To effectively describe the plasma with strong magnetic field, the force-free electrodynamics was introduced, within which the Grad-Shafranov equation plays the key role. The Grad-Shafranov equation governs the global structure of an electromagnetic field in equilibrium with symmetries. It is widely applicable in a variety of scenarios, such as the tokamak, the solar corona, the magnetosphere of Earth, neutron stars, and black holes, etc. However, in different situations, the Grad-Shafranov equation is expressed differently, and the derivations might be complicated. In this work, via the language of differential form, we provide a general expression of the Grad-Shafranov equation, from which the expression in any specific situation can be quickly obtained. Additionally, we present a Lagrangian density for a scalar field whose on-shell condition is precisely the Grad-Shafranov equation.

The so-called $I$-Love-$Q$ relations link some normalized versions of the moment of inertia, the Love number, and the quadrupole moment of a star. These relations, in principle, enable the inference of two of the quantities given the third. However, their use has been limited because the normalized versions of the multipole moments rely on the static mass derived from the Tolman-Oppenheimer-Volkoff equation, which is not directly observable. In this work, using perturbation theory, we find that the $I$-Love-$Q$ relations can also be formulated in terms of an alternative set of normalized quantities that do not depend on the static mass, but on the actual (observable) mass.

The aim of this work is to improve understanding of the resonant spectra of black holes under perturbations arising from e.g. compact objects or accretion disks in their vicinity. It is known that adding a weak perturbation to the radial potential can strongly disrupt the spectrum of quasinormal modes and Regge poles of a black hole spacetime. Here we examine the effect of (weak or strong) localized delta-function perturbations on the resonant spectra of spherically symmetric systems, to address fundamental questions around linear and nonlinear spectral stability. We examine two cases: the Nariai spacetime with a Poschl-Teller potential and the Schwarzschild spacetime. We show that, in either case, the spectrum deforms in a smooth and continuous manner as the position and strength of the perturbation is varied. As the strength of the perturbation is increased, resonances migrate along trajectories in the complex plane which ultimately tend toward attracting points determined by a hard-wall scenario. However, for weak perturbations the trajectory near the unperturbed resonance is typically strongly influenced by a set of repelling points which, for perturbations far from the system, lie very close to the unperturbed resonances; hence there arises a nonlinear instability (i.e. the failure of a linearized approximation). Taking a dynamical systems perspective, the sets of attracting and repelling spectral points follow their own trajectories as the position of the perturbation is varied, and these are tracked and understood.

The mass transfer process is prevalent during the inspiral phase of compact binary systems. Detection of gravitational waves from the inspiral phase of binaries with white dwarfs will allow us to measure the mass transfer rate. Mass transfer effects provide additional contributions to the phase of gravitational waves, which can break the degeneracy between binary masses and redshift. Based on the analytic mass transfer rate to the first order post-Newtonian evolution of orbital angular frequency, we use the Fisher matrix to forecast the ability of DECIGO to measure the redshift of compact binaries with mass transfer. We conclude that for compact binary systems containing white dwarfs the redshift can be determined to an accuracy of 10% for $z=0.01$ with a $\mathrm{S}\mathrm{N}\mathrm{R}\sim 30$.

Gravitational waves (GWs) within the LIGO-Virgo-KAGRA sensitivity band can be microlensed by stellar and intermediate-mass black holes, producing a frequency-dependent modulation of the signal amplitude. Microlensing analyses, however, are costly due to the increased dimensionality of the parameter space and waveform computation time. As a proof of concept, we show that the deep-learning-based framework, Deep Inference for Gravitational-Wave Observations (dingo), which employs a simulation-based inference approach to estimate posterior distributions, can perform efficient parameter inference for GW microlensing by an isolated point-mass lens. Using simulated microlensed GW signals, we train a lensed-dingo network and compare its performance with traditional Bayesian parameter estimation carried out with bilby. Our framework can be used to rapidly identify microlensed events in large GW catalogs. When the lensed-dingo network is combined with importance sampling, we find that, although sample efficiencies are somewhat reduced compared to the unlensed-dingo network, owing to the richer structure of microlensed signals, it still achieves $\mathcal{O}(10\times )$ speed-up relative to bilby. We further show that this framework is useful to efficiently estimate the background Bayes-factor distribution, which is crucial for assessing the significance of candidate lensed events. However, for foreground (lensed) events, the sampling efficiency can sometimes drop when analyzed with the unlensed-dingo network, providing a diagnostic indicator of out-of-distribution data. Our approach can be straightforwardly generalized to more complex and realistic lens models, enabling detailed studies of microlensed GWs.

Compact binary coalescences (CBCs), such as merging binary black holes (BBHs), binary neutron stars (BNSs), or neutron star black holes (NSBHs), hosted by dense stellar environments, could produce gravitational waves (GWs) that contain signatures of line-of-sight acceleration (LOSA) imparted by the environment’s gravitational potential. We calculate the post-Newtonian (PN) corrections to the (2,2) mode GW phase due to a finite LOSA, starting from the leading order at –4 PN below the quadrupole order, up to 3.5PN above the leading order correction. We do so for binaries whose component spins are aligned with the orbital angular momentum, as well as for binaries with nonzero tidal deformation. We implement these corrections into the LIGO-Virgo-Kagra (LVK) collaboration’s flagship parameter estimation (PE) software bilby_tgr. We study the systematics associated with recovering LOSAs. We find that, when the injection and recovery waveform models are identical, LOSAs are recovered as expected. We test the robustness of the pipeline against waveforms with strong higher-mode signatures or signatures of beyond-general-relativistic (beyond-GR) effects to delimit the range of applicability of our GR-consistent quasicircular LOSA-corrected waveforms.

We investigate elastic scattering by a compact, horizonless body in curved spacetime, considering a massless scalar wave incident on a static, spherically symmetric, uniform-density star of radius $R$ and mass $M$ with a Schwarzschild exterior. We introduce an exact Debye-series decomposition of the scattering matrix, in the spirit of Debye expansions in Mie scattering. This decomposition separates direct surface reflection from contributions involving transmission into the interior and subsequent propagation, and admits a natural trajectory interpretation. We then determine the associated Regge-Debye pole spectrum in the complex angular momentum plane. For neutron star–like tenuities ($R>3M$), the spectrum exhibits two pole families: a surface-wave branch associated with the surface matching condition and a broad-resonance branch associated with the interior regularity condition. For ultracompact objects ($R<3M$), the surface-wave branch persists, while the interior-resonance sector splits into broad- and narrow-resonance branches. We next reconstruct the scattering amplitude from the Debye partial-wave contributions and find excellent agreement with direct partial-wave calculations. Finally, we develop complex angular momentum representations order by order in the Debye series, making explicit how the pole families and nonpole sectors contribute to each Debye term. In the neutron star–like regime, we find a genuine competition between Regge-Debye pole sums and branch-cut contributions, and show that, at high frequency, the rainbowlike enhancement already arises from the first interior-transmission contribution and is dominated by the interior-resonance Regge-Debye poles. By contrast, in the ultracompact regime, the Debye amplitudes are overwhelmingly pole dominated.

Gravitational-wave echoes from the coalescence of black hole binaries are frequently viewed as signals beyond general relativity or standard model. In this work, we show that these echoes are possible even in the coalescence of standard general relativity. This is because the physical black holes formed through gravitational collapse serve as a faithful description of astro black holes. To all outside probes, only their asymptotic structure before the horizon formation is accessible. Here, we investigate the scattering of a gravitational-wave bursts on such physical black holes and pay special attention to the echoes. Our results uncover distinct features of this echo both in time and frequency domains.

We compute, at the first self-force accuracy level, the radiated energy from a radially infalling particle released from rest in a Schwarzschild spacetime. We examine both the cases of a scalar particle and that of a massive particle, in the context of gravitational perturbations. Our findings are accompanied by post-Newtonian checks. In spite of the specific interest for this kind of computations, we outline the building blocks for future higher-order post-Newtonian computations as well as for extending these results to other interesting situations out of the black hole case.

The evolution of large-scale structures within the standard model of cosmology is well posed only up to the onset of shell crossing, where particle trajectories appear to intersect. Beyond this point, the evolution equations become nonpredictive and perturbative approaches break down. We show that in general relativity, a matter horizon forms before caustics develop for a well-defined initial overdensity on an expanding Friedmann–Lemaître–Robertson–Walker spacetime. The matter horizon was first identified by Ellis and Stoeger in 2010 as a dynamical causal boundary that encloses a subregion of spacetime where structure formation actually takes place. We construct a multiscale hierarchical framework for the propagation of the geodesic congruences that avoids the shell-crossing singularity by cutting the spacetime at the matter horizon and gluing to another spacetime with opposite orientation. We identify a relationship between the multiscale hierarchical framework and the cosmological zoom-in N-body simulation approach, and relate the local subregion that decoupled from the Hubble flow to the region of interest in the cosmological zoom-in N-body simulation approach. Most importantly, the multiscale hierarchical framework provides a more robust way of implementing the boundary conditions, which could benefit the cosmological zoom-in N-body simulation approach.

The astrophysical foreground from compact binary coalescence signals is expected to be a dominant part of total gravitational-wave (GW) energy density in the frequency band of the third-generation detectors. The detection of any other subdominant stochastic GW background (GWB), especially a primordial GWB, will be disturbed by the astrophysical foreground. Although previous studies have proposed several cleaning methods, the foreground from subthreshold binary neutron stars (BNSs) has been a major obstacle to remove. In this paper, we propose the novel idea to better estimate the unresolved foreground, by using the information about its anisotropies. We simulate the BNS population and compute its angular power spectrum and shot noise. We find that the shot noise from BNSs is too faint to observe after subtracting loud signals due to the limited angular resolution of the third-generation detectors. This justifies the approximation regarding the unresolved foreground as an isotropic component. We also discuss the angular resolution necessary to make our method valid for the foreground subtraction.

In this work, we present updated observational constraints on the parameter space of the DMS20 dark-energy model, a member of the omnipotent dark-energy (ODE) class. Our analysis combines multiple cosmic microwave background datasets—including measurements from the Planck satellite (PL18), the South Pole Telescope (SPT), and the Wilkinson Microwave Anisotropy Probe (WMAP)—with Type Ia supernova data from the $\mathrm{Pantheon}+\mathrm{catalog}$ (PP), and baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument and Sloan Digital Sky Survey. We find that certain data combinations, such as $\mathrm{SPT}+\mathrm{WMAP}+\mathrm{BAO}$ and $\mathrm{P}\mathrm{L}18+\mathrm{BAO}$, can reduce the significance of the $H_0$ tension below $1\sigma$, but with considerably large uncertainties. However, the inclusion of PP data restores the tension in $H_0$. To provide a comprehensive view of the ODE phenomenology, we also investigate the evolution of its energy density, emphasizing its dynamical behavior at low redshifts. Our results generically exhibit multiple phantom divide line crossings in a single expansion history; if confirmed, this points beyond the simplest minimally coupled canonical single-field quintessence/phantom descriptions and motivates more general dark-sector realizations.

Twenty-one-centimeter intensity mapping is a powerful probe of the large-scale distribution of neutral hydrogen (HI) and cosmological observables such as baryon acoustic oscillations. A major challenge is contamination from bright foregrounds and frequency-dependent beam effects, which can lead to signal loss in traditional methods such as principal component analysis (PCA). We develop a hybrid approach that trains a U-shaped convolutional neural network (UNet) on two input channels derived from frequency differencing (FD) and PCA cleaning, enabling it to exploit their complementary behavior across different scales. This two-channel strategy achieves improved performance, maintaining the cross-correlation power spectrum close to unity on large scales under a cosine beam and improving by 5%–8% relative to either FD- or PCA-based UNet alone. We further show that the method can robustly recover the HI signal even when the beam model is imperfect and differs between training and testing, with the large-scale cross-correlation remaining close to unity within the $1\sigma$ level. These results demonstrate that the proposed approach provides a robust framework for HI signal reconstruction under realistic observational conditions.

Cosmological vector fields are central to many early-Universe phenomena, including inflationary dynamics, primordial magnetogenesis, and dark-matter scenarios. However, constructing models able to generate cosmological magnetic fields while avoiding strong coupling, backreaction, and cosmic microwave background constraints remains challenging. We study a novel mechanism in which brief non-slow-roll phases during inflation amplify primordial magnetic fields at small scales, while maintaining theoretical consistency and observational viability. We incorporate parity-violating interactions in the vector sector and demonstrate, for the first time in a non-slow-roll framework, that chirality can significantly boost magnetic-field amplitudes and imprint distinctive polarization-dependent spectral features. We complement detailed numerical computations with an analytical treatment yielding compact expressions for chiral vector mode functions that reproduce the main spectral properties. We then develop a systematic formalism to evaluate the stochastic gravitational-wave background naturally induced at second order by these amplified fields, identifying both an intensity component and a circularly polarized contribution with characteristic frequency profiles. We discuss detection prospects with future multiband gravitational-wave observatories, showing that chiral signatures could provide a distinctive observational probe. Our results introduce new avenues for enhancing primordial magnetic fields and their associated gravitational-wave signals, opening promising possibilities for their future detection and interpretation, both with cosmological and gravitational-wave probes.

We present the most up-to-date constraints on axion early dark energy (AEDE) from cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) measurements. In particular, we assess the impact of data from ground-based CMB experiments, the South Pole Telescope (SPT) and the Atacama Cosmology Telescope (ACT)—both with and without Planck—on constraints on AEDE. We also highlight the impact that BAO information from the Dark Energy Spectroscopic Instrument (DESI) has on these constraints. From CMB data alone, we do not find statistically significant evidence for the presence of AEDE, and we find only moderate reduction in the Hubble tension. From the latest SPT data alone, we find the maximal fractional contribution of AEDE to the cosmic energy budget is $f_{\mathrm{EDE}}<0.12$ at 95% confidence level (CL), and the Hubble tension between the SPT and Supernovae, H0, for the Equation of State of Dark Energy (SH0ES) results is reduced to the $2.3\sigma$ level. When combining the latest SPT, ACT, and Planck datasets, we find $f_{\mathrm{EDE}}<0.070$ at 95% CL and the Hubble tension at the $3.6\sigma$ level. In contrast, adding DESI data to the CMB datasets results in mild preference for AEDE and, in some cases, non-negligible reduction in the Hubble tension. From $\mathrm{SPT}+\mathrm{DESI}$, we find $f_{\mathrm{EDE}}=0.081_{-0.052}^{+0.037}$ at 68% CL, and the Hubble tension reduces to $1.5\sigma$. From the combination of DESI with all three CMB experiments, we get $f_{\mathrm{EDE}}=0.055_{-0.047}^{+0.024}$ at 68% CL and a weak preference for AEDE over $\mathrm{\Lambda }\mathrm{CDM}$. This data combination, in turn, reduces the Hubble tension to $2.6\sigma$. We highlight that this shift in parameters when adding the DESI dataset is a manifestation of the discrepancy currently present between DESI and CMB experiments in the concordance model $\mathrm{\Lambda }\mathrm{CDM}$.

We consider the stochastic gravitational wave background induced by arbitrary source fields that are amplified during cosmological inflation. The associated tensor spectral index is shown to be given, under minimal assumptions, by a simple formula easy to apply in most situations of accelerated expansion. For slow-roll inflation, the induced spectrum is nearly scale invariant, with an index deviating from the standard outcome of vacuum generated gravitational waves. Remarkably, we demonstrate that scale invariance remains true regardless of the original spectrum of the source. We show how this generic approach reproduces the literature on specific models of gravitational wave primordial sources, and discuss its limitations. It provides a very practical estimation of the tensor spectral index for future models, to which subleading corrections can then be added.

A prominent, 200-pc-scale high-energy nebula surrounding the microquasar V4641 Sgr is the brightest known gamma-ray source in the southern sky at $E>100\mathrm{TeV}$. In this paper, we develop self-consistent leptonic, hadronic, and leptohadronic models that reproduce both the observed spectrum and morphology of the source. Purely leptonic models are energetically more favorable yet they require rather specific morphological assumptions. The gamma-ray morphology of the source can be better explained within a hadronic scenario based on the identification of cold gas structures spatially correlated with the observed gamma-ray emission. However, a purely hadronic model for the source emission requires a substantial energy reservoir in protons and fails to reproduce the extended x-ray emission recently detected by XRISM. We show that emission including a combination of leptonic and hadronic components can reproduce both the spectral and morphological properties of the source. We provide predictions for the x-ray and neutrino spectra of the nebula that can discriminate the hadronic and leptonic contributions to the overall source signal.

Dark matter-neutrino interactions affect the propagation of astrophysical neutrinos, attenuating the flux of neutrinos arriving at Earth. Using the highest-energy neutrino event detected to date by the KM3NeT Collaboration as an example, and assuming an extragalactic origin, we derive limits on these interactions at $E_{\nu }=220_{-110}^{+570}\mathrm{PeV}$. Considering only the propagation on the Milky Way dark matter halo, we constrain the interaction cross section over the mass of the dark matter candidate to be ${\sigma }_{\mathrm{DM}-\nu }/m_{\mathrm{DM}}\lesssim {10}^{-22}{\mathrm{cm}}^2{\mathrm{GeV}}^{-1}$. If a transient source was positively identified, the high-energy neutrino would have crossed the dark matter halo of the source host as well, resulting in more stringent constraints (e.g., up to $\sim 6$ orders of magnitude assuming the blazar PKS 0605-085 is the source). These bounds on the dark matter-neutrino interaction cross section are translated into limits on the mass of the dark matter candidate, the mass of the mediator, and the coupling strength for different simplified models. We find that the constraints from the KM3-230213A high-energy event for these simplified models are almost entirely ruled out for masses above the mega-electron-volts by unitarity constraints. Therefore, the attenuation of such energetic neutrinos by dark matter calls for richer dark sectors in order to produce meaningful constraints.

We investigate the decay of bosonic dark matter with masses between 1 MeV and 2 TeV into Standard Model final states. We specifically focus on dark photons that kinetically mix with the Standard Model, as well as scalar dark matter models that have Yukawa couplings with the Standard Model. Using INTEGRAL and AMS-02 data, we constrain the dark matter decay lifetime into final states that include photons or positrons, setting strong constraints on the dark matter lifetime that reach ${10}^{25}\mathrm{s}$ for dark matter below 10 GeV and up to ${10}^{29}\mathrm{s}$ for dark matter above 10 GeV.