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Dimensionless observables of neutron stars, such as the moment of inertia, the tidal deformability, the spin-induced quadrupole moment, and the compactness, satisfy the I--Love--Q and Love--$C$ universal relations to percent-level accuracy over a wide range of equations of state. We investigate analytically the origin of this insensitivity in the stellar structure equations. We derive asymptotic expansions of these relations directly from the differential equations and boundary conditions for slowly rotating, tidally deformed stars described by a general piecewise-polytropic equation of state. Although the differential equations allow several forms of the asymptotic expansion, we find that only one class is consistent with the observed universality, and we use this class to analyze the universal relations. Because the observables are determined at the stellar surface, information about the deep-interior equation of state can enter them only through the parameters that survive in the asymptotic expansion at the surface. We find that the universal relations depend only on three parameters: two integration constants and one polytrope index of the outermost segment. By determining how these parameters deform the relations, we show that, throughout the region of parameter space occupied by realistic equations of state, the resulting deviations remain at the percent level, consistent with the observed accuracy of the universal relations. Within the same formalism, we classify violations of universality according to the additional degrees of freedom or input data responsible for them. Since the construction relies only on the underlying differential equations and boundary conditions, the same procedure can be applied to other systems once the corresponding equations and boundary conditions are specified.

There continues to be growing interest in using standard language constructs for parallel and accelerated HPC computing, avoiding the need for (sometimes vendor-specific) external APIs. For Fortran applications, language features such as 'do concurrent' loops open the door for compilers to implement multi-threaded, GPU-accelerated, and even distributed multi-node code with only the standard language. Here, we explore the current status of using 'do concurrent' for GPU-accelerated Fortran applications across three major GPU vendors (NVIDIA, AMD, and Intel). Using a production application, we test their current capabilities, showing where the standard language alone can be used, and where augmenting the code with a directive-based API (e.g., OpenMP) is still desirable or required. Multi-GPU tests are performed with GPU-aware MPI libraries. We find that the three GPU vendors can now GPU-accelerate pure Fortran (zero directives), but that manual data movement directives can help with performance and compatibility. The results show that there is rapid advancement towards making GPU-accelerated scientific HPC code performance portable using the Fortran standard language.

The postmerger phase of binary neutron star (BNS) mergers encodes valuable information about the equation of state (EOS) of supranuclear matter. Extracting this information from the analysis of the postmerger waveforms remains challenging due to the high-frequency limitations of current detectors. Future third-generation observatories, such as the Einstein Telescope (ET) and NEMO, will have the sensitivity required to resolve post-merger signals with high fidelity. In this work, we apply CLAWDIA, our recently developed sparse dictionary learning (SDL) framework, to classify different EOS models using the merger and postmerger gravitational-wave emission of simulated BNS mergers available in the CORE database. Our dataset comprises five EOS models representative of a broad range of neutron star properties. The SDL framework is optimized under realistic detection conditions by injecting signals into simulated noise matching the sensitivity curves of ET and NEMO. Our results show that classification is primarily driven by the dominant postmerger frequency, <inline-formula><mml:math><mml:msub><mml:mi>f</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math></inline-formula>, which encodes EOS-dependent information. At a modest signal-to-noise ratio of 5, our method achieves <inline-formula><mml:math><mml:msub><mml:mi>F</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></inline-formula> scores of 0.76 for ET and 0.70 for NEMO, with performance improving for higher signal-to-noise ratios. The reliability and generalization capabilities of the model are assessed with additional tests, including the classification of an EOS not included in the training dataset and the analysis of detector-specific biases.

Inspired by Mashhoon's bound state method, we propose a new bound state method for computing quasinormal modes (QNMs). By a two-step coordinate transformation where a real parameter $α$ is introduced, a QNM problem is mapped to a bound state problem, whose eigenvalues $E_n(α)$ are inversely mapped to the QNM frequencies $ω_n$ via analytic continuation. With this method, we numerically calculate various QNM frequencies for a Schwarzschild black hole directly from the bound state spectrum of the inverted Regge-Wheeler potential for the first time. It is found that the method yields QNM frequencies of high accuracy for low-lying modes with overtone $n\leq\ell$ ($\ell$ is the multipole number), while the accuracy degrades or the calculation fails for higher overtones. To identify the origin of this limitation, we analyze the singularity structure of the eigenvalues $E_n(α)$ using Padé approximants in the complex $α$-plane. For higher overtones, the singularities of $E_n(α)$ lie within the analytic continuation circle, providing a direct explanation for the limitation of the method. To mitigate this limitation, we suggest a homotopy deformation to the potential, which improves the method and enable us to compute a few more high overtone modes reliably.

We investigate static, spherically symmetric regular black holes with anti-de Sitter (AdS) asymptotics in arbitrary spacetime dimensions. They are solutions of Einstein gravity, sourced by an anisotropic fluid whose radial pressure corresponds to vacuum energy, while the tangential pressure satisfies a generalized polytropic equation of state. By solving the Einstein field equations, we derive a generic class of asymptotically AdS black hole solutions and determine the conditions required for spacetime regularity. We then investigate the dynamical formation of these regular black holes within the thin-shell formalism, assuming a linear barotropic equation of state for the shell matter. Next, we study the thermodynamics of the regular AdS black holes in arbitrary dimensions by verifying the first law of black hole thermodynamics and the corresponding Smarr relation. We analyze the thermodynamic stability and phase structure of solutions in four, five, and six spacetime dimensions, demonstrating the existence of dimension-dependent phase transitions.

We investigate whether optical and far-infrared [O III] emission from nearby metal-poor dwarf galaxies can be represented by a homogeneous one-zone ionized-gas model with a single electron temperature and density. Our sample comprises five galaxies from the Herschel Dwarf Galaxy Survey: HS1222+3741, SBS0335-052E, POX186, Haro11, and IZw18. We combine galaxy-integrated or nearly galaxy-integrated [O III] 4363 and 5007 measurements from Seimei/KOOLS-IFU observations and published or archival spectroscopy with Herschel/PACS [O III] 88um measurements. Because [O III] 4363 is not detected in HS1222+3741, the analysis is based on the remaining four galaxies. SBS0335-052E and Haro11 lie near or slightly beyond the low-density boundary of the one-zone diagnostic. Their nominal line ratios favor effective densities of ne<1cm-3, while conservative treatment of the uncertainties allows values up to 40 and 10cm-3, respectively. These remain substantially below densities inferred from independent diagnostics. By contrast, POX186 and IZw18 show no significant discrepancy between the optical--far-infrared [O III] and low-ionization optical diagnostics. Additional optical and ultraviolet diagnostics show that inferred densities can span several orders of magnitude within a galaxy. Representative two-zone models reproduce the [O III] 4363, 5007, and 88um emission in SBS0335-052E and Haro11 by combining relatively dense gas with cooler, low-density gas. The low-density component contributes approximately 61% and 72% of the 88um luminosity, but only 14% and 23% of the 5007 luminosity, respectively. These solutions are not unique and may represent a broader unresolved distribution of gas conditions. Our results show that temperatures and densities inferred from integrated one-zone analyses are effective quantities and that similar diagnostic discrepancies can arise in nearby metal-poor galaxies.

The Event Horizon Telescope (EHT) Collaboration's images of the supermassive black holes in M87 and the Milky Way have provided the first event-horizon-scale views of these objects, opening new avenues for studies of gravitation, accretion physics, and black hole astrophysics. Achieving these results, however, requires imaging under some of the most challenging conditions in radio astronomy, including low signal-to-noise ratios, severe calibration uncertainties, and sparse aperture coverage. With the aim of presenting independent analyses of the public EHT datasets for M87* and Sgr A*, we adopt an approach that is independent in observables, and reconstruction methodology. Our framework is based on closure invariants, a class of interferometric observables that are intrinsically immune to station-based calibration errors and therefore provide robust constraints on source structure. We combine these observables with Generative Deep learning Image Reconstruction with Closure Terms (GenDIReCT), a diffusion-based image reconstruction framework that operates in the latent space of images conditioned on closure invariants. We present independent reconstructions obtained using GenDIReCT on synthetic challenge data sets as well as real EHT data on 3C279 and Centaurus A, and compare them with previously reported results. This work demonstrates the potential of closure-invariant-driven generative imaging as a calibration-resilient framework for Very Long Baseline Interferometry (VLBI) and provides an independent and complementary avenue for interpreting horizon-scale black hole observations.

In this paper we employ the open quantum system framework with the influence functional formalism to non-perturbatively analyze the response of an Unruh-DeWitt detector modeled as a harmonic oscillator which interacts with a massless scalar field in impulsive plane wave spacetimes. Subtracting the Minkowski results, we obtain the expectation values for $\langle Q^2 \rangle$, $\langle P^2 \rangle$, and $\langle \{Q,P\} \rangle$, along with transition probabilities $P_{0\rightarrow 1}$ from ground state to the first excited state of the detector due to the influence of the wave. Explicit calculations are performed for both a pure gravitational wave (vanishing Ricci tensor) and a null electromagnetic wave (vanishing Weyl tensor). In both scenarios, the wave suppresses excitation transitions. Since our approach is non-perturbative, we are able to consider cases with both weak and strong coupling constants.

We study tensor perturbations propagating through a viscous relativistic medium in a spatially flat FLRW universe, with particular emphasis on the correction produced by spatial free streaming beyond a local causal relaxation model. We start from the relaxation-time Boltzmann equation used by Baym, Patil, and Pethick to describe the response of matter to a gravitational wave. In the zero-streaming limit, the tensor stress obeys a Maxwell-Cattaneo, or linear Muller-Israel-Stewart, relation. We then retain the spatial streaming term and evaluate the resulting angular response analytically for an ultrarelativistic isotropic medium. The resulting kinetic response is coupled to the tensor Einstein equation and solved numerically in a flat matter-plus-Lambda background, with comparison to the local MIS propagation model and an independent kinetic WKB calculation. For the illustrative normalization considered, the full numerical calculation produces a nonmonotonic correction to the tensor power transfer function, with a maximum of about 0.8 percent near x equal to 0.37 and a minimum of about minus 5.6 percent near x equal to 1.97. These features are stable under angular-resolution and ODE-tolerance tests and are reproduced by the kinetic WKB calculation. We also find a corresponding finite-momentum phase correction. The effect is a property of the specified single-relaxation-time kinetic model and should not be interpreted as a universal transport law.

Several recent observational analyses have suggested the possible existence of a large-scale anisotropy in our Universe. It is often thought that this would contradict the inflationary picture of the earliest times. We show that this is not the case: if we relax the artificial restriction that spacetime torsion must be zero, then such anisotropies arise naturally, indeed almost inevitably, in a theory of torsional Inflation. This is seen most clearly if one uses a ``$1\,+\,3\,$'' analysis of a torsional spacetime, leading naturally to concepts of intrinsic torsion and extrinsic torsion. An anisotropic quantum fluctuation of the inflaton leads to an extrinsic torsion field which is anisotropic and which grows throughout the inflationary era, even though the intrinsic geometry of the spatial sections is isotropised in the conventional manner. The competition between the intrinsic torsion (which does inflate away) and the extrinsic torsion leads to a short interval, early in the inflationary era, during which there is a torsion-induced energy flux, which leaves an anisotropic signal in superhorizon modes and thus ultimately at large scales in the present Universe.

The abundance of galaxy clusters is a powerful cosmological probe, but optical cluster cosmology is limited by selection systematics, in particular the projection effects that affect cluster finders based on galaxy populations such as the red sequence. The outer stellar mass ($M_\mathrm{out}$) of cluster central galaxies -- e.g., the stellar mass in a 50-100 kpc annulus -- offers an alternative selection that relies only on the central galaxy and is therefore largely free from projection effects. Its primary systematic is instead satellite contamination, since massive clusters can host more than one galaxy with high outer stellar mass. Using the IllustrisTNG300 simulation at $z=0.4$, we quantify this contamination and investigate a simple, proximity-based percolation method to mitigate it, in which galaxies with lower outer stellar mass lying within a given radius of a more massive galaxy are removed from the sample. We find that the satellite fraction defined by the friends-of-friends (FoF) algorithm is modest even without percolation ($\leq 15\%$ for $M_\mathrm{out} > 10^{10}\,\mathrm{M}_\odot$ and $<10\%$ for $M_\mathrm{out} > 10^{11}\,\mathrm{M}_\odot$), and that percolation reduces it further, with the improvement increasing for percolation radii up to $3.0\,R_{200c}$. For a moderately high outer stellar mass cut ($\sim 4\times10^{10}\,\mathrm{M}_\odot$) and percolation radius ($\sim 2.0\,R_{200c}$), we recover a cluster sample that is both highly complete and pure for halo masses $\gtrsim 10^{14}\,\mathrm{M}_\odot$. These results indicate that outer stellar mass, combined with simple percolation, has the potential to provide a clean and readily calibratable selection of massive galaxy clusters.

We use physics-informed neural networks (PINNs) to solve the gravitational quasinormal-mode (QNM) eigenvalue problem for Kerr spacetime directly in the two-dimensional hyperboloidal formulation of the Teukolsky equation. This formulation does not require separation of variables and thus retains the coupled radial--angular structure. Such a scheme provides a prototype for calculating the QNMs of beyond-Kerr black holes for which the perturbation equations are non-separable. Sequences with increasing angular momentum are constructed, reaching close to the extremal limit. We focus on the fundamental modes $(\ell,m,n)=(2,0,0)$, $(2,1,0)$, $(2,2,0)$, $(3,3,0)$ and $(4,4,0)$, together with the first overtone $(2,2,1)$. Independent benchmark evaluation shows that every reported real and imaginary frequency component remains below $0.5\%$ error, with a median deviation of $0.1\%$. This accuracy is maintained in the near-extremal regime, where the damping rate becomes small and the modes are longest-lived. The results establish a non-spectral numerical route to multidimensional black-hole perturbation eigenproblems which does not match the substantially higher precision of dedicated Kerr solvers but offers greater flexibility and requires less analytical pre-processing. Non-separable rotating backgrounds and coupled systems, such as gravitational--electromagnetic Kerr--Newman perturbations, are natural extensions of the same construction.

Quintessential $α$-attractor models of single-field inflation and evolving dark energy were constructed about a decade ago. Recently, it was pointed out that some of them might be disfavored due to dark-radiation constraints on gravitational waves and the higher values of $n_s$ favored by ACT. Here we present a class of updated quintessential $α$-attractor models in which a single field describes both inflation and evolving dark energy, yields higher values of $n_s$, and admits reheating scenarios consistent with the dark-radiation bound on $ΔN_{\rm eff}$. Depending on the value of the cosmological constant $Λ$, these models interpolate between $Λ$CDM with $Λ> 0$ (future dS universe), dynamical dark energy with $Λ= 0$ (future Minkowski universe), and dynamical dark energy with $Λ< 0$ (future cosmological collapse). We also study quintessential $α$-attractor models based on an axion-inflaton complex scalar field with hyperbolic geometry, which describe inflation and dark energy of a ``phantom illusion'' type compatible with DESI DR2.

In previous work arXiv:2604.00160, we found soliton solutions in a deformation of the sine-Gordon theory in AdS spacetime that, in the infinite-radius limit, reduce to single-soliton solutions in flat space. In this paper, we find another single soliton solution that has no analog in flat space.

To confirm $Λ$CDM deviations are due to missing physics (not systematics), one should demonstrate that the model fitting parameters exhibit qualitatively similar redshift drift across independent observables. This is the only way one guarantees new physics. Here, we show that a recent Dark Energy Spectroscopic Instrument (DESI) DR2 Full-Shape (FS) modelling Lyman-$α$ constraint at $z_{\rm eff} = 2.33$ combined with earlier DR1 FS modelling constraints with $0.295 \leq z_{\rm eff} \leq 1.491$ leads to a straight line $Ω_m(z) = m z + c$ with slope $m = 0.022 \pm 0.012$, $1.8 σ$ removed from constant $Ω_m$. Akaike Information Criterion and Bayesian evidence confirm that constant $Ω_m$ and increasing $Ω_m(z)$ are statistically indistinguishable. Through the $Om(z)$ diagnostic, we review how increasing and decreasing $Om(z)$ map to phantom and quintessence dark energy (DE) regimes, respectively. While FS modelling constraints map to phantom DE, the decreasing and increasing $Ω_m(z)$ trends in DESI BAO and DESI with external data make a phantom crossing inevitable. Since dynamical DE is but one interpretation for $Ω_m(z)$ trends, it is imperative that different datasets converge on their $Ω_m(z)$ trends before one jumps to physical conclusions. We forecast how DESI FS modelling $Ω_m$ constraints will improve up to the final data release and explore the implications for model selection.

We present new multi-frequency VLBA observations of \object{J0011+3443} (TXS\,0008+344, $z=0.89$) at 2.3, 4.9, 8.5, and, for the first time, 23.6\,GHz. The source consists of two compact components A and B at a projected separation of $314\pm2$\,pc, plus a third feature C detected at 23.6\,GHz at $0.6$\,mas from A. Archival low-resolution radio measurements confirm an integrated gigahertz-peaked spectrum, with an observed-frame peak frequency of $ν_\mathrm{peak}=0.73\pm0.08$\,GHz and a peak flux density of $S_\mathrm{peak}=879\pm125$\,mJy. Comparison with nearly frequency-matched low-resolution measurements shows that the VLBA recovers $0.85\pm0.11$ of the 4.85\,GHz flux density and $0.50\pm0.06$ of the 8.46\,GHz flux density. The lower recovered fraction at 8.5\,GHz suggests that low-surface-brightness emission is resolved out or falls below the VLBA surface-brightness sensitivity. We therefore interpret the VLBA component spectra as spectra of the compact recovered emission only. The 23.6\,GHz morphology, the absence of a detected flat-spectrum core, the similar compact spectra of A and B, and the steep integrated GHz spectrum favor an interpretation of \object{J0011+3443} as a GPS-class compact symmetric object, possibly in a short-lived or relic phase, although a dual-AGN origin cannot be excluded without multi-epoch astrometry.

The post-Minkowskian expansion of general relativity expands the metric in Newton's constant G around flat space-time, but much effort currently focuses on ways to extend its range of applicability by summing the perturbative series to all orders. A regime of particular interest is a specific high-energy limit where a formula derived recently provides the momentum kick of binary scattering problem to all orders, and even suggests an approach towards strong coupling. We show that this is an asymptotic expansion. Although the series diverges we give evidence that it is Borel summable, and the full function in integral form is finite. As a by-product we determine the transcendentality properties of the coefficients in the expanded expression.

We investigate a charged anisotropic radiating stellar configuration undergoing gravitational collapse in the presence of shear and heat flux within the Einstein Maxwell framework. The interior spacetime is described by a time dependent spherically symmetric geometry and is matched to an exterior charged Vaidya spacetime. The electromagnetic field is incorporated explicitly through Maxwell equations, allowing the electric charge to contribute to the matter variables, mass function, and boundary evolution. The charged junction condition is reduced to a Riccati type differential equation with suitable transformations and exact solution is obtained. The physical properties of the resulting shearing solution are examined through the energy density, radial and tangential pressures, pressure anisotropy, heat flux, electric charge, energy conditions, sound speeds, Herrera cracking criterion, and complexity factor. The energy density and radial pressure remain positive and decrease towards the stellar surface, whereas the tangential pressure remains negative, confirming the anisotropic character of the configuration. Heat transport and electromagnetic effects are strongest in the inner stellar region. The energy and causality conditions are satisfied. The cracking function indicates potential stability against cracking. The complexity factor remains positive, with electric charge providing an additional contribution alongside pressure anisotropy, density inhomogeneity, and dissipative heat flux. These results provide a comprehensive picture of the physical behavior and internal structure of the charged shearing radiative collapse model.

We analysed observations of the Fe I 617.3 nm, Ca II 854.2 nm, and Ca II H lines obtained with CRISP and CHROMIS at the SST. Spatially coupled non-LTE inversions constrained the chromospheric atmosphere, while the WFA provided estimates of the chromospheric line-of-sight magnetic field. We combined these photospheric and chromospheric constraints with an HMI magnetogram as input to a multi-height field extrapolation. We characterised the reconstructed topology using the twist number, squashing factor, current density, and field-line connectivity. Results. The Ca II H magnetic signal is concentrated mainly above the strongest photospheric field concentrations, whereas Ca II 854.2 nm yields stronger and more spatially extended line-of-sight fields. The chromosphere above the shared penumbra is approximately 300 K hotter than nearby quiet regions. The selected brightening follows a chromospheric loop, with enhanced temperature and a transition from blueshift to redshift along the structure. The extrapolation recovers field strengths broadly consistent with the inversions and reveals a left-handed, flux-rope-like core following the polarity inversion line. Enhanced currents and connectivity gradients occur near parts of its boundary, where field lines connect the twisted structure to overarching loops. Conclusions. The temperature and velocity patterns and magnetic topology are consistent with reconnection between the twisted polarity-inversion-line field and the surrounding loops, depositing energy in the chromosphere and driving plasma along reconfigured field lines. These signatures do not uniquely establish reconnection, but show that combining high-resolution spectropolarimetric inversions with multi-height extrapolations can relate chromospheric energy release to the local three-dimensional magnetic structure.

We study singular generalized Dirac-oscillator couplings in the near-horizon region of a nonextremal BTZ black hole. An effective covariant construction adapted to the stationary horizon congruence relates the two singular profiles to the proper acceleration and its radial gradient, whose leading near-horizon behaviors are $1/ρ$ and $1/ρ^2$. This motivates the family $\mathcal{L}_p(ρ)=λ_0+β_p/ρ^p$, with $p=1,2$. The $p=1$ system has a regular singular point and is Fuchsian, whereas $p=2$ is the first irregular case; more generally, a leading $ρ^{-p}$ interaction with $p>1$ has Poincaré rank $p-1$. For $p=1$, a constant spinor transformation reduces the matrix-Coulomb system exactly to the Whittaker equation, while elimination in the original basis gives an equivalent confluent-Heun representation with an apparent finite singularity. For $p=2$, the local branches contain the essential factors $e^{\pmβ_2/ρ}ρ^{-1/2}$, and their coefficient expansions exhibit generic factorial late-order growth. The finite-radius response $\mathcal{Z}_p(Ω;ρ_0)=ψ_{2,p}(ρ_0)/ψ_{1,p}(ρ_0)$ obeys an exact Riccati equation whose large-damping expansion first becomes sensitive to the radial gradient of the interaction at order $γ^{-3}$. Even when the two couplings are matched at $ρ_0$, this response retains information about their different pole orders. The response functions provide local spinorial data for subsequent matching to the complete BTZ exterior.

This work explores asymptotically de Sitter black-bounce spacetimes, obtained as a regular extension of the Schwarzschild-de Sitter geometry via the Simpson-Visser prescription. The resulting family of solutions provides a smooth interpolation between regular black holes, extremal configurations, and traversable wormholes within a single geometrical framework. In particular, we verify the regularity of the spacetime by showing that (some of) curvature invariants, including the Kretschmann and Ricci scalars, remain finite at the origin for any non-vanishing value of the regularization parameter $a$, ensuring geodesic completeness. An analysis of the effective stress-energy tensor reveals a violation of the null energy condition, which can be consistently interpreted in terms of a composite source involving a phantom scalar field coupled to nonlinear electrodynamics. Subsequently, we investigate the observational signatures of these geometries by studying: i) null geodesic propagation and ii) constructing the associated optical appearance. In particular, we determine the shadow radius and characterize the structure of photon rings through numerical ray-tracing procedure. Finally, we compute the spectrum of axial gravitational perturbations using a pseudospectral approach, obtaining the quasinormal mode frequencies and their overtones. Our results show a non-trivial interplay between the cosmological constant and the regularization scale $a$, which imprints itself on both the light-ring structure and the quasinormal spectrum. These features suggest potential observational discriminants that could distinguish these regular spacetimes from their singular counterparts in future gravitational-wave and high-resolution electromagnetic observations.

Freezing gravity (FG), a phantom-crossing dark energy model, was recently proposed in the absence of matter. In this work, we study FG minimally coupled to a perfect fluid through a detailed cosmological perturbation analysis and derive the conditions for the absence of ghost and gradient instabilities. The ghost stability conditions are obtained analytically without taking the high-$k$ limit, yielding the ghost-free range of scales and a finite cutoff when it exists. In the branch where a finite cutoff is already present in vacuum, we find that matter coupling lowers it relative to its vacuum value. Moreover, in the high-$k$ regime, the gradient stability condition guarantees a positive effective gravitational coupling for cold dark matter. We further show that two characteristic properties of FG persist in the presence of matter. First, the background and perturbation sectors remain separated, in the sense that they are controlled by independent sets of parameters, allowing FG to realize arbitrary background evolutions, including phantom crossing, while maintaining stable perturbation dynamics. Second, the scalar degree of freedom of FG becomes non-dynamical in the large-scale limit at linear order, while propagating with a finite speed of sound on small scales. Whether this behavior persists to arbitrarily high orders in perturbation theory, thereby avoiding the potential strong-coupling issue, requires further investigation through a nonlinear perturbation analysis. To make contact with large-scale structure and gravitational lensing observables, we also derive the effective gravitational coupling and gravitational slip within the quasi-static regime and express our results in terms of the EFT parameters.

Spin inversions appear in several settings. Analytical work predicts a single spin flip during unequal-mass supermassive binary inspiral, while numerical relativity and post-Newtonian calculations show repeated flip-flop motion in comparable-mass binaries. Secular spin evolution also predicts additional cases driven by spin-induced mass quadrupoles. Whether these effects can be distinguished in gravitational-wave data is still unclear. We combine the secular spin angle equations with a quasi-circular second post-Newtonian frequency evolution and build a restricted waveform weighted by the sky-averaged LISA sensitivity. We study five near-equal-mass injections with detector-frame total mass $M=2\times10^5M_\odot$, including Kerr flip-flops and one quadrupole-induced case. Each injection is compared with physically evolving waveforms constrained to have no orbital-plane crossings. We search all four no-inversion sectors, vary the masses, spin magnitudes, and initial spin angles, and maximize over time, phase, and overall amplitude. Large spin motion does not by itself lead to a clearly different waveform in this restricted model. A weak spin that sweeps through $133.26^\circ$ leaves a residual SNR of $0.806$ at reference signal SNR $ρ_\star=100$. A case where both spins cross the orbital plane many times gives the largest residual, $1.641$. The quadrupole case has a secondary-spin range of $128.11^\circ$ with five crossings, yet the best no-inversion candidate found leaves a residual SNR of only $0.454$. All largest matches found exceed $0.999865$. Within this restricted model, the spin inversion cases are therefore strongly degenerate with no-inversion binaries at $ρ_\star=100$. More complete waveforms, including observer-frame precession modulations, higher harmonics, separate polarizations, and the full LISA response, are needed to test whether this degeneracy can be broken.

Buchdahl transformations provide a geometric route from vacuum spacetimes to scalar-field solutions. We formulate this mechanism as a target-covariant solution generator for Einstein gravity coupled to nonlinear sigma models in $D>3$ dimensions. On any connected region in which a Ricci-flat seed admits a non-null hypersurface-orthogonal cyclic coordinate with fixed-sign nonzero norm, the logarithm of that norm defines a Buchdahl potential $Σ$. A one-parameter redistribution of the cyclic norm then generates the exact Ricci source $R_{AB}=C_D(β)\partial_AΣ\partial_BΣ$, with $C_D(β)=\frac{D-2}{D-3}(1-β^2)$, while $Σ$ remains harmonic in the deformed metric. Composing $Σ$ with an affinely parametrized geodesic of a non-degenerate target metric whose squared speed is $C_D(β)$ therefore yields an exact Einstein--sigma-model solution. For positive-definite targets, the corresponding pullback condition also implies that the nontrivial scalar map has one-dimensional image; for indefinite targets, the geodesic ansatz remains a sufficient solution-generating sector but need not exhaust all possible realizations of the same rank-one spacetime source. Through the Einstein/Jordan-frame correspondence, the construction gives vacuum tensor--multiscalar solutions as well. We illustrate the unified generator with flat, spherical, hyperbolic and axion--dilaton targets and with Tangherlini, Weyl, Kasner, Rosen-wave, Gowdy, Kaluza--Klein bubble and C-metric seeds. The result separates cleanly the geometric Buchdahl source from its target-space realization and extends this rank-one cyclic sector across static, cosmological, wave and accelerating geometries.

We construct an analytical relativistic two fluid star characterized by a mixed core, where ordinary matter and dark matter coexist as two independently conserved incompressible perfect fluids, and an envelope composed exclusively of ordinary matter. The fluids exchange neither matter nor energy and interact only through the common spacetime geometry, with the ordinary component extending across the core envelope interface while the dark component is confined to the core. Despite the mixed core--single-fluid envelope structure and the internal interface, the system remains analytically tractable, allowing us to obtain explicit expressions for the pressures and metric functions and to follow directly the effects of the dark-matter fraction and relative core size. We determine the physically admissible parameter space and derive a Buchdahl like critical compactness associated with the divergence of the central pressure, whose value depends on the relative dark matter density and the size of the mixed core. The Schwarzschild constant density star and its standard critical value, $2M/R=8/9$, are recovered in the corresponding one fluid limit. The mass--radius analysis further shows that configurations with the same global compactness can correspond to distinct internal matter distributions. Beyond providing an analytically controlled description of a core-confined second component, the construction offers a useful benchmark for identifying qualitative trends that may subsequently be examined in more realistic dark matter admixed neutron star models, whose detailed treatment lies beyond the scope of the present work.

We develop a semi-analytic and semi-numerical formulation of the harmonic-gauge second post-Newtonian (2PN) equations of motion for a general point-mass N-body system within Hadamard regularization. The equations of motion are separated into a closed analytic contribution and a non-closed integral contribution. We analyze the singular structure of the latter and further regularize it into a numerically evaluable representation. We apply the formulation to the Sun-Jupiter-Saturn and Sun-Mercury-Venus systems, evaluating the instantaneous non-closed 2PN acceleration along Newtonian trajectories and its leading finite-time relative-distance response through the corresponding perturbation equations. In both benchmarks, the non-closed acceleration remains a small fraction of the complete 2PN acceleration, while the induced relative-distance perturbation remains oscillatory and can reach larger oscillation amplitudes at later times.

We use lattice methods to study inflation in the scalar Gauss-Bonnet (SGB) gravity theory. We focus on the ultra-slow-roll scenario with the peak frequency falls into the PTA band. In the parameter range we consider, we find that the lattice results exceed the perturbative predictions, which differs from the case in Einstein gravity. We further find that lattice corrections become significant when the peak of the primordial curvature spectrum reaches $\sim 10^{-2}$. We calculate the energy density spectra of second-order scalar induced gravitational waves (SIGWs) using the primordial power spectra obtained from both the lattice method and the traditional perturbative method, and analyze the SGB model in light of current pulsar timing array (PTA) observations. Our results indicate that lattice corrections enhance the ability of the SGB model to dominate the PTA observations.

We present the thermo-mechanical design of the cryostat and camera optics for SPT-3G+, a new receiver being developed for the South Pole Telescope (SPT). The receiver consists of 14 detector arrays of 90/150 GHz dichroic polarization-sensitive pixels, totaling 24,080 transition-edge sensor detectors. Each detector array lies at the end of an optics tube, each approximately 240 mm in diameter and 772 mm in length, which are arranged in a hexagonal close-packed configuration to achieve a 4 degree diameter field of view. Each optics tube contains four anti-reflection coated lenses fabricated from different materials (alumina, silicon, and nylon) that are designed to also provide infrared filtering that reduces the radiative loading on the cryogenic stages. The optics and detectors are cooled by a combination of a pulse tube cooler for the 40 K and 4 K stages, and a dilution refrigerator for the 1 K and 100 mK stages. Thermal modeling predicts the heat load to be less than 26 W and 1 W for the 40 K and 4 K stages, respectively. The 1,550 kg cryostat has a 1.1 meter diameter at the vacuum window, which is located near the telescope Gregorian focus, and 1.75 meters in height and length. Fabrication of the cryostat will begin in 2026, with installation on the SPT scheduled for the 2028-29 austral summer, ahead of the 2029 winter observing season.

Infrared Dark Clouds are ideal sites for investigating the initial conditions of massive star and cluster formation. The A Lei Of the Habitat and Assembly of Infrared Dark Clouds (ALOHA IRDCs), a James Clerk Maxwell Telescope (JCMT) Large Program, has mapped nearby IRDCs with SCUBA-2. Complementary molecular line observations are needed to characterise the physical, kinematic, and chemical properties of the dense gas. We aim to determine the thermal, kinematic, and chemical properties of clumps identified in the ALOHA IRDCs, and to assess their evolutionary status and level of star-forming activity. We performed single-pointing K-band and W-band observations towards 56 ALOHA IRDCs clumps using the Effelsberg 100-m and Yebes 40-m telescopes, respectively. We derived NH3 kinetic temperatures using the hyperfine group ratio (HFGR) method and identified infall and shock signatures from HCO+, H13CO+, SiO, and HNCO profiles. Water masers and NH2D emission were used as complementary tracers of chemical evolution and star formation. The clumps exhibit kinetic temperatures of 15-29 K. We detect NH2D emission towards 18 sources, with NH2D centroid velocities consistent with NH3, indicating both species trace the same dense gas component. More than half of the clumps display blue-asymmetric HCO+ profiles, identifying them as infall candidates. Water masers are detected in 22 sources, with prominent velocity ranges and variability. Broad SiO emission (>~20 km/s) indicates strong shocks, while narrower extents (<~6km/s) likely trace large-scale interactions or low-velocity shocks. The widespread infall signatures, shock tracers, masers, and NH2D emission suggest that relatively quiescent, chemically young material can coexist with dynamically active gas affected by early protostellar feedback, providing insight into the coupled physical and chemical evolution of massive IRDC clumps.

The discovery of massive galaxies at redshifts $z\gtrsim10$ by the James Webb Space Telescope (JWST) has renewed interest in cosmological mechanisms capable of enhancing early structure formation while preserving the successful large-scale predictions of the standard $Λ$CDM model. We investigate a phenomenological scenario in which an exotic dark matter species can undergo a transient early dark energy-like phase during the radiation-dominated era ($10^{-7}\lesssim a\lesssim10^{-5}$) before reverting to pressureless cold dark matter. We utilize the generalized dark matter framework to model this species, which is restricted to a sub-percent fraction of the total dark matter component by CMB, BAO and Type Ia supernova data. Its background and perturbation dynamics are characterized by a time-dependent equation of state, $w(a)$, and a time- as well as scale-dependent sound speed, $c_s^2(a,k)$. The temporary negative equation of state, combined with our phenomenological pressure-response prescription, induces a finite interval of negative effective sound speed squared. This triggers an instability-driven growth of density perturbations over a limited range of comoving scales, thereby enhancing the formation of early dark matter halos. We find that the enhanced halo abundance can substantially reduce the star-formation efficiencies required to reproduce the observed abundance of JWST galaxies relative to the standard $Λ$CDM scenario, especially at higher redshifts. Our results demonstrate that transient early dark energy-like dynamics in a subdominant dark matter component provide a viable mechanism for enhancing early structure formation and offer a new framework for interpreting the abundance of high-redshift galaxies observed by JWST and future surveys.

Transverse baryon acoustic oscillation (BAO) measurements are increasingly used for cosmological inference, and carry a calibration that no such inference can constrain. A constant error in the transverse BAO scale is exactly degenerate with the combination $r_{\rm d} h$: it leaves the goodness of fit unchanged and the recovered parameters plausible, and is therefore invisible to any analysis that uses these measurements alone. The radial BAO sector removes this degeneracy, supplying $D_{\rm M}/r_{\rm d}$ by integration without reference to $H_0$ or to any model for the expansion rate. In flat Friedmann--Lemaître--Robertson--Walker (FLRW) geometry the relation between the two sectors is an identity, so the sound horizon and the dark-energy equation of state cancel as well. An integrated form of this identity reduces the consistency test to a straight line, whose slope measures a relative transverse calibration $\varepsilon$. A departure from $\varepsilon = 1$ cannot be produced by any dark-energy model, nor by spatial curvature: it indicates an inconsistency in the measurement chain rather than in the cosmology. We apply the test to the two main SDSS transverse BAO compilations, which give $\varepsilon = 1.073 \pm 0.021$ and $1.021 \pm 0.029$. The first differs from unity at $3.8σ$ using the published independent errors, while the second is consistent with unity. The two compilations themselves differ by $(5.4 \pm 1.4)\%$, or $3.9σ$, and the offset is constant in redshift. The test provides a direct diagnostic for current and future angular BAO measurements.

This work investigates whether the trace anomaly can diagnose the stellar response to a topological scalar field in tensor multi-scalar gravity. Eleven cold tabulated equations of state (EoSs) were examined, with six retained after general relativistic (GR) thermodynamic and causality checks. Their fiducial topological configurations were compared with the corresponding GR models under complementary matching prescriptions. After controlling for stellar mass and EoS dependence, the GR trace source strength $S_T$ remained strongly correlated with the topological mass response, with a partial Spearman coefficient $ρ=0.975$. Near $1.4\,M_\odot$, the topological configurations were systematically more compact, with Jordan frame radius reductions of $6.7$--$8.7\%$ at fixed baryonic mass and $0.87$--$1.29\,\mathrm{km}$ at fixed gravitational mass. These shifts are comparable to current uncertainties from the Neutron Star Interior Composition Explorer (NICER) and produce source dependent observational effects. Despite the global deformation, the interior effective source remained matter dominated, with a median topological contribution of about $0.8\%$. The GR matter trace therefore emerges as a useful diagnostic of the fiducial topological stellar response.

We present results from a multiwavelength study of the binary AGN candidate SDSS J095036.75+512838.1, which was identified as a candidate binary SMBH system due to its significant and variable broad H$β$ line shifts. We use available infrared-to-X-ray data to investigate the system's accretion properties. Analyzing recent Chandra observations, we characterize the X-ray emission and test the binary SMBH hypothesis. We find that the X-ray spectrum is well-modeled as a single AGN, with a 2--10 keV luminosity of $1.3 \times10^{43}$ erg s$^{-1}$. By assembling a comprehensive multiwavelength spectral energy distribution, we further examine the possibility of circumbinary accretion. The infrared-optical emission matches that expected from a single AGN, though we observe an excess in emission between $\sim 9500-19000 Å$ and a deficit near $\sim 2600 Å$. Archival optical spectra also suggest a deficit near $\sim 8500 Å$. We investigate whether these SED anomalies can be explained by long-term variability or interstellar reddening. We find no evidence of dimming, while reddening can account for the deficit in UV emission. However, the origin of the near-infrared excess remains unclear. Ultimately, the SED of SDSS J095036 is well described by emission from a single, reddened AGN. Future high-resolution infrared and X-ray spectral observations will be crucial for disentangling the origin of the infrared excess and testing the binary SMBH scenario in SDSS J095036.

In this work, we investigate the worldline deviation of spinning test particles in a weak gravitational wave (GW) spacetime. Within the pole-dipole approximation and the Tulczyjew spin supplementary condition, we consider the modified deviation equation, which contains the standard geodesic deviation term and an additional contribution generated by the Mathisson-Papapetrou-Dixon (MPD) force. We demonstrate how the deviation equation can be solved under viable approximations to yield a new expression for the change in the deviation vector in terms of the perturbation $h_{ij}$, its time derivative, the spin vector components and the longitudinal and transverse components of the deviation. The spin-curvature coupling is shown to play a crucial role in controlling the change in deviation. We then use this result to investigate the changes in the form and expressions of the net GW signal as well as our understanding of GW memory, in the presence of spin. We conclude with our attempts on the measurability of this spin-induced effect \emph{vis-a-vis} present GW observations.

We determine the optimal local extension regularity of the future black-hole event horizon in the exact spatially flat McVittie solutions sourced by a positive cosmological constant and a barotropic fluid with constant equation-of-state parameter $w>-1$. Let $H_\infty$ be the asymptotic Hubble constant, $κ$ the surface gravity of the limiting black-hole root, and $p=3(1+w)H_\infty/κ$. Ingoing radial null geodesics reach the horizon in finite affine length. A parallelly propagated angular curvature component is asymptotic to $C s^{p-2}$, with $C\ne0$ and $s$ the remaining affine distance, which excludes every anchored $C^2$ extension for $0<p<2$. For $p\ge2$ we construct a parameter-uniform Gaussian-null compactification and an explicit two-sided Lorentzian collar. If $p=N+\vartheta$ is nonintegral, with $N\ge2$ and $0<\vartheta<1$, the optimal regularity is the standard big Hölder class $C^{N,\vartheta}$: extensions of this class exist, whereas no $C^{N,\vartheta'}$ extension exists for $\vartheta'>\vartheta$. Every integer $p\ge2$ instead belongs to an analytic island and admits a real-analytic local extension. At the critical value $p=2$ the boundary Einstein endomorphism has a nonzero rank-one nilpotent part. The ratio of cosmological decay to horizon redshift therefore determines a sharp, arithmetic hierarchy of geometric regularity.

De Sitter unitarity and reflection positivity are logically independent. We study their relation for a free scalar field on a fixed de Sitter background, restricting attention to the one-particle sector. Motivated by Witten's de Sitter pairing and the radial adjoint of Bousso, Maloney and Strominger, we compose the invariant Hilbert product with equatorial reflection. In the standard principal-series realization, this form vanishes identically and its Osterwalder-Schrader quotient contains no states. For the complementary series, the reflected product becomes a nonzero reflected kernel on the unit ball. A result of Neeb and Ólafsson shows that this kernel is positive semidefinite precisely when the lower weight satisfies the scalar conformal unitarity bound. The resulting Hilbert space with the reflected inner product furnishes a positive-energy representation of AdS isometries according to Neeb and Ólafsson. We identify that the range coincides with the Klebanov-Witten alternative-quantization window from physics point of view. This correspondence suggests a novel relation from the representation viewpoint between AdS and dS without the conventional analytic continuation of radius.

Heisenberg uncertainties lead to inevitable fluctuations in the measurement outcomes for quantum-mechanical observables. For quantum fields, these uncertainties result in random spatial structures in snapshots of a field, even when the field is in its ground (vacuum) state. Such `vacuum fluctuations' are at the heart of a wide range of phenomena, from spontaneous decay processes to the Casimir force and Hawking radiation. Their existence is a key manifestation of the quantumness of the physical world, but usually it is only their consequences that are directly observed. Here, we directly observe spatial vacuum fluctuations of a bosonic quantum field. Our experiments are based on a homogeneous planar atomic Bose--Einstein condensate. The condensate comprises two coherently coupled interacting components (spin states), and the quantum field describes its spin degrees of freedom. In the regime where the interactions dominate over the coherent coupling, our system emulates a (massive relativistic) sine-Gordon field. Images of the field reveal simultaneous fluctuations on different length scales, with scale-dependent amplitudes consistent with theoretical predictions for a vacuum state. Observing such fluctuations in the sine-Gordon limit opens many possibilities for laboratory simulations of relativistic fields in regimes that are presently not theoretically tractable.

This paper presents an experimental investigation of magnetic reconnection between two laser-produced expanding plasmas, focusing on the quantitative evaluation of the reconnection rate and energy conversion under varying initial conditions. By changing the separation distance between the drive laser focal spots (1 mm and 2 mm), we systematically controlled the inflow parameters. The reconnection region was probed using a two-directional laser Thomson scattering (LTS) system, which simultaneously measured the local plasma parameters parallel to the outflows and along the current sheet. Based on our established method incorporating macroscopic energy and mass conservation laws to derive the upstream magnetic field directly from LTS spectra, we characterized the temporal evolution of the current sheet and the reconnection rate. The larger spot separation allows the plasma bubbles to expand for a substantially longer time before the formation of a reconnection current sheet, resulting in different upstream conditions. Nevertheless, both configurations yielded comparable upstream magnetic fields and reconnection rates. These results suggest that the reconnection rate is relatively insensitive to the global inflow conditions and is primarily controlled by the local physics of the reconnection layer once a current sheet is formed.

Stellar activity complicates exoplanet transmission spectra, particularly for smaller planets around M dwarfs with JWST. The transit light source (TLS) effect, the imprinting of spectral differences between the average stellar disk and the occulted transit chord onto the transmission spectrum, makes it challenging to directly use the out-of-transit spectrum to correct for stellar contamination. Theory and observations suggest that spots may concentrate towards higher latitudes when the Coriolis force is substantial relative to buoyancy, leaving the equatorial region relatively quiet. Here, we evaluate how the latitudinal distribution of active regions shapes the strength of the TLS effect for planets spanning a range of impact parameters ($b$), using TRAPPIST-1 as a testbed. We first construct a fiducial model to illustrate two distribution regimes. With our model, the moderate-$b$ outer TRAPPIST-1 planets (f, g, h) occult a more typical region of the stellar disk than the inner planets and are thereby less affected by the TLS effect, though their bias may vary more from visit-to-visit as these active regions evolve with time. More generally, our results imply an impact parameter "sweet spot" for atmospheric characterization, independent of the sign of the active region temperature contrast, whose location depends on the distribution of active regions. The distribution may be revealed by transit residuals as multiple planets probe different latitudes, while longitudes are sampled in time, such that the variance and frequency of the correlated scatter could constrain active-region filling factors, sizes, and separations.

We study semiclassical tunneling in scalar field theories with slowly evolving homogeneous backgrounds. We formulate the problem by combining tadpole subtraction with an adiabatic expansion: the former maps the rolling system to an instantaneous multi-field tunneling problem, while the latter systematically tracks the slow evolution of the background. This formulation is particularly useful for tunneling during slow-roll inflation, where the tunneling direction may be transverse to the rolling inflaton direction. For a time-reflection-symmetric bounce on a fixed on-shell geometry, we show that the real tunneling exponent receives no direct correction linear in the rolling velocity. The tunneling rate nevertheless drifts along the rolling trajectory because the frozen tadpole-subtracted potential evolves. We also find that the exponent approaches a finite but nonanalytic limit as the tangential curvature vanishes, suggesting that a weakly tachyonic tangential direction can yield an exponent of the same order.

Higher-curvature terms modify the action but do not necessarily generate new vacuum geometries on the branch perturbatively connected to GR. We develop a first-order framework for static, spherical vacuum black holes in 4D metric theories with $\mathcal L_{\mathrm{grav}}=R/2+λΨ(R,X,Y)$, $X=R_{μν}R^{μν}$, and $Y=R_{μνρσ}R^{μνρσ}$. On the coupling-analytic branch, purely Ricci-based terms $Ψ(R,X)$, analytic in curvature with $Ψ(0,0)=0$, do not deform a Ricci-flat background under adopted regularity and boundary assumptions. Riemann-dependent terms can, since Kretschmann scalar is nonzero. In areal-radius gauge, we derive model-independent first-order expressions for the horizon shift, ISCO, epicyclic frequencies, periapsis advance, photon sphere, critical shadow impact parameter, Wald entropy, and Hawking temperature. For $Ψ_η=\ell_λ^{-2+4η}\mathcal G^η$, treating noninteger powers as phenomenological parametrizations of nonlinear curvature, we obtain a closed first-order Schwarzschild-connected solution. Perturbations decay for $η>1/2$, while fixed-ADM interpretation requires $η>2/3$; at $η=2/3$, sourced $1/r$ term mixes with asymptotic mass mode. For positive effective coupling, the horizon, ISCO, photon sphere, and critical shadow impact parameter increase for $2/3<η<1$ and decrease for $η>1$. On the fixed-ADM branch, mass, Wald entropy, and Hawking temperature satisfy $dM=T_H,dS_{\rm W}$ to first order at fixed couplings. At $η=1$, the linear 4D Gauss--Bonnet term leaves local geometry and geodesic observables unchanged but adds a constant topological entropy shift. Finally, an Event Horizon Telescope-inspired shadow-size criterion gives a conservative first-order sensitivity estimate for the effective dimensionless coupling, a geometric consistency test rather than a complete observational constraint.

Short tensor modes can generate a white noise contribution to the local scalar $K=8πGρ/3-θ^2/9$, but this does not induce an infrared-enhanced adiabatic curvature spectrum. For a conserved causal source, analyticity of the longitudinal velocity correlator requires $P_V=\mathcal O(k^2)$, hence $P_{\mathcal R}=\mathcal O(k^0)$ and $Δ_{\mathcal R}^2=\mathcal O(k^3)$, excluding the $Δ_{\mathcal R}^2\propto k^{-1}$ relic. We also construct a conserved conversion of radiation into gravitational waves: the white field resides in a compensated entropy mode, and the fluid response cancels the slowly decaying $a^{-2}$ relic. Adiabatic bounds on such sources are therefore source- and matching-dependent.

Warm inflation in $F(Φ)R$ scalar-tensor theories of gravity is investigated in the `defining' frame, where the theory and its parameter values are specified. Translating the resulting dynamics to the Einstein frame, we find that the dissipation ratio is suppressed by the modified-gravity effects. Thus, although the effective warm-inflation dynamics can be consistently analysed in either frame, the dissipative regimes need not coincide between them. In particular, we find that quantum perturbations can dominate over thermal fluctuations in the scalar power spectrum even in a high-temperature, strong-dissipation regime in the defining frame. Finally, we compute the scalar spectral index and tensor-to-scalar ratio for a non-minimal coupling function $F(Φ) = 1+ξ(Φ/m_{\rm P})^2$ with a quartic potential and both constant and quadratic field-dependent dissipation coefficients, and identify benchmark points compatible with current CMB constraints.

Galaxy-galaxy strong gravitational lensing is an established method to detect and characterise low-mass haloes, which are otherwise too faint to be directly observed. Recent analyses have shown empirically that there exists a characteristic radius within which the projected enclosed mass of these haloes can be robustly measured. Here we provide a physically and mathematically motivated definition of this robust radius based on the Fisher information matrix. We show that for any spherically symmetric smooth profile with at least two free parameters, there exists a pivot radius at which estimates of the projected mass become decorrelated from the local logarithmic slope and have minimum relative uncertainty. As a result, the projected mass within this radius can be recovered consistently by any profile that fits the data well enough. This robust radius coincides, to leading order, with the weighted geometric mean of the arc pixel distances from the halo, where the weights depend on the perturber deflection angle, the macro-model magnification, and the source surface brightness gradient. Beyond leading order, corrections are of order the weighted log-width of the arc. The data constraining power on the local properties of the halo profile beyond amplitude is shown to depend on the radial leverage of the arc around the perturber, and on the imprint of the perturber deflection angle on high signal-to-noise-ratio pixels. Our definition generalises to both subhaloes and line-of-sight haloes and naturally captures the important physical aspects of the problem and the effect of the data resolution and signal-to-noise ratio.

We study the one-point probability distribution function (PDF) for matter densities averaged with an arbitrary spherically symmetric window function. The PDF is analytically modeled within the path integral framework, enabling a non-perturbative description of large-scale structure. It contains a leading order contribution controlled by the spherically symmetric gravitational collapse dynamics, as well as an order-one factor arising from aspherical fluctuations. We develop a numerical pipeline to compute the leading spherical-collapse part of the PDF and apply it to a family of window functions interpolating between the TopHat and Gaussian filters in coordinate space, as well as to a window function with non-monotonic radial dependence. We find that the PDF weakly depends on the choice of the filter, provided the width of the filter is normalized to yield a fixed linear averaged density variance. For each filter and each value of the averaged density, our pipeline gives the most probable density profile. We find that these profiles vastly differ for different filters in the case of overdensities, but closely follow a universal curve at underdensities. We obtain a perturbative expression for the aspherical part of the PDF valid at small density contrasts. We find from it that all PDFs are equally sensitive to the effective field theory (EFT) corrections accounting for short-scale clustering, regardless of how smooth the filter's boundary is. We test our PDF model against the results of high-resolution N-body simulations. The agreement is excellent for filters with widths larger than 10 Mpc/h. Small discrepancies at a few percent level arise for narrower filters and are interpreted as higher-order perturbative corrections.