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The Laser Interferometer Space Antenna is expected to observe gravitational waves from massive black hole binaries across cosmic time. Many are anticipated to be detectable hours to weeks before coalescence. We present a fast algorithm for the premerger detection and preliminary characterization of such binaries. The method performs a search for excess power with a chirping time-frequency morphology in short-time Fourier transform spectrograms. By tiling the time-frequency plane with slices defined by the quadrupole frequency evolution, we define a signal significance relative to a fitted background distribution of instrumental noise and Galactic foreground. Individual search triggers are followed by a coherence tracker that groups triggers consistent with the same physical signal over time. Doing so, our analysis provides progressively refined estimates of the chirp mass and coalescence time. We validate our algorithm on the SangriaHM LISA Data Challenge dataset, successfully detecting all 15 injected massive black hole binaries; 14 of them hours to weeks before merger, while one is only detected after the binary coalescence. The algorithm yields chirp mass relative errors below 3% for high-SNR sources and coalescence time uncertainties of up to a few hours. With a computational cost of less than a second to process a 10-day data segment on a single core, our approach is suitable for generating real-time alerts, triggering protected observational periods, and providing informative priors for Bayesian parameter estimation.

The LIGO-Virgo-KAGRA consortium has sporadically detected inspiral-dominated gravitational-wave events such as GW170817 and GW190425. These events offer an opportunity to constrain possible initial (residual) orbital eccentricities using purely inspiral template families. We detail the implementation of an LALSuite approximant, TaylorF2Ecck, which analytically models inspiral gravitational waves from nonspinning compact binaries in post-Newtonian (PN)-accurate eccentric orbits and restricts the initial-eccentricity contributions to leading order. Specifically, our frequency-domain approximant consistently incorporates orbital, advance of periastron, and gravitational-wave emission effects fully up to 3PN order. We conduct detailed parameter-estimation studies of GW170817 and GW190425 using TaylorF2Ecck, following comprehensive sanity checks to validate model performance and investigate the influence of eccentricity and periastron advance in the relevant parameter space. The results indicate that the initial eccentricity at 20 Hz is negligible within the 90% credible intervals (less than 0.016 for GW170817 and less than 0.023 for GW190425, with both posterior distributions railing toward zero), and Bayes factors show no strong evidence favoring the eccentric waveform over the quasicircular waveform. At such negligible initial eccentricities, comparisons between eccentric models with and without periastron advance show no clear signature of this effect, with no significant model-dependent shifts in the posterior distributions and no strong Bayes-factor evidence favoring one model over the other. Additionally, these detailed studies reveal the importance of incorporating initial-eccentricity contributions at least up to 3.5PN order and discuss its implications. We substantiate this inference by employing versions of the quasicircular TaylorF2 approximant that incorporate Fourier phase contributions beyond the conventional 3.5PN order.

We investigate the detectability of gravitational wave modes (emitted by black holes and neutron stars) by third-generation, ground-based gravitational wave detectors planned to be operational in the next decade. Our analysis focuses on the Cosmic Explorer and Einstein Telescope projects, which are expected to have arm lengths of tens of kilometers and to experience the amplification of a gravitational wave signal at their free spectral range frequencies. We find that both projects will also observe with good signal-to-noise ratio the elusive w-modes, which are expected to be emitted at these frequencies by spinning neutron stars.

This article delves into the observational properties of a Schwarzschild-like black hole (BH). Initially, the research provides a succinct examination of the spacetime geometry and the configuration of its horizon. Furthermore, we study the photon dynamics around the Schwarzschild-like BH in the presence of plasma using the Hamiltonian formalism. We found that the photon sphere radii increase under the influence of plasma frequency and vice versa for the spacetime parameters. Further exploration is dedicated to understanding how plasma affects the shadow of the BH, and we find that the radius of the BH shadow shrinks with the rise of the ξ parameter and plasma frequency. We then turn to constraining the spacetime parameters and the plasma frequency by using the observational data released by the Event Horizon Telescope (EHT) collaboration for M87* and Sgr A*. Additionally, the research scrutinizes the phenomenon of gravitational weak lensing in the vicinity of a Schwarzschild-like BH, considering both uniform and non-uniform plasma scenarios. The outcomes demonstrate that the angle of deflection increases under the influence of a uniform plasma frequency, whereas the opposite is true for non-uniform plasma. In both scenarios, a rise in the spacetime parameters results in a decrease in the deflection angle. Finally, we investigate the magnification of the gravitationally lensed image. The effect of the spacetime parameters and plasma frequencies on the total magnification is the same as in the deflection angles. *This research is funded by the National Natural Science Foundation of China (NSFC) (U2541210)

We present the results of directed searches for continuous gravitational waves from unknown neutron stars in five Milky Way globular clusters. We carry out these searches in the LIGO data from the first eight months of the fourth LIGO-Virgo-KAGRA observing run using the WEAVE semicoherent program, which sums matched-filter detection-statistic values over many time segments spanning the observation period. No gravitational wave signal is detected in the search band of 20--475 Hz. Injections of simulated continuous wave signals in the data indicate that we achieve the most sensitive results to date across most of the explored parameter space volume, obtaining median 95% confidence level upper limits as low as <inline-formula><mml:math><mml:mo>~</mml:mo><mml:mn>4.2</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>26</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> near 282 Hz for NGC 6397. We also derive upper limits on neutron star ellipticity and <inline-formula><mml:math><mml:mi>r</mml:mi></mml:math></inline-formula>-mode amplitudes, reaching <inline-formula><mml:math><mml:mo>≲</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math><mml:mo>≲</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, respectively, at frequencies above 200 Hz.

Modeling extreme-mass-ratio inspirals hinges on the accurate and efficient computation of gravitational-wave fluxes from generic Kerr orbits. Conventional frequency-domain techniques are often limited by costly auxiliary parameter searches and numerical instabilities in the strong-field or high-frequency regimes. We address these challenges by reformulating both the angular and radial Teukolsky equations in terms of confluent Heun functions. Employing a hybrid analytic continuation algorithm to compute the connection coefficients eliminates the dependence on auxiliary parameters, directly yielding globally convergent solutions and scattering amplitudes. To resolve the highly oscillatory source integrands for generic orbits, we implement an adaptive bipower mapping quadrature. Comprehensive benchmarks under standard double-precision arithmetic demonstrate that, for the total radiative flux summed over 168 low-order modes, our method achieves relative errors of order <inline-formula><mml:math><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>11</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, with computational costs typically reduced by factors of 3--13 compared to the state-of-the-art GeneralizedSasakiNakamura.jl and PYBHPT packages. Notably, for highly oscillatory high-order modes, our framework achieves a speedup of up to 60 times compared to specialized oscillatory integrators like GeneralizedSasakiNakamura.jl. These demonstrated gains in precision and efficiency establish the framework as a robust tool for strong-field perturbation theory, providing the numerical foundation for high-order, self-force calculations and rapid, high-precision waveform generation.

We determine the future sensitivity of the TRIDENT neutrino telescope to dark matter annihilation in the Galactic Center. By applying the full detector design and assuming an Navarro-Frenk-White (NFW) halo profile, we show that TRIDENT will probe annihilation cross section down to <inline-formula><mml:math><mml:mo>⟨</mml:mo><mml:mi>σ</mml:mi><mml:mi>v</mml:mi><mml:mo>⟩</mml:mo><mml:mo>≈</mml:mo><mml:mn>5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>27</mml:mn></mml:mrow></mml:msup><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:msup><mml:mrow><mml:mi>cm</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup><mml:mtext> </mml:mtext><mml:msup><mml:mi>s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for 10 TeV dark matter, falling below the thermal freeze-out benchmark. The analysis is carried out with all-flavor neutrino interactions, where we demonstrate that cascade events, primarily due to <inline-formula><mml:math><mml:msub><mml:mi>ν</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mo>,</mml:mo><mml:mi>τ</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, show greater sensitivity to a dark matter signal compared to the more commonly studied track events. Furthermore, we highlight the impact of a previously overlooked background, Galactic neutrinos produced from interactions between hadronic cosmic rays and interstellar gas. We find dark matter sensitivities are more strongly degraded in the high energy region above <inline-formula><mml:math><mml:mo>~</mml:mo><mml:mn>10</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>TeV</mml:mi></mml:math></inline-formula>, with a maximal weakening of approximately a factor of 2. This effect remains smaller than the uncertainty associated with the dark matter density profile but can nonetheless mimic a positive annihilation signal. We contextualize these results with a concrete particle model and show that TRIDENT will be able to probe the most interesting untested parts of parameter space.

In this work, we develop analytic asymptotic methods for computing the Fourier modes of gravitational waves from post-Newtonian binary systems in the quasi-Keplerian parametrization in the high eccentricity regime. We also derive the large-eccentricity asymptotic expansion of the eccentricity enhancement function appearing in the tail contributions to the radiation. Furthermore, based on these results, we construct an end point-constrained analytic approximation that significantly accelerates the computation of the Fourier modes at large eccentricity. The overall error of this analytic approximation is controlled within <inline-formula><mml:math><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and it remains valid for Fourier modes with <inline-formula><mml:math><mml:mi>p</mml:mi><mml:mo>&lt;=</mml:mo><mml:mn>200</mml:mn></mml:math></inline-formula> and <inline-formula><mml:math><mml:mi>e</mml:mi><mml:mo>&lt;=</mml:mo><mml:mn>0.9</mml:mn></mml:math></inline-formula>. This approach provides analytic building blocks for modeling frequency-domain gravitational waves from highly eccentric binaries.

We investigate the dynamics of asymmetric binaries in extensions of general relativity (GR) featuring a massless scalar field nonminimally coupled to gravity, focusing on the interplay between eccentricity and inclination in fully generic bound orbits. Building on an effective field theory framework tailored to extreme- and intermediate-mass-ratio inspirals, we compute scalar-field perturbations using a new arbitrary-precision C++ code capable of evolving perturbations along generic Kerr geodesics, STORM. We investigate the complete set of scalar fluxes at infinity and through the horizon across the relevant parameter space and analyze their harmonic structure as a function of orbital geometry and black-hole spin. Our results advance ongoing efforts to construct accurate waveform models for asymmetric binaries beyond GR and lay the groundwork for precision tests of fundamental physics with next-generation gravitational-wave detectors.

In this paper, we show how the dynamical tidal response of a neutron star can be systematically defined within the worldline effective field theory (EFT) framework, and relate it to the gauge-invariant amplitude for gravitational-wave scattering off an isolated star. We compute this amplitude both within the EFT, using standard quantum field-theory techniques, and within stellar perturbation theory (the corresponding ultraviolet theory), solving the coupled metric and matter perturbation equations numerically in the stellar interior and matching to the analytical Mano-Suzuki-Takasugi solutions in the vacuum exterior. Matching the amplitude between the two theories fixes the dynamical tidal response. The result is consistent with known expectations, including the static limit and the behavior near the star's resonant modes, and it recovers the imaginary part of the dominant oscillation mode induced by gravitational-wave dissipation. We conclude with a discussion of potential improvements within both the EFT and the perturbation theory.

The foundation for modeling the coupling of the internal structure of compact objects in binary systems to their dynamics and emitted gravitational waves is a systematic effective field theory (EFT) framework, where each compact object is replaced by a worldline endowed with a set of internal degrees of freedom. These degrees of freedom encode finite-size effects and thereby distinguish between different classes of compact objects. Among finite-size effects, tidal interactions play a central role, as they are associated to various kinds of deformations of a body under the influence of external tidal fields. In this work, we analyze the dynamical tidal response of Kerr black holes to generic-spin perturbations, focusing primarily on the scalar and gravitational cases, and working to linear order in frequency. We establish an EFT description of the perturbed black hole that accounts for the couplings between the spin, gravitoelectric and -magnetic tidal fields. We match this to wavelike solutions to the full black hole perturbation equations in order to determine the tidal response coefficients. In particular, we obtain the dynamical Love number, which appears at linear order in frequency for spinning black holes, and derive an approximate expression for the dynamical tidal response, including both dissipative and conservative pieces. We also examine several technical subtleties that arise in the matching procedure, with special emphasis on the mixing of multipolar modes induced by the spin of the compact object, which proves to be essential for a consistent treatment.

The Laser Interferometer Space Antenna (LISA) mission aims to detect gravitational waves by interferometrically measuring the change of separation between free-falling test masses (TMs). LISA's interferometers must deliver <inline-formula> <mml:math><mml:mrow><mml:mtext>pm</mml:mtext><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msqrt><mml:mtext>Hz </mml:mtext></mml:msqrt></mml:mrow></mml:math></inline-formula> sensitivity while accommodating beam tilts up to 1 mrad at the photodiodes (PDs), which degrade the interferometric amplitude and increase the induced readout noise coupling. This paper uses an analytical framework developed by the authors in a previous work, based on minimal and justified approximations, that relates beam tilt to the resulting heterodyne signal amplitude in a generic two-beam interferometer with circular-area PDs. A set of interferometric topologies is analyzed, all of high relevance for LISA. We derive the exact amplitude response for an infinite detector and a closed-form approximation for finite detectors, and we validate both against numerical simulations and experimental measurements on an ultra-stable LISA-representative testbed. We then use this model to quantify the phase-noise amplification arising from reduced signal-to-noise ratio under tilt, showing that curvature mismatches between the interfering beams substantially enhance this effect. Finally, we introduce a compact function that captures the angular dependence of correlated and uncorrelated phase noises in quadrant PD-based readouts. Here, a new noise feature, caused by wavefront curvature mismatch, is predicted and measured for the first time. These results indicate that controlling wavefront curvature mismatch in the TM interferometer is essential to limit excess phase noise. The models and results derived in this paper, although originating in the context of LISA, are general and can be applied to any interferometric topology undergoing tilts with pivot on the detector plane.

We introduce WimPyC, a Python code for the calculation of the capture rate of Weakly Interacting Massive Particles (WIMPs) by celestial bodies through nuclear scattering in the optically thin regime. WimPyC is an extension of the WimPyDD code, that calculates WIMP--nucleus scattering signals in direct detection (DD) experiments, and allows to combine DD and capture in celestial bodies in virtually any scenario within the framework of Galilean--invariant non--relativistic effective theory (NREFT), including inelastic scattering, an arbitrary WIMP spin and a generic WIMP velocity distribution in the Galactic halo. WimPyDD and WimPyC are suitable for both top--down approaches, where the interaction operators of a high--energy physics model are matched to those of the NREFT, and for bottom--up studies, where the Wilson coefficients of the NREFT are explored in a model--independent way and/or where the velocity distribution is written in terms of a superposition of streams taken as free parameters. As in the case of WimPyDD WimPyC exploits the factorization of the three main components that enter in the calculation of the capture rate: i) the Wilson coefficients that encode the dependence of the signals on the ultraviolet completion of the effective theory; ii) a response function that depends on the nuclear physics; iii) the halo function that depends on the WIMP velocity distribution. In WimPyC these three components are calculated and stored separately for later interpolation and combined together only as the last step of the signal evaluation procedure. This makes the phenomenological study of the capture rate with WimPyC transparent and improves computational speed. PROGRAM SUMMARY Module Title: WimPyC CPC Library link to program files: ``https://doi.org/10.17632/bg5wxh6mgj.1 '' Licensing provisions: MIT Programming language: Python3 Developer's repository link:wimpydd.hepforge.org Nature of problem: Stars and planets in our galaxy are expected to be embedded in an extended dark matter (DM) halo made of Weakly Interacting Massive Particles (WIMPs). When they cross a celestial body DM particles can lose energy and become gravitationally captured by the same WIMP--nucleus scattering process driving direct detection in terrestrial detectors. The rate at which this process occurs is called the capture rate, and, under proper conditions, can lead to a dense population of DM particles inside the celestial body with a consequent enhancement of their annihilation rate. This can produce indirect observational signatures such as a flux of high--energy neutrinos from the celestial body, or an increase in its temperature/luminosity. Combining direct and indirect signals can potentially improve our chance to detect WIMPs, but can be cumbersome especially in generalized scenarios. Solution method: The WimPyC module seamlessly integrates with the WimPyDD code, that calculates WIMP--nucleus scattering signals in direct detection experiments. It allows to calculate the WIMP capture rate in virtually any scenario, including an arbitrary spin, inelastic scattering, and a non-standard halo function. Each ingredient, including the celestial body, can be set up independently in an easy and intuitive way.

In this work we study the possibility to detect the gravitational waves generated by a secluded self-interacting dark sector. ``Secluded'' means that the dark sector has almost no portal to the visible sector and thus its entropy is conserved by itself, and ``self-interacting'' means that dark matter in this model has a significant interaction to itself, making it consistent with the small-scale structure observations. A spontaneously broken U(1)' is introduced for the interactions in the dark sector, and nearly massless dark radiation is also introduced to avoid the over-closure problem. Through a parameter space scan, we find that this model is highly constrained by the currently observed effective number of neutrinos (N<SUB>eff</SUB>) and the large-scale structure observable Lyman-α. Together, these two constraints exclude a large parameter space that is favored by future gravitational-wave detectors, but there is still a small portion of the model parameter space that can be detected by SKA.

We present realistic forecasts for the constraining power of the Nancy Grace Roman Space Telescope on fundamental cosmological parameters, with particular emphasis on the absolute neutrino mass scale, using full-shape analyses of the galaxy power spectrum. We analyze simulated light cone mock catalogs of <inline-formula><mml:math><mml:mrow><mml:mi>H</mml:mi><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> emission-line galaxies spanning the redshift range <inline-formula><mml:math><mml:mn>0.5</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>z</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>2</mml:mn></mml:math></inline-formula> over <inline-formula><mml:math><mml:mn>2400</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:msup><mml:mi>deg</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math></inline-formula>, designed to reproduce the expected properties of the Roman High Latitude Wide Area Spectroscopic Survey. We perform parameter inference on the galaxy power spectrum multipoles using two complementary theoretical frameworks: a model-dependent approach based on the effective field theory of large-scale structure (EFT of LSS) within <inline-formula><mml:math><mml:mi>Λ</mml:mi></mml:math></inline-formula> cold dark matter (<inline-formula><mml:math><mml:mi>Λ</mml:mi><mml:mi>CDM</mml:mi></mml:math></inline-formula>), and a model-independent phenomenological approach that makes no assumptions about the background cosmological model. In the <inline-formula><mml:math><mml:mi>Λ</mml:mi><mml:mi>CDM</mml:mi></mml:math></inline-formula> analysis, we find <inline-formula><mml:math><mml:msub><mml:mi>m</mml:mi><mml:mi>ν</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn>0.380</mml:mn><mml:mo>(</mml:mo><mml:mn>0.162</mml:mn><mml:mo>)</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>eV</mml:mi></mml:math></inline-formula> at 95(68)% CL using big bang nucleosynthesis (BBN) prior and a broad prior on <inline-formula><mml:math><mml:msub><mml:mi>n</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></inline-formula>, which tightens to <inline-formula><mml:math><mml:msub><mml:mi>m</mml:mi><mml:mi>ν</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn>0.276</mml:mn><mml:mo>(</mml:mo><mml:mn>0.121</mml:mn><mml:mo>)</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>eV</mml:mi></mml:math></inline-formula> when Planck priors on <inline-formula><mml:math><mml:msub><mml:mi>ω</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math><mml:msub><mml:mi>ω</mml:mi><mml:mi>cdm</mml:mi></mml:msub></mml:math></inline-formula>, and <inline-formula><mml:math><mml:msub><mml:mi>n</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></inline-formula> are added. Our forecasts show that Roman can additionally constrain <inline-formula><mml:math><mml:msub><mml:mi>H</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math><mml:msub><mml:mi>Ω</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:math></inline-formula>, and <inline-formula><mml:math><mml:msub><mml:mi>σ</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:math></inline-formula> with precisions of 1.3%, 4.3%, and 2.9% in line with stage IV galaxy survey measurements and forecasts. In the model-independent analysis, we demonstrate that the phenomenological model can robustly recover unbiased measurements of the angular diameter distance, the Hubble parameter, and the growth of structure across all redshift bins, in the same range of scales as the EFT model, and obtain <inline-formula><mml:math><mml:msub><mml:mi>m</mml:mi><mml:mi>ν</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn>0.63</mml:mn><mml:mo>(</mml:mo><mml:mn>0.36</mml:mn><mml:mo>)</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>eV</mml:mi></mml:math></inline-formula> at 95(68)% CL when Planck priors are included.

The integrated Sachs--Wolfe (ISW) effect describes how photons are gravitationally redshifted, producing anisotropies in the cosmic microwave background. We study the inverse problem and show that primordial gravitational perturbations, in particular their polarizations in the transversally traceless gauge can be identified from the local observation of the ISW effect.

We consider a dark sector consisting of fermionic dark matter (DM) charged under a broken dark <inline-formula><mml:math><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mo>)</mml:mo><mml:mi>D</mml:mi></mml:msub></mml:math></inline-formula> gauge symmetry, interacting with the Standard Model through kinetic mixing. In such models, the DM annihilation cross section is typically suppressed by the small kinetic mixing and or a heavy mediator, often leading to an overabundant relic density. We show that the observed DM abundance can be achieved if the dark Higgs undergoes a strong first order phase transition after DM freeze-out. In this scenario, the relic abundance is set by thermal freeze-out in the symmetric phase and subsequently reduced by entropy injection from the phase transition, rather than by annihilation in the broken phase. We find that to reproduce the observed relic abundance, the required phase transition is generically supercooled. The resulting stochastic gravitational wave signal lies within the sensitivity of future experiments, providing a complementary probe of this framework. Moreover, a strongly supercooled phase transition can potentially account for the NANOGrav signal for DM masses below <inline-formula><mml:math><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>10</mml:mn><mml:mo>)</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi></mml:math></inline-formula>.

Extreme-mass-ratio inspirals (EMRIs) are one of the main sources of gravitational waves expected in the low-frequency band, where space-based detectors like Laser Interferometer Space Antenna (LISA) will operate. The large number of gravitational-wave cycles accumulated in the EMRI signal in the strong-field regime makes them very precise probes of the local spacetime geometry that are highly sensitive to deviations from the Kerr black hole paradigm. In this work, we investigate EMRIs around generic, non-Kerr compact objects characterized by an arbitrary and rich multipolar structure. At leading post-Newtonian and linear mass-ratio orders, we incorporate in the waveform model both the axisymmetric and nonaxisymmetric components of the mass quadrupole and octupole moments, parametrizing in this way the breaking of two fundamental symmetries of the Kerr metric. We study the impact of these modifications on the waveform following the philosophy of the EMRI analytic kludge models. In our case, the orbital evolution follows from Lagrangian that contains of the multipolar structure of the primary, including for the first time the nonaxisymmetric multipole moments that break axial symmetry. Then, using Fisher-matrix analysis, we assess the capability of LISA to constrain deviations of the multipole moments from their Kerr values and, in particular, the possibility of detecting symmetry-breaking effects. In this way, we analyze how effectively LISA will be able to probe models beyond General Relativity that predict horizon-scale modifications, such as the fuzzball model proposed in string theory. Our results demonstrate that future LISA observations of EMRIs will provide powerful and unprecedented tests of black hole structure and the underlying theory of gravity. In particular, with one year of LISA data from the inspiral of a <inline-formula><mml:math><mml:mn>10</mml:mn><mml:msub><mml:mi>M</mml:mi><mml:mo>⊙</mml:mo></mml:msub></mml:math></inline-formula> compact object into a rotating supermassive black hole of <inline-formula><mml:math><mml:msup><mml:mn>10</mml:mn><mml:mn>6</mml:mn></mml:msup><mml:msub><mml:mi>M</mml:mi><mml:mo>⊙</mml:mo></mml:msub></mml:math></inline-formula> and signal-to-noise ratio of 30, it will be possible to place tight bounds on deviations from the two fundamental symmetries of the Kerr metric, constraining equatorial symmetry breaking in the mass multipole sector to the <inline-formula><mml:math><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> level and axial symmetry breaking to the <inline-formula><mml:math><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> level.