We use the nonlinearly coupled Einstein-matter field equations to prove four theorems that bound from above the dimensionless force function $\mathcal{F}=4\pi r^2·p(r)$ in spatially regular curved spacetimes of spherically symmetric self-gravitating matter configurations [here, $p(r)$ is the radially dependent pressure inside the spatially regular matter configurations]. In particular, for generic (not necessarily isotropic) matter configurations, it is proved that (i) $\mathcal{F}\le 2$ for matter fields that satisfy the dominant energy condition and (ii) $\mathcal{F}\le 1$ for matter fields with a nonpositive energy-momentum trace. In addition, for self-gravitating isotropic matter configurations, we derive the stronger upper bounds: (iii) $\mathcal{F}\le 1$ for matter fields that satisfy the dominant energy condition and (iv) $\mathcal{F}\le 1/2$ for matter fields with a nonpositive energy-momentum trace. Our analytically derived results are in accord with the spirit of the maximum force conjecture in general relativity.

The Hubble tension and the unknown origin of dark energy motivate the exploration of alternative mechanisms for late-time cosmic acceleration. We investigate gravitationally induced particle creation (PC) as a nonequilibrium process that can effectively mimic dynamical dark energy. Within the thermodynamic framework of open systems, we adopt an agnostic approach to the extra created component, leaving its equation-of-state parameter $w_E$ free. We consider four phenomenological parametrizations of the PC rate, allowing deviations from the standard cosmological model ($\mathrm{\Lambda }\mathrm{CDM}$) only at late times ($0<z<3$). The PC models are constrained using a joint analysis of cosmic chronometers, Type Ia supernovae, local $H_0$ measurements, baryon acoustic oscillations, and cosmic microwave background data. The constraints on $w_E$ are consistent with dark energy, while particle creation of pressureless matter is disfavored. All PC scenarios provide fits comparable to $\mathrm{\Lambda }\mathrm{CDM}$, with one showing effective dynamical dark-energy behavior. When early- and late-time datasets are analyzed separately, the PC models reduce the Hubble tension to $\simeq 2.4\sigma –3\sigma$, compared to $4.3\sigma$ in $\mathrm{\Lambda }\mathrm{CDM}$. Gravitationally induced dark energy thus offers a consistent late-time extension of $\mathrm{\Lambda }\mathrm{CDM}$ and a viable theoretical framework for dynamical dark energy.

Baryon acoustic oscillation data from the Dark Energy Spectroscopic Instrument show evidence of a deviation from a cosmological constant $\mathrm{\Lambda }$ within a Bayesian analysis. In this work, we validate that frequentist constraints from profile likelihoods on the Chevallier-Polarski-Linder parameters $w_0$, $w_a$ are in excellent agreement with the Bayesian constraints when combining with Planck cosmic microwave background, Planck and Atacama Cosmology Telescope lensing, and either $\mathrm{Pantheon}+$ or Dark Energy Survey Year 5 supernova data. Further, we assess which datasets drive these constraints by considering the contributions to the ${\chi }^2$ from the individual datasets. For profile likelihoods of the matter fraction ${\mathrm{\Omega }}_{\mathrm{m}}$, such an investigation shows internal inconsistencies when assuming $\mathrm{\Lambda }$, which are resolved when assuming a $w_0{w}_a$ dark-energy model. We infer the equations of state $w(z)$ at the pivot redshifts, supporting previous interpretations that current data appear to be more sensitive to the derivative of $w(z)$ rather than a mean offset from $\mathrm{\Lambda }$. Thus, our frequentist analysis corroborates previous findings on dynamical dark energy.

We present a harmonic-space estimator for the cross-correlation between the kinematic Sunyaev-Zel’dovich (kSZ) effect and the reconstructed galaxy momentum field that offers several practical advantages over the traditional stacking approach. The estimator is easy to deploy using relatively modest computational resources and recovers all information available in the galaxy-kSZ cross-correlation. In particular, by using well-understood power spectrum estimation techniques, its statistical uncertainties, including potential correlated uncertainties with other large-scale structure observables, can be easily and accurately estimated. Moreover, standard kSZ stacking measurements can be reconstructed exactly from the estimator at a lower computational cost, employing harmonic-space, catalog-level techniques to recover all small-scale information.

This work is part of a series establishing the redshift framework for the $3\times 2\mathrm{pt}$ analysis of the Dark Energy Survey Year 6 (DES Y6). For DES Y6, photometric redshift distributions are estimated using self-organizing maps (SOMs), calibrated with spectroscopic and many-band photometric data. To overcome limitations from color-redshift degeneracies and incomplete spectroscopic coverage, we enhance this approach by incorporating clustering-based redshift constraints (clustering-z, or WZ) from angular cross-correlations with BOSS and eBOSS galaxies and eBOSS quasar samples. We define a WZ likelihood and apply importance sampling to a large ensemble of SOM-derived $n(z)$ realizations, selecting those consistent with the clustering measurements to produce a posterior sample for each lens and source bin. The analysis uses angular scales corresponding to 1.5–5 Mpc to optimize signal-to-noise ratio while mitigating modeling uncertainties and marginalizes over redshift-dependent galaxy bias and other systematics informed by the N-body simulation cardinal. While a sparser spectroscopic reference sample limits WZ constraining power at $z>1.1$, particularly for source bins, we demonstrate that combining SOM with WZ improves redshift accuracy and enhances the overall cosmological constraining power of DES Y6. We estimate an improvement in $S_8$ of approximately 10% for cosmic shear and $3\times 2\mathrm{pt}$ analysis, primarily due to the WZ calibration of the source samples.

Strong evidence for an isotropic, Gaussian gravitational wave background (GWB) has been found by multiple pulsar timing arrays (PTAs). The GWB is expected to be sourced by a finite population of supermassive black hole binaries (SMBHBs) emitting in the PTA sensitivity band, and astrophysical inference of PTA data sets suggests a GWB signal that is at the higher end of GWB spectral amplitude estimates. However, current inference analyses make simplifying assumptions, such as modeling the GWB as Gaussian, assuming that all SMBHBs only emit at frequencies that are integer multiples of the total observing time, and ignoring the interference between the signals of different SMBHBs. In this paper, we build analytical and numerical models of an astrophysical GWB from circular, inspiralling binaries inclined relative to the line-of-sight of the observer, without the above approximations, and compare the statistical properties of its induced PTA signal to those of a signal produced by a Gaussian GWB. We show that finite population and windowing effects introduce non-Gaussianities in the PTA signal, which are currently unmodeled in PTA analyses.

We use supersymmetric chiral dynamics perturbed by anomaly-mediated supersymmetry breaking to obtain a high-quality, composite axion that solves the strong $CP$ problem. The strong dynamics arises from a supersymmetric SU(10) chiral gauge theory with massless matter chiral superfields. This leads to a stable, nonsupersymmetric vacuum, calculated exactly, where a spontaneously broken $U(1)$ global symmetry, identified with the Peccei-Quinn (PQ) symmetry, gives rise to a composite QCD axion. The chiral gauge theory also admits a discrete ${\mathbb{Z}}_4$ (or ${\mathbb{Z}}_{8,16}$) gauge symmetry that forbids PQ-violating operators up to dimension eight. An extension to an $SU(14)\times {\mathbb{Z}}_{12}$ chiral gauge theory incorporates $SO(10)$ grand unification where the unification scale is identified with the PQ-breaking scale and PQ-violating operators are forbidden up to dimension 20. The supersymmetry breaking scale, near 100 TeV, ameliorates the Higgs hierarchy problem, while colored Nambu–Goldstone bosons may be detected at future colliders via decays to gluons or form heavy isotopes.

We investigate the atmospheric production and subsequent detection of sub-GeV dark mesons within the framework of a confining dark sector coupled to the Standard Model (SM) via a $U(1{)}_{\mathrm{D}}$ vector portal. High-energy cosmic-ray interactions in the atmosphere produce dark quarks through proton bremsstrahlung, rare decays of Standard Model mesons, and Drell-Yan processes, which subsequently hadronize into dark mesons. We adopt a modified quark combination model to describe the nonperturbative dark hadronization process, allowing for a detailed event-level characterization of the dark meson flux. We simulate the flux and the interactions of these relativistic dark mesons in the Jiangmen Underground Neutrino Observatory (JUNO) using the genie generator, considering both elastic scattering off nuclei and deep inelastic scattering channels. Adopting a large-energy-singles-inspired conservative signal definition with $15\mathrm{MeV}<E_{\mathrm{vis}}<100\mathrm{MeV}$ and vetoing events containing final-state neutrons, we derive projected 90% C.L. sensitivities to the coupling strength between the dark gauge boson and the SM sector for a $20\mathrm{kton}·\mathrm{year}$ exposure. For the representative benchmark masses $m_{Z^{\prime }}=0.001$, 0.01, and 0.1 GeV, the projected JUNO reach corresponds to $g_{\mathrm{SM}}^{90}=6.48\times {10}^{-5}$, $7.75\times {10}^{-5}$, and $2.37\times {10}^{-4}$, respectively. This reach is found to be only mildly sensitive to order-one variations of the hadronization parameter, as illustrated by the choices ${\kappa }_{\beta }=1/3$, 1, and 3.

Quantum data learning (QDL) provides a framework for extracting physical insights directly from quantum states, bypassing the need for any identification of the classical observable of the theory. A central challenge in many-body physics is that the identity of quantum phases, especially those with topological order, is often inaccessible through local observables or simple symmetry-breaking diagnostics. Here, we apply QDL techniques to the $2+1$-dimensional toric-code loop-gas model in a magnetic field. Ground states are generated across multiple lattice sizes using a parametrized loop-gas circuit with a variational quantum-eigensolver approach. We then train a quantum convolutional neural network across the full field-parameter range to perform phase classification and capture the overall phase structure. We also employ a physics-aware training protocol that excludes the near-critical region ($0.2\le x\le 0.4$) around $x_c\approx 0.25$, the phase-transition point estimated by quantum Monte Carlo simulation, reserving this window for testing to evaluate the ability of the model to learn the phase transition. In parallel, we implement an unsupervised quantum $k$-means method based on state overlaps, which partitions the dataset into two phases without prior labeling. Our supervised QDL approach recovers the phase structure and accurately locates the phase transition, in close agreement with previously reported values; the unsupervised QDL approach recovers the phase structure and locates the phase transition with a small offset as expected in finite volumes; both QDL methods outperform classical alternatives. These findings establish QDL as an effective framework for characterizing topological quantum matter, studying finite volume effects, and probing phase diagrams of higher-dimensional systems.

We present an analysis of the radiative decay $\varphi \to \gamma {\pi }^0{\pi }^0$ in a dispersive framework, where the two-pion subsystem undergoes strong final-state interactions that cover the $f_0(500)$ and $f_0(980)$ regions. We employ a coupled-channel Muskhelishvili-Omnès framework that allows for a consistent treatment of two scalar resonances and crossed-channel singularities induced by the Born and vector-meson exchanges. We explicitly verify the equivalence between the modified and standard Muskhelishvili-Omnès representations for vector-meson pole contributions when the isoscalar Omnès matrix is chosen asymptotically bounded, and we adopt the standard representation in decay kinematics. This yields, for the first time, a parameter-free dispersive prediction for the kaon Born rescattering, which provides a dominant contribution. To obtain a good fit to the KLOE and SND data, we employ a once-subtracted coupled-channel dispersion relation with heavier left-hand cut contributions and two unknown subtraction constants. The results demonstrate the consistency among the data for $\pi \pi$ scattering, $\gamma \gamma$ fusion, and $\varphi$ radiative decay, thereby validating the underlying dispersive formalism and the input used for the hadronic Omnès matrix and left-hand cuts.

We study neutrino-induced charged-current coherent pion production (${\nu }_{\mu }\mathrm{CC}-\mathrm{Coh}\pi$) as a tool for constraining the neutrino flux at the Deep Underground Neutrino Experiment (DUNE). The neutrino energy and flavor in the process can be directly reconstructed from the outgoing particles, making it especially useful to specifically constrain the muon neutrino component of the total flux. The cross section of this process can be obtained using the Adler relation with the $\pi$-Ar elastic scattering cross section taken either from external data or, as we explore, from a simultaneous measurement in the DUNE near detector. We develop a procedure that leverages ${\nu }_{\mu }\mathrm{CC}-\mathrm{Coh}\pi$ events to fit for the neutrino flux while simultaneously accounting for relevant effects in the cross section. We project that this method has the statistical power to constrain the uncertainty on the normalization of the flux at its peak to a few percent. This study demonstrates the potential utility of a ${\nu }_{\mu }\mathrm{CC}-\mathrm{Coh}\pi$ flux constraint, though further work will be needed to determine the range of validity and precision of the Adler relation upon which it relies, as well as to measure the $\pi$-Ar elastic scattering cross section to the requisite precision. We discuss the experimental and phenomenological developments necessary to unlock the ${\nu }_{\mu }\mathrm{CC}-\mathrm{Coh}\pi$ process as a “standard candle” for neutrino experiments.

In this work, we propose a novel approach for identifying, constructing, and validating precise and accurate universal relations for neutron star bulk quantities. A central element is simulation-based inference (SBI), which we adopt to treat uncertainties due to the unknown nuclear equation of state (EOS) as intrinsic nontrivial noise. By assembling a large set of bulk properties of nonrotating neutron stars across multiple state-of-the-art EOS models, we are able to systematically explore universal relations in high-dimensional parameter spaces. Our framework further identifies the most promising parameter combinations, enabling a more focused and traditional construction of explicit universal relations. At the same time, SBI does not rely on explicit relations; instead, it directly provides predictive distributions together with a quantitative measure of systematic uncertainties, which are not captured by conventional approaches. As an example, we report a new universal relation that allows us to obtain the radius as a function of mass, fundamental mode, and one pressure mode. Our analysis shows that SBI can surpass the predictive power of this universal relation while also mitigating systematic errors. Finally, we demonstrate how universal relations can be further calibrated to mitigate systematic errors accurately.

We investigate the imprints on the angular power spectra of cosmological perturbations of a preinflationary bounce phase, as described by the hybrid and dressed metric approaches to loop quantum cosmology. For this purpose, we derive a new parametrization of the primordial power spectrum at the end of the inflationary regime. Apart from slow-roll coefficients and cosmological parameters that are present in the standard cosmological scenario without quantum modifications, this parametrization additionally depends only on preinflationary physics. More specifically, we find a dependence on the number of e-folds during the bounce epoch and on a characteristic suppression scale which, given the e-folds accumulated during cosmic evolution, is determined by the energy density at the bounce. Recall that this density depends on the Immirzi parameter and the area gap known from loop quantum gravity. This leads to a robust and accurate parametrization of the primordial power spectrum. Since in preinflationary scenarios there is no preferred vacuum state, we adopt the nonoscillatory adiabatic Hamiltonian diagonalization proposal, which selects a vacuum that is optimally adapted to the background dynamics and yields a nonoscillatory primordial power spectrum. With this choice, we show that the tensor-to-scalar ratio in both quantization approaches coincides with its expression in the standard $\mathrm{\Lambda }\mathrm{CDM}$ model when the observed scales are not much smaller than the power-suppressed region. Computing also the angular power spectrum, we find that, for a total cosmic expansion of about 140 e-folds, both the hybrid and the dressed metric approaches exhibit excellent agreement with Planck data at high multipoles, while apparently improving the fit with respect to $\mathrm{\Lambda }\mathrm{CDM}$ for low multipole numbers.

Based on the general principles of Lorentz symmetry and unitarity, we introduce two consistency conditions—on-shell gauge symmetry and strong massive-massless continuation—in constructing amplitudes of massive gauge theory with elementary particles. In particular we argue that on-shell gauge symmetry can be understood as a consequence of Lorentz symmetry, unitarity, and massive-massless continuation. Based on these two conditions, combined with the little group transformation and consistent factorization, we construct three-point and four-point vector-boson/scalar amplitudes that correspond to renormalizable interactions, then analyze the underlying theories and models. Given the particle masses, almost all possible vertices, including those involving Goldstone modes, are uniquely fixed. The only exceptions are triple and quartic scalar self-couplings, as well as mixing angles between vacuum expectation values (VEVs) and scalars. In addition, all particle masses must have the same physical origin. If the number of vector bosons is smaller than 3, the underlying theories for the amplitudes are either massive gauge theories with spontaneous symmetry breaking (SSB) or Stueckelberg theory. The necessary condition for the latter is that the scalars have equal masses. We also discuss different models depending on the number of scalars involved. If the number of vector bosons is larger than 3, the underlying theory must be Yang-Mills theory with SSB. In both Abelian and non-Abelian cases, the specific shape of the Higgs potential cannot be determined, which explains the fact that scalar self-couplings are undetermined, and the relations between the masses are generally nonlinear.

Quantum effects are studied in both Schwarzschild spacetime and a spacetime in which a null shell collapses to form a black hole via the vacuum polarization $⟨{\varphi }^2⟩$ and stress-energy tensor $⟨T_{ab}⟩$ for a massless minimally coupled scalar field in two dimensions. For Schwarzschild spacetime, the focus is on the Boulware and Unruh states. For the collapsing null shell spacetime, the in vacuum state is used. Instabilities of the Unruh and in states resulting from the behavior of $⟨{\varphi }^2⟩$ in the regions inside and outside of the horizon are found. The question of how well the Unruh state for the eternal black hole approximates quantum effects in the interior of a black hole that forms from collapse is addressed.

We develop a formulation of the strong deflection limit for the scattering of particles following timelike geodesics in asymptotically flat, static, and spherically symmetric spacetimes. For fixed specific energy, as the angular momentum approaches its critical value from above, the particle passes arbitrarily close to the associated unstable circular orbit, undergoes many windings around it, and the deflection angle diverges logarithmically. Using the geodesic deviation equation, we show covariantly that the coefficient of this logarithmic divergence is determined by the radial instability exponent of the critical trajectory, defined per unit azimuthal angle. We express this instability exponent in terms of local curvature data on the unstable circular orbit, thereby providing both kinematic and geometric interpretations of the strong deflection limit. In general relativity, its matter dependence enters only through a single local scalar combination constructed from the static-frame energy density and the principal radial and tangential pressures.

The gravitational lensing of relativistic and nonrelativistic neutral massive particles in the black-bounce-Schwarzschild black hole spacetime is investigated in the strong deflection limit. Beginning with the explicit equations of motion of a massive particle in the regular spacetime, we achieve the equation of the particle sphere and thus the radius of the unstable timelike circular orbit. It is interesting to find that the particle sphere equation can reduce to the well-known photon sphere equation, when the particle’s initial velocity is equal to the speed of light. We adopt the strong field limit approach to calculate the black-bounce-Schwarzschild deflection angle of the particle subsequently, and obtain the strong-deflection lensing observables of the relativistic images of a pointlike particle source. The observables mainly include the apparent angular particle sphere radius, the angular separation between the outermost relativistic image and the other ones that are packed together, and the ratio between the particle-flux magnification of the outermost image and that of the packed ones (or equivalently, their resulting magnitudelike difference). The velocity effects induced by the deviation of the initial velocity of the particle from light speed on the corresponding strong-field lensing observables of the images of a pointlike light source in the regular geometry, along with these on the strong deflection limit coefficients and the critical impact parameter of the lightlike case, are then formulated. The influence of the spacetime bounce on the Schwarzschild lensing properties of the images of a massive-particle-emission source in the strong field limit is also considered. Serving as an application of the results, we finally concentrate on evaluating the astronomical detectability of the velocity- and bounce-induced effects on the lensing observables and analyzing their dependence on the parameters, by modeling the supermassive black hole at the galactic center (i.e., Sgr ${\mathrm{A}}^{*}$) and the one at the center of galactic M87 (i.e., $\mathrm{M}{87}^{*}$) as the lens, respectively.

We present the construction of stationary solutions of Bose-Einstein condensate dark matter (BECDM) around a pointlike gravitational source representing a black hole. The problem is formulated for general axisymmetric configurations, and we focus on two cases: the ground-state core solution and the first nonzero winding number configuration corresponding to a line vortex solution. The stationary equations are solved using an imaginary-time approach, which enables the construction of families of solutions across a wide range of self-interaction and black hole masses. We analyze the impact of these parameters on the density distribution and on the stability properties of the solutions, assessing stability through the turning point criterion based on the enthalpy functional, which allows us to identify stable and unstable branches along each family of solutions. It has been shown in the past that spherical core solutions act as attractors in the collapse of BECDM around black holes in the noninteracting case ($g=0$), supporting their astrophysical relevance. In the present work, the existence of a maximum mass for configurations with attractive self-interaction ($g<0$) allows us to infer the parameter range in which such solutions may also arise in this regime. Building on this picture, we show that stable vortex solutions of BECDM can also exist in the presence of a black hole, whose stability properties suggest that these configurations may likewise be compatible with physically relevant formation scenarios.

We investigate the charging process of a rotating Kerr black hole of mass $M$ and angular momentum $J$ immersed in a stationary, axisymmetric, asymptotically uniform magnetic field of strength $B_0$. In Wald’s classic analysis [1], which was based on the assumption of vanishing injection energy, the black hole was predicted to acquire a universal “saturation charge” $Q_{\mathrm{w}}=2B_{0}J$. However, the physical mechanism that sets the saturation charge must ultimately be governed by the competition between the absorption rates of positively and negatively charged particles. Motivated by this observation, we revisit the problem in the framework of a simple accretion model, where two dilute, equivalent fluxes of charged particles of opposite signs are injected from infinity along the magnetic field lines. The problem then reduces to that of individual particle motion in the electromagnetic field of the magnetized Kerr black hole. Using a combination of numerical and analytical tools, we determine the domains of absorption and establish both lower and upper bounds on the corresponding absorption cross sections. At $Q=Q_{\mathrm{w}}$ these bounds reveal a systematic difference between the two charge signs. In particular, for sufficiently strong magnetic fields, the lower bound on the absorption cross section for the “attracted” charge exceeds the upper bound for the “repelled” one. This charge accretion imbalance (which we find to become extreme at the limit of large $B_0$) indicates a persistent net charge accretion at $Q=Q_{\mathrm{w}}$, implying that the actual saturation charge must differ from Wald’s charge $Q_{\mathrm{w}}$.