic gravitational wave background (SGWB) at frequencies detectable by the LISA detector. We develop tools for a template-based analysis of the SGWB and introduce a template databank to describe well-motivated signals from inflation, prototype their template-based searches, and forecast their reconstruction with LISA. Specifically, we classify seven templates based on their signal frequency shape, and we identify representative fundamental physics models leading to them. By running a template-based analysis, we forecast the accuracy with which LISA can reconstruct the template parameters of representative benchmark signals, with and without galactic and extragalactic foregrounds. We identify the parameter regions that can be probed by LISA within each template. Finally, we investigate how our signal reconstructions shed light on fundamental physics models of inflation: we discuss their impact for measurements of e.g., the couplings of inflationary axions to gauge fields; the graviton mass during inflation; the fluctuation seeds of primordial black holes; the consequences of excited states during inflation, and the presence of small-scale spectral features.
