We analyze the decoherence of a particle’s spatial superposition moving along a stationary worldline through the Minkowski vacuum. The particle is modeled via an internal degree of freedom that couples to a scalar field, and an external degree of freedom, i.e., its quantized center-of-mass motion around the stationary worldline. Assuming a separation of timescales between the particle’s internal and external dynamics, we first obtain an effective redshifted polarizability of the particle, characterizing the trajectory-dependent linear response of the internal oscillator to the field. We then derive a quantum Brownian motion master equation for the particle’s center of mass, under the Born-Markov approximation, which describes its decoherence in the position basis, as well as Hamiltonian modifications corresponding to a dispersive potential. The resulting decoherence has two components: (1) arising from a modified field spectrum observed by the particle; and (2) due to a differential time dilation over the particle’s extended spatial wave function. For stationary trajectories, both contributions take an effectively thermal form. We evaluate the decoherence rates for two specific cases, hyperbolic and uniform circular motion.

A quantum macroscopic “Kruskal” black hole solution that incorporates quantum geometry effects has been derived in loop quantum gravity as the counterpart to the classical Schwarzschild solution with a distinct imprint outside the event horizon, even at scales much larger than the Planck length. This resulting black hole quantum geometry is supported by an effective energy density of quantum origin, outside the horizon, which prevents asymptotic flatness at large distances and confines massive particles to finite radii, thereby preventing their escape to infinity. In this work, we adapt to these solutions the extended Anderson-Candelas-Christensen-DeWitt approach to compute the quantum vacuum polarization in order to provide an accurate measure of the quantum activity around these black holes. We carry out a numerical implementation of the formalism and present, to our knowledge for the first time, the scalar vacuum polarization $⟨{\varphi }^2⟩$ exterior to this quantum-corrected geometry. We find that the quantum-gravity exponent $\epsilon$ enhances the near-horizon polarization and induces, farther out, a small negative tail that we identify—through a parameter-free DeWitt-Schwinger comparison—with the field’s response to the nonzero curvature of the background (absent for Ricci-flat Schwarzschild). The correction scales linearly with $\epsilon$, the parameter tracking the quantum gravitational corrections, so that, for astrophysically realistic (i.e., tiny) $\epsilon$, the result is numerically indistinguishable from Schwarzschild. The calculation furnishes a consistency check on the quantum activity around these solutions, the fluctuations tracking the local curvature without anomalous growth in the exterior.

We apply a convenient parametrization of all Plebański-Demiański black holes of algebraic type D with the Kerr rotation, NUT twist, acceleration, electric and magnetic charges, and any value of the cosmological constant $\mathrm{\Lambda }$, recently found by Astorino. This represents a complete class of exact solutions to the Einstein-Maxwell-$\mathrm{\Lambda }$ equations such that the (non-null) electromagnetic field is aligned with both the (geodesic, shear-free, double) principal null directions of the Weyl tensor. We derive a novel appropriate metric form and the corresponding canonical frames naturally adapted to both the de Sitter-like ($\mathrm{\Lambda }>0$) and the anti–de Sitter-like ($\mathrm{\Lambda }<0$) conformal infinity, and we demonstrate that these geometric objects are useful for investigation of radiation properties. In particular, using the Fernández-Álvarez-Senovilla criterion, it confirms that the gravitational radiation is present if, and only if, these black holes are accelerating.

We characterize the gravitational radiation present in the general Plebański-Demiański type-D solution with cosmological constant $\mathrm{\Lambda }$ of any sign. We show that radiation escapes toward infinity if and only if the acceleration parameter is nonzero. We calculate the Cotton-York tensor and the boundary stress-energy tensor at infinity for negative $\mathrm{\Lambda }$, and for positive $\mathrm{\Lambda }$ the $D$ tensor that complements initial or final data at $𝒥$. In addition, we recast a recent parametrization of this family of metrics into a new form by a simple homothety, correctly identifying $\mathrm{\Lambda }$, and study the existence and regularity of the possible axes of symmetry, searching for a relation between deficit angles and radiation. We also identify the branch of general nonradiating solutions with nonvanishing Cotton-York tensor at $𝒥$.

We construct two exact nonlinear electrodynamics generalizations of the Kerr-Newman-NUT-$\mathrm{\Lambda }$ spacetime, where NUT stands for Newman-Unti-Tamburino. Imposing alignment between the principal directions of the electromagnetic field and the metric tetrad reduces the Maxwell-Faraday sector to a pair of potentials constrained by a single integrability condition, the key equation. Within the polynomial aligned ansatz considered here, the key equation selects two admissible families, corresponding to electromagnetic potentials that are cubic and quartic polynomials. For each family the Einstein equations reduce to a single radial ordinary differential equation for the deformation of the Kerr-like radial metric function, which we solve exactly. We derive the corresponding metrics, electromagnetic fields, stress tensors, horizon structure, and energy conditions. The nonlinear sector breaks conformal invariance and, in the cubic family, can mimic an effective cosmological contribution. The corresponding on-shell Lagrangian densities are reconstructed along the aligned solution branches, while the problem of finding closed, solution-independent constitutive relations is identified as a separate open issue. The curvature invariants show that the nonlinear contribution does not remove the Kerr-like curvature singularity, while the solutions present the NUT axial conical singularity.

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 $\mathrm{\Sigma }$. A one-parameter redistribution of the cyclic norm then generates the exact Ricci source $R_{AB}=C_D(\beta ){\partial }_A\mathrm{\Sigma }{\partial }_B\mathrm{\Sigma }$, with $C_D(\beta )=\frac{D-2}{D-3}(1-{\beta }^2)$, while $\mathrm{\Sigma }$ remains harmonic in the deformed metric. Composing $\mathrm{\Sigma }$ with an affinely parametrized geodesic of a nondegenerate target metric whose squared speed is $C_D(\beta )$ 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.

Magnetic fields are a critical foundation for interpreting high-energy astrophysical phenomena across cosmic scales. In this work, we investigate the parametrized post-Einsteinian (ppE) waveform imprints induced by external magnetic fields around Kerr-Bertotti-Robinson (KBR) and Kerr-Bonnor-Melvin (KBM) black holes, to disentangle magnetic signatures from environmental effects in massive black hole binary gravitational wave signals. For a small compact object inspiraling into a massive KBR black hole, the leading-order magnetic correction enters at $-2$ post-Newtonian (PN) order, with a spin-induced next-to-leading correction at $-1.5$ PN. For a spinning KBM black hole, the leading magnetic correction appears at $-3$ PN, alongside a spin-induced $-1.5$ PN term. These leading ppE corrections show no intrinsic degeneracy with modified gravity effects, but closely resemble the gravitational pull from power-law matter distributions with indices $\gamma =1$ and $\gamma =0$, respectively. Using a multievent statistic $F$ to break this degeneracy, we find that robustly distinguishing magnetic effects from matter-induced pull is not uniformly efficient, especially for the KBR case. For the KBM scenario, a clear transition emerges at ${\rho }_0\sim {10}^{-4}\mathrm{kg}/{\mathrm{m}}^3$ ($B\sim {10}^4\mathrm{T}$): above this threshold, the magnetic signature can be reliably separated, while no efficient distinction is achievable below it. Our results highlight that future detections of anomalous $-3$ or $-2$ PN corrections may originate from either magnetic fields or dense matter environments, emphasizing the necessity of combining multievent statistics and multimessenger validation for robust gravitational wave astronomy tests.

We present a physically motivated model of dark energy (DE) rooted in the topological structure of the quantum chromodynamics (QCD) vacuum. In this framework, DE arises from the difference between the QCD vacuum energy in an expanding Universe and in Minkowski spacetime, with the relevant contribution generated by tunnelling between distinct topological sectors. The QCD scale, ${\mathrm{\Lambda }}_{\mathrm{QCD}}\sim 100,\mathrm{MeV}$, naturally produces a vacuum-energy density of the same order of magnitude as the observed one, without introducing new fundamental fields, couplings, or fine-tuning. We show that the same mechanism can naturally accommodate an evolving dark-energy component. The resulting effective equation-of-state parameter ${\omega }_{\mathrm{DE}}$ can evolve with redshift, lie on either side of $-1$, and cross the ${\omega }_{\mathrm{DE}}=-1$ boundary, while asymptotically approaching $-1$ in the future. The framework offers a common physical origin for both the small amplitude of dark energy and its possible time evolution, the latter being suggested by recent Dark Energy Spectroscopic Instrument observations. Here, we develop the physical and cosmological aspects of the framework; its confrontation with cosmological data is presented in a companion paper.

It is well known that, in potentials that are quadratic near the minimum but shallower away—such as small-$\alpha$ ($\alpha \ll M_P^2$) attractors—the inflaton condensate fragments into localized compact objects known as oscillons during self-resonance preheating. In this work, we investigate the self-resonance in deformed $\alpha$-attractor T-models with a Gaussian feature near the minimum, distant from inflation’s end. Linear analysis reveals altered resonance bands and deformed Floquet charts dependent on feature parameters, primarily through the localized modification of $V^{\prime \prime }(\varphi )$. In fully nonlinear lattice simulations, we find that the potential feature has only a modest influence on gradient-energy transfer during resonance, whereas the subsequent evolution becomes strongly dependent on the Gaussian feature’s dimensionless amplitude $h$. Increasing $|h|$ suppresses the formation and persistence of compact oscillons, resulting in fewer objects and a smaller fraction of energy stored in them. The total-energy and internal-gradient-energy diagnostics give consistent lifetime trends. Within the directly resolved range, the oscillon lifetime decreases nonlinearly with increasing $|h|$, with negative $h$ generally producing shorter lifetimes than positive $h$ of the same magnitude. The gravitational-wave emission is dominated by the resonant stage and becomes strongly suppressed after oscillon formation. We further find an enhancement in the high-frequency tail of the spectrum, sourced by the potential feature. Although a complete reheating description requires external couplings and higher-resolution simulations, clear qualitative differences in the postinflationary expansion history already emerge within our simulated time window. These results highlight the important role of potential features in shaping reheating dynamics and their cosmological implications and provide a deeper understanding of preheating dynamics and the properties of oscillons.

In this letter we argue that the commonly adopted Chevallier-Polarski-Linder (CPL) parametrization for the dark energy equation of state (EoS) is biased toward preferring such model over the constant $w$ while the latter bounds are still compatible with their $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) values. For that we compare constraints on the EoS parameters $w_0$ and early type $w_a$ (CPL) against those with a late-time parametrization on $w_a$ (hereafter LZ) and the constant $w$ model, using cosmic microwave background, Supernovae, and baryonic acoustic oscillations from Dark Energy Spectroscopic Instrument datasets. We found, the same as was the case with the CPL model, preference for dynamical dark energy within the LZ model, but for values almost symmetrically distributed with respect to their $\mathrm{\Lambda }\mathrm{CDM}$ limits. This is due to the fact that the presence of $w_0$ allows to recast each parametrization into making it compensate the preference for $w\sim -1$ in the opposite direction. To further test our hypothesis, we fixed $w_0$ to $-1$ and followed a minimal investigation approach by considering models that deviate only by one free parameter following the same previous parametrizations, making them now genuinely different from each other. On the other hand, we extend our models to more general ones by either incorporating parametrizations that group both late and early $w_a$ effects, which we name the generalized dark energy equation of state (GEoS) model, or by allowing the presence of two dark energy components, fluidlike ${\mathrm{\Omega }}_{\mathrm{DE}}$ and constantlike ${\mathrm{\Omega }}_{\mathrm{CC}}$. We also complement conclusions drawn from the significance levels from the resulting confidence contours with that of the Bayes factor calculation. We found that all the variants, except the original CPL or LZ, are still compatible with $\mathrm{\Lambda }\mathrm{CDM}$, with likelihoods peaking close to $w_0=-1$, $w_a=0$, or 0.68 for ${\mathrm{\Omega }}_{\mathrm{CC}}$, with the constant $w$ and the late time $w_a$ (minimal LZ) being the ones with the tightest constraints. Although we found that the evidence from CPL or LZ is stronger than those for the more minimal cases, however, the preference increases further for the more generalized parametrizations, instead of penalizing the addition of the extra degrees of freedom, while still staying compatible with $\mathrm{\Lambda }\mathrm{CDM}$ in terms of the significance levels. We conclude that considering the CPL model is not sufficient on its own to test deviations from the simple cosmological constant model, and that it is necessary to conduct further minimal or more general approaches when confronting models to observations, so as to localize biases, if they exist, or to better understand the outcomes from model testing and inference methods.

Note that the word “bias” here is considered to mean any artifact effect in general and not specifically only a shift in the parameter confidence contours.

Ultrafaint dwarf galaxies serve as powerful testing grounds for wave dark matter models through dynamical stellar heating. Previous simulation-based work derived a lower bound on the fuzzy dark matter (FDM) particle mass using a diffusion approximation valid only when the de Broglie wavelength is much smaller than the galaxy’s half-light radius. We simulate the dynamical evolution of stellar clusters in FDM halos across a wide mass range and find that for sufficiently low masses, where the de Broglie wavelength is much larger than the cluster size, tidal heating is the main mechanism. We also find that a reduced soliton mass and tidally stripped halo can suppress the heating. We demonstrate that in order to constrain FDM mass from cluster heating, the structure and environment of the FDM halo must be carefully considered.

We develop a general Fokker-Planck framework describing the dynamical evolution of Keplerian binaries subjected to stochastic perturbations. The formalism provides an algorithmic way to obtain the Fokker–Planck drift and diffusion coefficients of any set of orbital variables given the statistics of the perturbations. We apply the method to three physically distinct regimes: adiabatic tidal perturbations, white-noise tidal perturbations, and impulsive encounters with a third body of arbitrary density profile. In each regime we provide explicit drift and diffusion coefficients for all six orbital elements, derive the associated evolution timescale, and obtain analytic steady-state distribution functions. Our results extend previous treatments by including the evolution of the binary’s orientation, retaining the complete tensor structure of tidal correlators, treating nonpointlike perturbers, and resolving the exact geometry of impulsive encounters. The latter correction leads to a steady-state eccentricity distribution that is slightly subthermal. We also show how these equations can be applied directly in several astrophysical scenarios, including binaries perturbed by dark matter subhaloes, ultralight dark matter, and the interstellar medium. This work delivers both a complete mathematical framework and a practical toolkit for stochastic binary evolution, providing ready-to-evaluate equations to be applied directly to binary population data.

The identification of NGC 1068 as an extragalactic high-energy neutrino source raises the question of the physical conditions required for neutrino production. Motivated by the newly updated IceCube data (down to $\sim 0.2\mathrm{TeV}$) for NGC 1068, we present a statistical, model-independent inference primarily constrained by the multimessenger observations. We calculate neutrino production from hadronic channels (including hadronuclear and photomeson processes) and the accompanying cascade gamma rays, and then employ the Latin hypercube sampling (LHS) method to explore the parameter space comprehensively, constrained by observational data. According to our results, the emission region is tightly limited: $R\gtrsim 10R_{\mathrm{s}}$ is excluded at $\sim 5\sigma$, and $R\gtrsim 6R_{\mathrm{s}}$ at $\sim 3\sigma$, where $R_{\mathrm{s}}$ is Schwarzschild radius of supermassive black hole (SMBH). Furthermore, reproducing $\gtrsim 80\%$ of the observed neutrino flux further restricts the emission to $R\lesssim 3R_{\mathrm{s}}$. Finally, we explore the possible particle acceleration mechanisms and find that stochastic acceleration naturally satisfies all constraints, whereas alternative mechanisms require extreme, fine-tuning parameters. We therefore identify stochastic acceleration as the most viable origin of the neutrino emission from NGC 1068.

Despite many years of development in integration-by-parts reduction, reconstructing all reduction coefficients, which are rational functions of kinematic variables and the space-time dimension, remains a nontrivial problem. The main difficulty comes from the large number of unknowns in a general ansatz, which can lead to a linear system that is too large to solve. In this paper, we present an algorithm for reconstructing reduction coefficients through a sequence of intermediate bases. The resulting analytic reduction coefficients are products of a few analytic matrices, whose nonzero entries are simple rational functions. We demonstrate the efficiency of this algorithm with two cutting edge examples; a three-point massive box-triangle and a four-point massive pentagon-triangle. Reconstructing all reduction coefficients for the box-triangle (pentagon-triangle) requires 3289 (13, 013) numerical samplings, significantly fewer than the number of unknowns in the general ansatz, 1, 407, 406 (21, 638, 331).

Quantum entanglement provides a quantitative probe of the internal structure of hadrons and offers a sensitive means to study the quantum correlation in the hadron wave functions. For baryons, the spin state of the three valence quarks forms a tripartite qubit system, whose entanglement structure can be characterized by the four classes of three-qubit states. In this work, we compare the proton spin entanglement obtained from Basis Light-Front Quantization (BLFQ) with that from a quark-diquark model. By analyzing both bipartite and tripartite entanglement, we find that the quark-diquark model yields a substantially more entangled spin state than the BLFQ wave function in the valence Fock sector. This difference mainly originates from the larger W-type and Bell-type entanglement in the quark-diquark model. Within BLFQ, a larger coupling constant and smaller quark mass drive the spin correlation among the valence quarks towards an effective quark-diquark configuration with an active $d$ quark and a correlated $uu$ pair.

Ultralight dark matter exhibits an order-1 density fluctuation at the scale of its wavelength. This density fluctuation exists across the entire dark matter halo and interacts with stars and planets, perturbing their motion via gravitational interactions. We investigate the possibility of using precision solar system dynamics to search for ultralight dark matter. We examine this possibility with interplanetary radio range measurements. We show that the precision of current range measurements can probe ultralight dark matter at masses around ${10}^{-15}\mathrm{eV}$, had its density in the solar system been ${10}^5$ larger than the so-called local dark matter density. This limit complements other constraints, such as the one from analyses of pulsar timing observations.

We study static quark-antiquark interactions in rotating SU(3) gluodynamics using quenched lattice simulations at imaginary angular velocity. At zero temperature, we extract the static potential from Wilson loops for quark-antiquark pairs aligned with the rotation axis, for transverse pairs with one source on the rotation axis, and for symmetric transverse pairs across the rotation axis. Within the present accuracy, no significant rotation dependence or anisotropy is observed in the zero-temperature potential. At finite temperature, imaginary rotation suppresses the color-averaged free energies obtained from Polyakov-loop correlators in both longitudinal and transverse geometries. Axial-diagonal comparisons are used to identify a bulk region where open-boundary artifacts are reduced. In this region, the large-distance longitudinal free-energy shift is well described by $\mathrm{\Delta }{F}_z(R_{xy})=A{R}_{xy}^2+B$. The transverse channels exhibit the same qualitative suppression, while their distance dependence additionally reflects the radial arrangement of the static sources and is compatible with a radial single-source free-energy shift in the bulk region. For the finite-temperature observables studied above $T_c$, the response weakens as the temperature is increased. These results provide lattice evidence for a position- and geometry-dependent response of bare static-source free energies to imaginary rotation in a gluonic medium.

The chromomagnetic monopoles (CMM), emergent topological excitations of non-Abelian gauge fields carrying chromomagnetic charge, have long been postulated to play an important role in the vacuum confinement of quantum chromodynamics (QCD), the deconfinement transition at temperature $T_c\approx 160\mathrm{MeV}$, as well as the strongly coupled nature of quark-gluon plasma (QGP). While such CMMs were found to help provide resolutions for challenging puzzles from heavy-ion collision measurements, they were typically introduced as model assumptions in the past. Here we perform a data-driven Bayesian inference of the chromomagnetic component, within the CUJET framework, and extract its temperature-dependent abundance for the first time. Using the cujet3 framework for calculations of jet energy loss and analyzing a comprehensive experimental dataset for nuclear modification factor ($R_{\mathrm{AA}}$) and elliptic flow ($v_2$) of high-transverse-momentum hadrons, the fraction of CMMs in the QGP is obtained by Bayesian inference and is found to be substantial in the $1\sim 2T_c$ region. The posterior CMM fraction is further tested against additional data and is also shown to predict QGP transport properties that are quantitatively consistent with the state-of-the-art knowledge.