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We use statistical tools to analyse data from the Solar Dynamics Observatory Helioseismic and Magnetic Imager to determine the distribution of the magnetic flux of photospheric magnetic features and its variation over a full solar cycle. In particular, we use statistical figures of merit to test how well different types of probability density function represent the magnetic flux distribution inferred from the data and how their shape changes over the solar cycle. Our analysis shows that a double power law provides the best representation of the data over the full solar cycle and we present the dependence of the power law exponents on the phase of the solar cycle. The nature of the observed flux distributions at different times during the solar cycle is significant because it could be used to try and infer information about solar magnetic field generation mechanisms. We discuss potential implications of a double power law distribution for solar magnetic field generation.

With nearly 400 Gravitational Wave (GW) events detected by the LIGO-Virgo-KAGRA network and many more expected, similarities between signals produced by different astrophysical effects can complicate template-based searches and parameter estimation. In particular, GW modulations from spin precession can resemble the beating pattern induced by microlensing from compact objects with masses of $10$-$10^5,M_\odot$. We investigate this degeneracy and assess whether machine learning can distinguish between these effects. We generate 20,000 simulated GW signals for each class with a network optimal signal-to-noise ratio above 20 and train a convolutional neural network on time-frequency (Q-transform) spectrograms. The classifier achieves up to 95% accuracy in Gaussian noise and 82% in real detector noise. We also study classification between microlensed (ML) and unlensed non-spinning (UN) signals, as well as between unlensed non-spinning (UN) and unlensed precessing (UP) signals. While distinguishing UN from UP remains difficult even in Gaussian noise, ML vs. UN classification reaches up to 80% accuracy in real noise. We identify the regions of parameter space where the classifier performs best and evaluate the ML-UN network on real GW events, finding that the model trained on Gaussian noise generalizes better than the one trained on real noise. This work presents the first low-latency machine-learning pipeline for distinguishing microlensed from unlensed non-spinning GW signals.

Cosmic rays are widely held to drive outflows from star-forming galaxies and profoundly influence galaxy evolution. Direct evidence for cosmic-ray carrying outflows is however lacking. At the same time there is increasing awareness of the importance of massive star clusters in the acceleration of cosmic rays in galaxies. Here we report on the discovery of a nascent outflow driven by the massive star cluster Westerlund 1. Giga-electronvolt gamma-ray emission coincident with a cavity visible in atomic hydrogen traces the emergence of a population of relativistic electrons out of the Galactic Disc. The emission is offset from tera-electronvolt gamma-ray radiation surrounding the cluster, but connects to it smoothly spectrally and spatially. The implied energy density of co-accelerated protons and nuclei, assuming standard non-thermal electron/proton injection efficiencies, is at least an order of magnitude higher than that in the general interstellar medium. These particles therefore have the potential to dynamically influence the outflow. This discovery suggests that cosmic-ray loaded outflows may be a common feature of young massive star clusters, with implications for the transport of cosmic rays into the halo of the Galaxy.

Lya emitters (LAEs) are galaxies with strong Lya emission, tracing early star formation and ionizing radiation. Their connection to active galactic nuclei (AGNs) is key to understanding the mechanisms behind (extended) Lya emission. In this work, we measure the fraction of LAEs identified as radio-emitting AGN (fAGN,radio) and the fraction of radio sources that exhibit Lya emission (fLya) to investigate the connection between radio AGN activity and Lya emission at 1.88 < z < 3.52. We identify 928 sources detected in both the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) and the LOw Frequency ARray (LOFAR) surveys. These matches are drawn from 55,109 spectroscopically confirmed LAEs and 27,625 radio sources. After applying completeness corrections, we obtain fAGN,radio = 1.77 $\pm$ 0.04% and fLya = 18.15 $\pm$ 0.14%. The fraction fAGN,radio increases from 0.4 $\pm$ 0.1% to 9.7 $\pm$ 1.3% with increasing Lya luminosity, while fLya rises from 0.7 $\pm$ 0.1% to 55.8 $\pm$ 14.5% with radio luminosity. `LAEs with radio AGN' and `optical AGN with Lya emission' show similar radio luminosities above the AGN threshold, although optical AGN have higher Lya luminosities. We find no significant correlation between Lya luminosity and either radio luminosity or spectral index. Lya line width increases with Lya luminosity but shows no correlation with radio size. Our results show that most Lya emission at 1.88 < z < 3.52 is powered by star formation, with radio AGN activity confined to a small luminous subset (1.77 $\pm$ 0.04%). The absence of correlations between Lya and radio properties suggests that Lya emission is governed primarily by host-galaxy gas properties rather than direct AGN jet coupling.

We study the gravitational interaction of very strong pulses of electromagnetic radiation, up to and beyond gravitational collapse. We demonstrate the existence of very compact states close to the threshold of collapse, both for a single pulse, and a head-on collision of such pulses, and we measure their compactness to be above the maximum value proposed by the hoop conjecture. For a single pulse above the threshold of collapse, a fast black hole is produced. Depending on the amount of tuning, head-on collisions can form two horizonless states, two small black holes or one big black hole. Our results show that the gravitational interaction of massless fields can lead to nontrivial final or intermediate states, while giving rise to extremely high luminosity and compactness.

Changing-look active galactic nuclei (CL AGNs) show the appearance or disappearance of broad emission lines on timescales of years. Among them, the repeating CL (RCL) AGNs may provide a clear clue for our understanding of the CL transitions because the same nucleus crosses some physical boundaries more than once. We search for RCL AGNs in known CL-AGN samples using long-term multi-band light curves, and selected 34 candidates for spectroscopic follow-up. We confirm 25 RCL AGNs, including 22 newly identified cases. Properties of these RCL AGNs are analyzed. The observed rest-frame intervals of the second transitions are mostly 3--4 yr, while the variations of the optical light curves suggest that some transitions might occur on timescales of several months. The latest spectra show that the on/off states correspond to higher/lower Eddington-ratio, in the expected direction relative to the parent CL-AGN samples. As seven RCL AGNs are well covered by nearly continuous single-band light curves, their on/off states can be found to follow multi-year optical excursions, and their Eddington ratios vary consistently with the photometric changes. We also find that the H$β$-only transitions occur at higher Eddington ratios than the transitions involving both H$α$ and H$β$, suggesting a line-dependent Broad-Line-Region (BLR) visibility threshold. These results support a picture in which different accretion-flow processes drive reversible changes in the central ionizing emissions, while the observed RCL transitions are produced by the BLR breathing across line-dependent visibility thresholds.

Stellar rotation plays a key role in the transfer of angular momentum, and a large sample of Be-type stars with reliable projected rotational velocities is crucial for understanding their formation and evolution. In this work, we derive the projected rotational velocities ($v$\,sin\,$i$) of 479 Be-type stars using the Fourier transform method, based on their LAMOST Medium-resolution Survey (MRS) spectra. Our results suggest that the Fourier transform method can provide reliable $v$\,sin\,$i$ values for Be-type stars by analyzing the \ion{He}{1}\,lines at 4922, 5015, 5047, and 6678 \,Åin their LAMOST MRS spectra. A K-S test indicates that Be-type stars with different H$α$ emission line morphologies exhibit different $v$\,sin\,$i$ distributions, and Be-type stars with double-peaked emission have a higher fraction of rapid rotators than those with single-peak emission. The $v$\,sin\,$i$ distributions of our Be-type stars in the field, OB associations, and clusters show no significant differences. The deconvolved $v$\,sin\,$i$ distribution of our entire Be-type star sample does not exhibit a bimodal distribution but rather a single peak at $v\approx260$\,km$\cdot$s$^{-1}$. Based on the analysis of 105 stars in our sample, we find that the mean equatorial rotational velocity is 0.74 times the critical velocity. Furthermore, we investigate the relationship between $v$\,sin\,$i$ and the H$α$ peak separation velocity for Be-type stars exhibiting double-peak H$α$ emission lines, using Pearson and Spearman rank correlation coefficients.

AGN emission is intrinsically variable across the electromagnetic spectrum. Mapping the coupling between the accretion disk, the X-ray corona, and ejection flows is key to understanding the energy flow within the central engine. We characterize the multi-wavelength variability of 14 hard X-ray selected AGN from the INTEGRAL/IBIS catalog in the radio, optical, and X-ray bands, to determine the coupling between these frequencies and how variability relates to the physical properties of the central engine, with emphasis on the radio band. We analyzed multi-epoch observations from AMI-LA at 15 GHz, ZTF in the g and r bands, and Swift/XRT over 2018--2020. Variability was quantified using the normalized excess variance, the fractional variability amplitude, and the Mexican Hat filter at 70- and 200-day timescales. We also characterized the radio-loudness of the sample and evaluated the impact of variability on the Fundamental Plane of black hole activity by comparing time-averaged with strictly simultaneous data. Significant variability is detected in 86% of the sample, with a clear amplitude stratification: the fractional rms amplitude is highest in X-rays, with a median of 30% (11-67%), followed by the optical g and r bands at 19% (2-33%) and 8.5% (0.2-24%), and the radio band at 10% (4-23%). The Mexican Hat analysis reveals a red-noise power spectrum dominated by long-term fluctuations. The sample follows the expected Fundamental Plane scaling; although individual sources shift within the relation due to stochastic fluctuations, this dispersion accounts for only ~3% of the total scatter. Our findings support a core-dominated origin for the 15 GHz emission, likely a compact jet base or a magnetized corona, while differences in variability patterns, radio-loudness, and Fundamental Plane location point toward distinct accretion/ejection processes and degrees of corona-jet coupling.

We report on two deep XRISM observations of the central and northern regions of Hydra-A's X-ray atmosphere covering the bubbles inflated by jets from the central galaxy's active galactic nucleus (AGN). We use spatial-spectral mixing that combines Chandra's high spatial resolution with XRISM's high spectral resolution to investigate atmospheric kinematics. The atmospheric velocity dispersion in the northern region, $σ_v = 140^{+30}_{-20}$ km s$^{-1}$, is comparable to that in the central region ($σ_v = 162 \pm 10$ km s$^{-1}$). We show that the motion of the large-scale cocoon shock front could be responsible for the large dispersion toward the north. The velocity dispersion in the northeast quarter of the central pointing, $σ_v = 260 \pm 50$ km s$^{-1}$, is among the highest dispersions measured. This region contains an X-ray-bright feature previously identified as metal-rich, possibly consisting of gas uplifted in the wake of previous-generation cavities. The dispersions in all other quarter regions are low ($σ_v \leq 120$ km s$^{-1}$) and consistent with previous XRISM results from other objects. The kinetic energy at the center is comparable to the enthalpies of the cavities, while in the north, it is roughly an order of magnitude smaller. The jet thus drives gas motion efficiently at smaller scales ($r < 95$ kpc) and inefficiently at larger scales ($95-317$ kpc toward the north along the jet). A bulk flow toward our line of sight of $-100 \pm 30$ km s$^{-1}$ in the southwest quarter of the central pointing is also observed, possibly due to sloshing.

In Jordan-frame scalar--tensor gravity, a timelike scalar gradient defines an effective thermodynamic medium. We show that a transverse--traceless perturbation of a homogeneous shear-free background activates the local shear-work channel $\mathcal W_φ=π_{ab}^{(φ)}σ^{ab}$, with leading pure-TT contribution $\mathcal P_{\rm TT}^{[1,1]} =\overline{\mathcal K\mathcal T} \dotχ_{ij}^{\rm TT}\dotχ_{\rm TT}^{ij}/4$. This stress power follows from local traction mechanics, enters the scalar-sector energy balance, and is gauge invariant at second order. The same scalar--tensor coupling controls non-GR tensor damping and appears with the opposite sign in a GR-normalized amplitude balance, although its interpretation as a separate tensor-energy source is normalization dependent. Scalar--tensor gravity thus provides a controlled example in which a propagating spin-2 mode acquires an intrinsically gravitational thermodynamic interpretation.

We investigate the production of particles much heavier than the characteristic scale of a cosmological first-order phase transition through collisions of highly boosted bubble walls. Using the scalar order-parameter field, we derive the ultraviolet behavior of its Fourier-space profile for both elastic and inelastic collisions. In the regime $χ\equivω^2-\mathbf{k}^2\gg M_h^2$, we find the universal result $\tildeφ(χ) = -2V^\prime(2v_φ)χ^{-2}+O(χ^{-3}),$ implying that the spectral density scales as $F(χ)\propto [V^\prime(2v_φ)]^2χ^{-4}$. Thus, heavy-particle production is localized near the instant of collision and, at leading order, depends on the scalar potential only through $V^\prime(2v_φ)$. We verify this behavior using high-precision numerical solutions of the trapping equation, carefully suppressing spectral leakage from the finite integration domain, and obtain agreement over a broad ultraviolet range. We then derive analytical production rates for general heavy-particle thresholds and for fermion pairs, together with their cosmological number density and yield. Finally, we extend the analysis to $(3+1)$ dimensions and incorporate the finite bubble radius, finding an order-one suppression relative to the parallel-wall approximation. Our results revise the ultraviolet scaling used in previous treatments and have direct implications for superheavy dark-matter production and baryogenesis from bubble collisions.

In this work, we investigate the prospects for probing primordial non-Gaussianity and associated symmetry of parity through scalar-induced gravitational waves (SIGWs), with third-generation gravitational-wave detectors. We develop a framework that accounts for contributions to the energy density spectrum of GWs arising from the scalar non-Gaussianity quantified by bispectrum and trispectrum, and perform parameter inference using simulated data from Einstein Telescope and Cosmic Explorer. The parity-odd component of the scalar trispectrum induces circular polarization in the stochastic gravitational-wave background (SGWB), providing a direct probe of parity-violation in the primordial Universe. We show that future interferometers can place competitive constraints on the parity-odd scalar trispectrum, along with the bispectrum and parity-even trispectrum. Moreover, we include the astrophysical contribution, which could act as a foreground for the SIGWs. We show that, despite the addition of such a foreground, we are still able to effectively constrain the cosmological parameters related to SIGWs and the astrophysical parameters as well.

We examine $f(R,T)=R+λT^ε$ gravity models by finding the best fit parameters for various values of $ε$. This is accomplished by analyzing data from the cosmic microwave background, baryon acoustic oscillation observations, cosmic chronometer, and Type Ia supernovae introducing correlations and radiation effects to our previous work. We find the probability distribution for the best fit model around the value of $ε=0.010^{+0.013}_{-0.021}$, consistent with the standard cosmological model value of $ε= 0$.

Interactions between dark matter and dark energy can lead to an apparent phantom-crossing behavior that mimics the expansion history preferred by the latest cosmological observations from DESI baryon acoustic oscillations (BAO), Cosmic Microwave Background (CMB), and Type Ia supernovae (SNe Ia) data. In a previous paper [Khoury, Lin, and Trodden 2025 arXiv:2503.16415], we proposed a concrete particle physics realization of this idea, consisting of a strongly coupled dark sector in which a dark axion is coupled to dark baryons. In this paper, we investigate this idea further by comparing its predictions to the latest cosmological data. We implement the dark axion-dark baryon interaction model in a Boltzmann code and confront it with CMB, DESI DR2 BAO, and SNe Ia data. For the CMB+DESI DR2+DES-Dovekie combination, the best-fit model improves the fit relative to $Λ$CDM by $Δχ^2=-14.48$. The preferred solution exhibits a non-monotonic dark-matter mass evolution: the mass decreases between matter-radiation equality and recombination, while increasing over the BAO/SNe-sensitive epoch, leading to an apparent phantom crossing in an effective dark-energy description. Interestingly, the same dynamics produces an Early Dark Energy-like energy injection near matter-radiation equality, but in the data-preferred region this component is too small to raise $H_0$ enough to substantially reduce the current tension.

Cosmology is an observational precision science, and detailed and scientifically rich simulations are necessary components of many analyses. These simulations are often computationally expensive and produce massive amounts of complex data. Sharing that data widely to enable further explorations, comparison with observations, and communication with general audiences is crucial to advancing the scientific frontier and engaging a broader community. In this paper, we introduce the OpenCosmo project, designed to provide flexible access and analysis modes to large cosmological simulation datasets. We make available an easy-to-use web-based data portal for retrieving downloadable subsets of flagship-scale cosmological datasets, and a sophisticated analysis library for further analysis on the returned data. OpenCosmo supports multiple levels of interaction -- from simple search and download to interactive exploration and computation -- by integrating with existing HPC and data infrastructure. Its architecture, based on Globus Compute, provides a scalable and adaptable framework that can be extended to other scientific domains seeking to couple data sharing with computational capability.

Unlike the gravitational waves classically generated by moving macroscopic masses, the diffuse backgrounds of gravitons originate most likely from zero-point fluctuations of the gravitational field amplified by the evolution of the space-time curvature. The resulting entangled states lead to specific second-order correlation effects that could be eventually detected. For a quantitative analysis of this empirical expectation we scrutinize the interactions between the cosmic gravitons and the fundamental mode of a quantized electromagnetic field confined inside a closed optical resonator with perfectly-reflecting walls. We show that the Hanbury-Brown Twiss correlations of the photons are insensitive to the degrees of second-order coherence of the gravitons even barring for the exceedingly small couplings of the problem. Since the degree of second-order coherence of the photons does not reflect the correlation properties of the gravitons, the statistical properties of the gravitons (and their super-Poissonian statistics) cannot be inferred, even in principle, from the intensity correlations of the cavity modes.

We study quasinormal modes (QNMs) of a minimally coupled massless scalar field on four-dimensional Schwarzschild--anti-de Sitter black holes using a Chebyshev spectral method. After compactifying the exterior domain, the radial problem is formulated as a quadratic matrix pencil in the dimensionless frequency. For the standard Dirichlet, or vanishing-field, boundary condition at the conformal AdS boundary, we reproduce the known scalar spectra across small, intermediate, and large black holes, including long overtone sequences and the expected approach to pure-AdS normal modes in the small black hole limit. We then deform the AdS boundary condition by imposing a generalized relation between the two independent asymptotic coefficients of the massless scalar. This deformation is treated as a generalized coefficient boundary condition for the massless scalar, and not as the usual alternative quantization for scalars in the Breitenlohner-Freedman window. The Dirichlet endpoint recovers the stable standard spectrum. For every non-Dirichlet value examined, and for representative small, intermediate, and large black holes, we find an additional mode with positive imaginary part, signaling a boundary-condition-induced instability. A near-Dirichlet refinement finds no finite critical angle down to the smallest deformation probed.

The fragmentation of massive molecular clumps into dense cores sets the initial conditions for stellar clusters, yet how core mass distributions evolve remains unclear. Using the ALMAGAL survey (1,013 clumps and 6,348 cores), we analyze the Gini coefficient of core mass distributions for the 514 clumps containing at least four cores ($N_{\rm frag} \ge 4$), which host 5,728 cores in total. We find that the most massive core consistently accounts for $\sim 38\%$ of the total core mass ($f_{\rm core,max} \approx 0.38$), with no systematic trend with the total mass of the core per clump $M_{\rm core,tot}$. The Gini coefficient increases with total core mass ($M_{\rm core,tot}$, $r=0.55$) and evolutionary stage ($L/M$, $r=0.38$). Clumps with $L/M > 6.0$ have significantly higher Gini values (median $0.62$) than those with $L/M \le 6.0$ (median $0.49$; $p = 4.23\times10^{-15}$). These results demonstrate that while the mass fraction of the most massive core is constant, overall mass inequality among cores grows systematically as clumps evolve.

Dynamical friction prescriptions used for common-envelope and planetary engulfment inspirals often assume a homogeneous medium and/or rectilinear perturber motion. A gravitating object embedded in a giant-star envelope instead excites an orbit-scale wake while moving on a curved orbit through a finite, radially stratified medium. We formulate the linear barotropic acoustic response of a weak point perturber on a circular orbit in a hydrostatic, spherically stratified gaseous medium. We apply the formulation to single perturbers in power-law density profiles and giant-star envelope models, and to double perturbers in power-law density backgrounds. We find that stratification affects dynamical friction through the global structure of the wake. The radial component is set by the low-order, orbit-scale wake and can strongly differ in amplitude and sign from the homogeneous-medium result. The azimuthal component is also modified by stratification, but in the supersonic regime it retains the Coulomb-logarithmic sensitivity of the homogeneous problem. In double-perturber systems, the companion wake can substantially change the radial force and reduce the azimuthal drag on a given component, but, unlike the perturber's own wake, it has no local Coulomb-logarithmic contribution. For the adopted giant-star envelope profiles, the azimuthal drag exerted by the stratified wake gives shorter inspiral times than uniform-medium prescriptions evaluated with the same local background quantities. The formulation provides a flexible tool for computing embedded-perturber wakes in prescribed radial stratifications and is a first step toward computationally efficient, self-consistent models of common-envelope and planetary-engulfment inspirals.

We construct an $R^2$ cosmology based on scale invariance and unimodular gravity in which the Goldstone boson of dilatations establishes a predictive connection between inflation and dark energy. The conservation of the corresponding Noether current confines the inflationary trajectory to a one-dimensional orbit in field space, freezing the Goldstone direction and rendering the inflationary dynamics effectively single field. After inflation, the system settles on a Minkowski vacuum manifold. The unimodular integration constant, already present in the full theory but negligible during inflation, lifts the flat Goldstone direction, generating an exponential potential for the canonically normalised field. Unlike in phenomenological quintessence models, its slope is not a free DE parameter, but is instead fixed by the field-space geometry inherited from the inflationary attractor. This geometry excludes matter-era tracking and, throughout the inflationary viability region, places the field in the thawing regime compatible with accelerated expansion. For a representative inflationary benchmark, the now pseudo-Goldstone field remains frozen until close to the present epoch, yielding DE equation-of-state parameters $(w_0,w_a)\simeq(-0.992,-0.011)$ in the CPL parametrisation $w(a)=w_0+w_a(1-a)$. More generally, the same parameter controlling the inflationary spectral tilt also fixes the slope of the DE potential, leading to a tight correlation between early- and late-Universe observables: increasing the thawing signal lowers $n_s$, while values of $n_s$ closer to unity drive the model towards $Λ$CDM.

The excursion-set formalism provides a key connection between primordial density fluctuations and the abundance of cosmic structures such as dark matter halos and voids, traditionally assuming Gaussian random walks. In this work, we extend this framework to fluctuations whose distribution presents strongly non-Gaussian tails. Such tails are beyond the reach of perturbative approaches to primordial non-Gaussianity based on moment expansion. We address the problem with rigorous, analytical derivations relying on the large deviation principle, suited for the study of rare fluctuations. We derive new first-passage time distributions for random walks with non-Gaussian statistics and obtain updated predictions for the halo mass function. We also study the two-barrier problem relevant to cosmic void formation, leading to a new analytical prediction for the void size function, with improved accuracy on large scales. Our results demonstrate the potential of large deviation techniques as a bridge between inflationary scenarios, often leading to strongly non-Gaussian tails, and late-Universe observables.

We investigate the dynamics of vector excitations localized on cosmic strings in the Abelian-Higgs model. These confined gauge field fluctuations behave as massive vector degrees of freedom propagating along the string. We show that they remain bounded for all values of the scalar self coupling $λ$, including parameter regimes in which the previously studied conventional shape mode is no longer present. After determining their spectra and spatial profiles, we analyze their decay through nonlinear coupling to bulk radiation. Their amplitudes exhibit the characteristic power law relaxation associated with non-linear radiation. For sufficiently large $λ$ the scalar radiation channel becomes kinematically inaccessible and the decay is instead mediated by quasinormal modes which can be interpreted as Feshbach resonances of the string. We then study the full $3+1$ dimensional dynamics of the vector-excited string. Field theory simulations reveal a parametric instability between the vector mode and the Goldstone sector. In contrast to the shape mode, the vector mode resonantly excites both transverse directions simultaneously. In addition, we build an effective model that captures the instability and identifies the nonlinear couplings responsible for it. Our results show that vector excitations constitute a long-lived massive degree of freedom with a non-trivial role in the dynamics of local strings.

We formulate and numerically solve the real-frequency scattering problem for a neutral, minimally coupled, massless scalar on the rotating Kerr--Bertotti--Robinson (Kerr--BR) black-hole geometry, using a specified transparent boundary condition at the coordinate end. Since the Maxwell stress tensor of the background is traceless, the minimally coupled wave equation reduces to the four-dimensional conformal wave equation, enabling exact Carter-like separation after scaling the scalar field by the conformal factor. Unlike the asymptotically flat case, the coordinate end $r\to\infty$ lies at a finite tortoise distance. We show that the resulting reflection data are conditional on this boundary prescription rather than defining a unique, observer-independent cross section. Within the transparent-end model,open-channel superradiance is governed by a double-gate mechanism requiring both the local horizon condition and the outer propagation condition $q_\infty^2>0$. At the benchmark spin $a/M=0.9$, the co-rotating dipole amplification decreases as the external magnetic field increases. Crucially, the field narrows and closes the open superradiant window at $BM\simeq0.243$. Near the propagation threshold, the amplification coefficient vanishes linearly with the outer wave number.

The polarized Sunyaev Zel'dovich (pSZ) effect is a cosmic microwave background (CMB) polarization anisotropy induced by Thomson scattering from free-electrons in non-linear structure. The pSZ signal is determined by the distribution of ionized gas tracing the cosmic web and the CMB quadrupole at the location of free-electrons - the remote quadrupole field. Measuring the pSZ effect provides a consistency check of the optical depth to reionization and sheds light on the anomalous nature of the large-scale CMB temperature anisotropies, such as the low observed CMB temperature quadrupole. In this paper, we demonstrate that a CMB-CMB-galaxy bispectrum summarizes several existing pSZ statistics, and that in our observable Universe the ideal galaxy sample to detect pSZ is at $z \sim 1-2$. We evaluate the bispectrum using CMB data from Planck and ACT with galaxy density from the unWISE galaxy redshift catalog as well as Planck cosmic infrared background (CIB) maps. We do not make a statistically significant detection of the pSZ effect, which is consistent with the expected O$(1)$ signal-to-noise from this data combination. The measured amplitude of the pSZ bispectrum provides constraints on the optical depth bias associated with large-scale structure (the amplitude of the pSZ signal) of $b_q=1.02 \pm 2.64$, the optical depth to reionization of $τ_{\rm rei} = -0.01 \pm 0.14$, and the tensor-to-scalar ratio $r$ of $σ_r \sim 150$ ($n_t = 0$) or $σ_r \sim 3$ ($n_t = -1$). We forecast that future measurements could tighten the constraints on these quantities by roughly a factor of 3, which is sufficient to provide independent confirmation of the low CMB quadrupole and the optical depth to reionization.

Using the $C-$metric in the context of $F(R)$ gravity coupled with the ModMax nonlinear electromagnetic field (the $F(R)-$ModMax theory), we derive an exact black hole solution in a four-dimensional spacetime. We then examine how various parameters influence the behavior of accelerating ModMax black holes. Treating this black hole as a thermodynamic system, we calculate the Hawking temperature and entropy for the accelerating ModMax black holes within the framework of $F(R)$ gravity. Subsequently, we explore the impact of the parameters in $F(R)-$ModMax theory on the Hawking temperature and entropy. We also assess local stability by analyzing the heat capacity. Additionally, we investigate both the angular shadow and the shadow radius of an accelerating black hole in the context of $F(R)-$ModMax gravity.

Constraining the total mass of protoplanetary disks is crucial to determine the availability of material for planet formation. Yet, providing accurate and precise measurements of the disk mass is challenging. Investigating the gas dynamics is a powerful, tracer-independent method to precisely characterize disk masses. By fitting the velocity rotation curves of different molecular tracers with an accurate model including the disk thermal stratification and self-gravity, we constrain the stellar masses, disk masses, and scale radii for the disks around HD 97048 and WaOph 6. We obtain $M_\star=2.226 ^{+0.054}_{-0.049}\ M_\odot$, $M_\mathrm{d}=0.3 ^{+0.055}_{-0.061}\ M_\odot$ and $R_\mathrm{c}=172 ^{+24}_{-14}$ au for HD 97048, and $M_\star=0.956\ ^{+0.006}_{-0.006}\ M_\odot$, $M_\mathrm{d}=0.21 ^{+0.045}_{-0.038}\ M_\odot$ and $R_\mathrm{c}=647 ^{+193}_{-155}$ au for WaOph 6. We also measure the corresponding gas-to-dust and disk-to-star mass ratios. We efficiently extend the dynamical method to characterize embedded sources exhibiting features of absorption, for which a careful analysis is required to avoid biases in the retrieved velocity profiles. We prove the importance of including a beam smearing correction to the curves: if not, this observational effect can systematically bias the velocity profiles, altering the disk mass estimates up to $\sim45\%$. We provide comprehensive estimates of the systematic uncertainties on the best-fit parameters by bootstrapping over both the retrieved geometry and 2D thermal structure of the two disks: the overall uncertainty on the disk masses is $\sim20\%$. Finally, we investigate the connection between disk stability and the appearance of spiral morphologies in the mm continuum emission, by comparing the Toomre parameter of all dynamically weighed disks to date, showing that disks with mm-dust spirals have systematically lower values of Q.

The interplay of Hoyle-Narlikar (HN) creation field cosmology and scalar field models for the dark sector, including the generalized Chaplygin Gas (GCG), is investigated . Though originating from distinct theoretical frameworks, both the inclusion and the non-inclusion of the creation field degree of freedom (DoF) involve a scalar DoF, which addresses some of the limitations of the standard $Λ$CDM model. Using a Lagrangian scalar field formulation and the first-order Hamiltonian reconstruction method, the HN $c$-field dynamics is shown to be encompassed by the GCG equation of state through an equivalent modified scalar field theory. Late-time acceleration and stability of linear perturbations are derived within this unified description. Our results suggest that creation field cosmologies may be embedded in a broader class of scalar field models which encompasses subtle modifications to the Hubble expansion rate and related physical observables.

Sunspot oscillations probe magnetic-plasma interactions in the solar atmosphere. We investigate oscillation periods in six sunspot active regions observed in the 8-10 um band with the Accurate Infra-red Magnetic-field Solar Telescope (AIMS) at Lenghu Observatory. Light curves were extracted from umbra, penumbra, and quiet Sun regions. Wavelet analysis was applied using four methods: pixel-wise with mean/median aggregation, and spatial mean/median prior to analysis. The weighted mean period is more physically meaningful than the dominant period, better representing multi-mode oscillations. A consistent period sequence holds across all datasets: umbra (U) < penumbra (P) < quiet Sun (Q), with typical values of 260-313 s, 286-374 s, and 294-382 s. This pattern is recovered with 100% consistency by pixel-wise mean/median and spatial median methods. Spatial mean shows 1/6 full, 3/6 partial, and 2/6 inconsistency. Spatial smoothing increases periods by up to 21%, most strongly in the umbra. All peak ratios are below 0.3 (mean 0.14 +/- 0.03), confirming multi-mode oscillations. These results establish the 8-10 um band as a valuable diagnostic window for sunspot magneto-convection and wave propagation.

We present a data-driven measurement of galaxy bias and scale-dependent relative bias for elliptical and spiral galaxies using angular auto- and cross-power spectra from DES and DESI Legacy Imaging Surveys DR8. We introduce the cross-tracer clustering ratio (CTCR), which uses the ratio of auto- to cross-power spectra to isolate the relative clustering of morphological tracers as a function of angular multipole $\ell$. Across both surveys, ellipticals are more strongly clustered than spirals; the cleanest CTCR constraints come from DESI, where the two morphological samples have better-matched redshift distributions. The difference is scale dependent: the relative bias is close to unity on large angular scales, $\ell \lesssim 50$, but increases toward smaller scales, reaching an average separation of $2.6σ$ at $\ell \sim 150-200$. A complementary linear-bias analysis confirms that ellipticals are positively biased relative to the matter field, while spirals are consistent with weak bias or anti-bias. Unlike narrowly selected LRG samples, our morphologically selected elliptical samples show little redshift evolution, consistent with a broader halo-mass distribution. The results are robust to two covariance estimators, contamination tests, luminosity splits, and comparisons with two N-body mock catalogs. These new findings provide empirical evidence that galaxy morphology imprints both the amplitude and scale dependence of galaxy bias, and establish CTCR as a useful observable for testing halo occupation and assembly-bias models with future imaging surveys.

Testing Lorentz invariance violation (LIV) is notoriously difficult, as its characteristic energy scale, $M_\star$, in modified dispersion relations typically lies beyond current experimental reach. To enable a low-energy probe, we investigate the quantum coherence of an inertial Unruh-DeWitt (UDW) detector interacting with a massless scalar field with a Lorentz-violating dispersion relation $ω_{|\textbf{k}|}=|\textbf{k}|f(|\textbf{k}|/M_\star)$. Unlike the Lorentz-invariant case where quantum coherence is rapidity-independent, we find for the Lorentz-violating quantum field case the dynamics of detector's quantum coherence exhibits a strong dependence on its rapidity -- offering a potential low-energy signature of LIV. Applying this to the polymer-quantized scalar field theory inspired by loop quantum gravity, we show that the detector's quantum coherence exhibits a pronounced dependence on rapidity and undergoes a sharp transition near a critical rapidity $β_c \approx 1.3675$, a value within reach of existing facilities like the Relativistic Heavy Ion Collider. We also show how the detector's rapidity and its energy-level spacing enhance the response to the test of LIV. Our results establish quantum coherence as a sensitive and practical probe of LIV, providing a complementary avenue for testing quantum gravity-induced modifications to field theory.

We present the results of a survey program with JWST's MIRI LRS that obtained 5$-$14 $μ$m R~100 spectra of twenty-three L0$-$T6 dwarfs. This spectral type range spans the formation, growth, and sedimentation of silicate condensate clouds, as well as the appearance of methane and ammonia in the atmospheres of brown dwarfs. The initial onset of silicate absorption at spectral type L0 as well as the evolution of this feature with spectral type are both examined in unprecedented detail. We detect 7.5$-$9.5 $μ$m gas-phase SiO absorption for the first time in dwarf stars, with detections in M5.5$-$L2.5 dwarfs from combined Spitzer IRS and JWST spectra. This feature has previously been detected in K and M giants, with stronger absorption in these giants than in higher-gravity M dwarfs. In contrast, low-gravity L dwarfs show weaker SiO absorption than field-gravity L dwarfs. We also confirm water, ammonia, and methane absorption trends with spectral type previously seen in Spitzer IRS observations. We report the possible detection of CS2 in a T3.5 dwarf, although confirmation would require higher-dispersion spectroscopy. We find two newly resolved binaries, confirm two near-equal flux unresolved candidate binaries, and identify two additional possible non-equal flux binaries. After accounting for contamination by resolved and candidate binaries, we find that single field dwarfs are ~0.15$-$0.20 mag underluminous compared to existing empirical relations. The presented spectral library offers a spectrophotometrically calibrated basis for future interpretation of JWST MIRI spectra of brown dwarfs or of directly imaged or transiting exoplanets.

We present a detailed thermodynamic analysis of a sloshing spiral discovered in the intracluster medium (ICM) of the galaxy cluster Abell 2107, based on deep Chandra X-ray Observatory observations. Spectral analysis reveals that the spiral arm is significantly cooler and exhibits lower entropy and higher metallicity compared to the surrounding ICM, consistent with an origin in the cool, dense cluster core. We detect three cold fronts at the edges of the spiral, roughly aligned along an east-west axis. This alignment is consistent with predictions from numerical simulations of off-axis merger events. Subregion analysis of the spiral shows that the coldest and lowest-entropy gas is concentrated in the central part of the arm, while the side regions show evidence of mixing and interaction with the ambient medium. Among the examined thermodynamic quantities, entropy provides the most robust contrast between the sloshing gas and its surroundings. Notably, no optical or X-ray counterpart to a potential perturber is detected, suggesting that the responsible perturber may currently be below the detection limit or otherwise difficult to identify, while a dark matter-dominated or dark matter-only subhalo remains one possible scenario. Our findings provide new insights into the dynamical history of A2107 and demonstrate the importance of deep X-ray exposures for revealing subtle ICM structures in apparently relaxed clusters.

The 21 cm line of atomic hydrogen (HI) is a sensitive tracer of the outer disk of galaxies, where environmental signatures are most apparent. The relative extent of HI disks compared to optical disks ($D_{\rm HI}$ vs $D_{25}$) is thought to provide a quantitative measure of such imprint, yet systematic comparisons between extreme environments remain scarce. We quantify the relative extent of HI disks in Hickson Compact Groups (HCGs) and in the Analysis of the interstellar Medium in Isolated GAlaxies (AMIGA) sample, using AMIGA as a control sample that captures secular evolution with minimal external influence. We calculate HI diameters by directly fitting an ellipse to the $1\,M_{\odot}\,{\rm pc}^{-2}$ iso-density contour. Because $D_{\rm HI}$ and $D_{25}$ are nonlinearly related, we avoid the traditional $D_{\rm HI}/D_{25}$ ratio, which carries a size-dependent bias, and instead quantify truncation as the residual from the isolated-galaxy $D_{\rm HI}$-$D_{25}$ baseline, which we establish for AMIGA via Bayesian analysis. The full analysis is provided as a reproducible Python package and Snakemake workflow. HCG galaxies lie systematically below the isolated-galaxy baseline in the $D_{\rm HI}$-$D_{25}$ plane. When members with HI nondetections are included as upper limits, HCGs have HI disks at least ~71% smaller than expected for isolated galaxies of the same optical diameter. The truncation increases monotonically along the HCG evolutionary sequence, from Phase 1 to Phase 3. A comparison with literature samples places HCGs at the most-truncated end, statistically indistinguishable from the Virgo cluster sample (VIVA). Compared to AMIGA, HI disks are typically smaller relative to the optical disk in loose groups, compact groups, and cluster infall/field environments, and are most strongly truncated in HCGs and in the Virgo cluster sample.

The Local Volume Complete Cluster Survey (LoVoCCS) is a volume-complete survey of over one-hundred nearby ($0.03 < z < 0.12$), X-ray luminous ($L_{500} > 10^{44} \text{ erg s}^{-1}$) galaxy clusters in the southern sky. Observations for the survey concluded in December 2025, reaching Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) Year 1-2 depth in each field and providing observations with $\lesssim 1"$ seeing for weak lensing science. In this paper, we present the latest pipeline for reducing observations using the third-generation of the LSST Science Pipelines. We use recent observations of the Hercules Supercluster to validate the pipeline's data-products and conduct an extensive multi-plane weak-lensing analysis of a $\sim 16 \text{ deg}^2$ complex covering Abell 2147, 2151, 2152, and several additional structures. We confirm that the dynamical mass of the complex is biased due to the dynamical state of Abell 2147, which is consistent with being $\sim 0.2-0.4 \text{ Gyr}$ out-of periapsis, and estimate that the total mass of the supercluster is $8.9^{+1.7}_{-1.4} \times 10^{14}~M_{\odot}$.

Motivated by growing observational indications that dark energy may be dynamical, we introduce Rolling Galileon gravity: a minimal shift-symmetry-breaking extension of the cubic Galileon in which the coupling coefficients are allowed to vary, giving rise to an evolving braiding strength. The full theory space, shown to be closed under field redefinitions, is characterised by two functions. We derive analytical conditions to satisfy three phenomenological requirements: i) a phantom-crossing equation of state at late times, ii) a positive integrated Sachs-Wolfe signature, and iii) absence of pathologies in the screened scalar force in cosmic voids. We show that these conditions are collectively satisfied by an increasing braiding strength relative to the kinetic sector. A Bayesian analysis of minimal Rolling Galileon models finds that they can satisfy the viability requirements i)-iii) whilst providing an acceptable fit to expansion-history data.

In Friedmann cosmology with Einstein--Cartan torsion, the homogeneous torsion mode compatible with a separately conserved matter sector scales as $Φ\propto a^{-3}$ and enters the Friedmann constraint as a stiff component of negative energy density, $-3Φ^{2}\propto a^{-6}$. It has recently been claimed that this mode rescues the Hubble radius as an infrared cutoff for holographic dark energy, producing late-time acceleration and a phantom-divide crossing of possible relevance to DESI. We show that it cannot. With the Hubble cutoff the holographic density drops out of the deceleration parameter, and the only accelerating regime is the transient window $\bar{a}\leq a<4^{1/3}\bar{a}$ around the torsion bounce at $H(\bar{a})=0$; placing that window at observable redshifts would force the Hubble rate to vanish in our recent past, against the measured expansion history. Requiring a viable history yields nested upper bounds on $Ω_Φ\equiv(Φ_{0}/H_{0})^{2}$: fitting the official DESI DR2 BAO likelihood gives $Ω_Φ<8.7\times10^{-4}$ ($95\%$ CL), the existence of a spectroscopically confirmed galaxy at $z=14.32$ gives $8.4\times10^{-5}$, the CMB gives $3.1\times10^{-10}$, and Big Bang nucleosynthesis gives $5\times10^{-24}$. Today's imprint on the dark energy equation of state, $|1+ω_{0}|\leq2Ω_Φ/Ω_Λ$, falls short of the DESI preference by two orders of magnitude at best and twenty-two at worst, and on the phantom side. In the Granda--Oliveros cutoff, torsion deepens rather than prevents the big-rip singularity. An appendix derives the Friedmann pair from the Einstein--Cartan field equations and shows that the $a^{-3}$ scaling is the kinematics of a diluting spin fluid; escaping the no-go requires breaking exactly that.

We investigate convolutional neural network (CNN) methods for reconstructing the high-redshift density field from late-time large-scale structure, focusing on how the physical scale of the CNN input changes when standard first-order reconstruction is applied beforehand. Using dark-matter-only $N$-body simulations, we compare three approaches: a single-input CNN, a dual-input CNN combining two physical scales, and a single-input CNN applied to the density field after standard reconstruction. We vary the physical side length of the input sub-box over $L_\mathrm{sub}\sim38$-$380~h^{-1}\mathrm{Mpc}$ while keeping its numerical size fixed at $39^3$ voxels, allowing us to examine the trade-off between spatial context and resolution. For the CNN applied directly to the evolved density field, the reconstruction performs best at $L_\mathrm{sub}\sim150$-$200~h^{-1}\mathrm{Mpc}$. After standard reconstruction, however, the preferred scale shifts to $L_\mathrm{sub}\sim38$-$114~h^{-1}\mathrm{Mpc}$. The single-input CNN after standard reconstruction consistently outperforms both the single- and dual-input CNNs without standard reconstruction according to the normalized loss, density probability distribution, Kullback-Leibler divergence, residual field, and Fourier-space correlation. These results indicate that coherent large-scale displacements are more efficiently recovered by perturbative reconstruction, while the CNN is better suited to modelling the remaining quasi-linear and non-linear evolution on smaller scales. The preferred post-reconstruction input range includes the effective receptive scale of approximately $60~h^{-1}\mathrm{Mpc}$ adopted in previous hybrid reconstruction studies. Our findings therefore support a physically motivated separation of scales between analytic and data-driven reconstruction and demonstrate the advantage of combining the two approaches.

We investigate the impact of spontaneous Lorentz symmetry breaking on scalar wave propagation, null geodesics, and thermodynamic behavior of four-dimensional asymptotically AdS black holes in bumblebee gravity. The static, spherically symmetric solutions are characterized by a dimensionless parameter $\ell > -1$ arising from the vacuum expectation value of the bumblebee vector field, which globally rescales the radial geometry. Massless scalar fields are analyzed via the radial Klein--Gordon equation cast into a generalized Helmholtz form, yielding an effective frequency-dependent refractive index that identifies oscillatory and evanescent regions, classical turning points, and confinement induced by curvature and Lorentz violation. In the high-frequency limit, wave propagation coincides with null geodesics, with $\ell$ controlling radial scaling and governing the geometric-optics limit. The AdS boundary reflects waves, while the horizon acts as a one-way absorber. Thermodynamic analysis in non-extended and extended phase spaces confirms the first law and Smarr relation, with $\ell$ influencing heat capacity, free energy, and stability. \textcolor{black}{Modeling these black holes as heat engines, we construct explicit cycles and show that efficiency increases with $\ell$, leading to an upper bound imposed by $η\leq 1$. Our results provide a framework connecting Lorentz violation, wave propagation, geometric optics, and AdS black hole thermodynamics in bumblebee gravity.

We investigate the behavior of Einstein crystals in noncommutative backgrounds described by the Snyder and Snyder-de Sitter models. Possible novel effects, which may arise in realistic systems such as diamond crystals, are analyzed within a thermodynamical framework. We show that noncommutativity influences the key thermodynamic quantities, including internal energy and specific heat. These corrections can be directly related to modifications of the underlying uncertainty relations, of the generalized uncertainty principle (GUP) and generalized extended uncertainty principle (GEUP) types.

Context. The upcoming GaiaNIR mission is currently planning to add a near-infrared spectrograph to its payload in order to enhance its scientific return, particularly for mapping the dust-obscured regions of the Milky Way. Aims. This study aims to identify the optimal wavelength region between 800 and 2300 nm for the proposed GaiaNIR spectrograph to maximize the precision of radial velocities and atmospheric parameters. Methods. To find its spectral range, we generated 10000 synthetic spectra from the BOSZ library across a wide range of stellar parameters, with resolutions varying from 5000 to 20000. By cross-correlating these mock observations with ideal templates, we assessed the statistical scatter of velocity residuals to isolate six candidate windows for further atmospheric parameter testing. Results. Our analysis finds that the 1926 - 1968 nm window at R = 16100 - 20100 in the K-band is the preferred strategic choice, because it has the potential to reach radial velocity precision for the brightest FGKM stars of about 160 - 260 m/s depending on resolution, while providing precision of the atmospheric parameters close to Gaia's Radial Velocity Spectrometer. We also identified a second region between 1158 and 1202 nm (R = 9300 - 11600), that has slightly lower radial velocity precision, but at a wider temperature range than the K-band. Both regions make it possible to derive abundances of ten species at these resolutions: O, Na, Mg, Si, Ca, Ti, V, Cr, Mn, Ni in the K-band, and Mg, Si, K, Ca, Ti, V, Cr, Mn, Co, Ni between 1158 - 1202 nm. Conclusions. The K-band delivers sufficiently precise measurements for the mission's primary cool star targets while taking advantage of significantly lower interstellar extinction, enabling the mapping of the dust-obscured regions of the Milky Way.

We review the present status of observations of the Cosmic Microwave Background. This book chapter is an update to an earlier review "Physics of the Cosmic Microwave Background Anisotropy" that appeared a decade ago in the compilation "One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity." The earlier contribution summarized the state of the field then as well as the underlying cosmology and gravitational physics. This contribution reports on what new has occurred in the field during the intervening time 2015-2025. We also review future prospects.

Non-Lorentzian theories of gravity, most common of which are Galilean and Carrollian gravity, arise from General relativity under suitable scalings. General relativity can be obtained by gauging the Poincaré algebra. A convenient formulation of non-Lorentzian gravity follows the contraction of the Poincaré algebra in the tangent space to its non-Lorentzian counterparts, e.g. Galilean and Carrollian algebras. In existing literature, different non-Lorentzian theories of gravity have been addressed separately. In this paper, we introduce a single unified framework of expansion to address all these different theories. We show that different scalings can be unified into a single covariant form parametrized by $(s,n)$, alongside the contraction parameter $ε$. Keeping these parameters unfixed in the limit $ε\to 0$ defines a $\textit{unified flat geometry}$ and its $\textit{unified algebra}$, which reduces to a specific non-Lorentzian geometry for a particular choice of $s$ and $n$. Using this setup in the tangent space, we systematically expand the Einstein-Hilbert action in even powers of $ε$, which we call a $\textit{unified expansion}$ of Einstein's gravity, whose leading-order theory is fixed by $(s,n)$. This reproduces various classes of gravitational theories, including Einstein gravity (the trivial case), Galilean gravity, Carroll gravity, all of which can be extracted from this expansion. Using the expansion, we then formulate String Carroll (SC) gravity, where the local metric has two vanishing eigenvalues. The near-horizon region of generic non-extremal black holes has been recently shown to be a SC geometry. By considering explicit examples, we confirm that these near-horizon geometries constitute solutions of SC gravity, paving the way of understanding physics near the horizon of generic black holes in terms of SC gravity.

The process of Hawking evaporation, shadows and thermal fluctuations are investigated within the fabric of f(R) AdS Black Hole (BH). Specifically, the Hawking evaporation process is analyzed numerically using the Stefan-Boltzmann law. The results indicate that the BH lifetime is always infinite, which means the BH becomes a remnant in the late time. Additionally, the evaporation rate depends on the AdS radius and coupling parameters. We further examined the visual properties of BH shadows observed for various values of the two parameters. The results reveal that the BH shadow radius decreases with $ψ_{0}$, while it increases with $λ$. Consequently, we further investigate the infalling accretion matter in the vicinity of BHs. The results depict that while variations in relevant parameters do influence the central region, the important factor is the change in optical appearance of the bright photon ring, which is exhibited at the position of the photon sphere. Next, we discuss many thermodynamical quantities, such as temperature, entropy, Helmholtz free energy, internal energy, corrected pressure, enthalpy, Gibbs free energy and specific heat and interpret how the variations in $λ$ and $ψ_{0}$ impact on the stability and phase transitions of the AdS BHs.

We develop a deterministic, scale-resolved formulation of energy transfer in the three-dimensional incompressible Navier-Stokes equations based on an explicit triadic decomposition of the nonlinear term in Fourier space. Using a systematic dyadic localization of the velocity field, we derive an exact representation of the nonlinear energy flux across scales and organize it in terms of interactions between well-defined scale components. Under suitable smoothness assumptions, we obtain an absolutely convergent triadic expansion and quantitative bounds that distinguish local and nonlocal contributions in scale space. This framework provides a transparent and fully explicit description of how energy transfer is mediated by triadic interactions and how scale locality emerges as a structural property of the nonlinearity. Building on this formulation, we revisit the classical inertial-range picture of turbulence from a deterministic perspective. We show that, under a scale-invariant flux assumption, the Kolmogorov $-5/3$ scaling is formally consistent with the triadic energy-transfer mechanism at a structural level. The result does not rely on statistical assumptions, but instead follows from the structural properties of the Navier-Stokes equations combined with a scale-resolved representation of the energy flux. The present work thus provides a coherent synthesis of triadic interaction analysis, dyadic scale decomposition, and classical turbulence phenomenology, offering a deterministic framework that clarifies how Kolmogorov-type scaling constraints arise in the scale-resolved structure of the underlying equations.