We propose that Feynman integral reduction is controlled by solutions of the Landau equations. We study integral relations with prescribed propagator powers using syzygy methods and discuss how syzygies can be expressed as a sum over components of the Landau singularity locus. This leads to a determinantal approach to solving the syzygy problem, giving rise to highly compact and physically transparent solutions. We demonstrate the method in applications to planar two-loop five-point integrals relevant for the $pp\to t\overline{t}H$ process. Our results suggest an efficient method of Feynman integral reduction and provide a novel physical perspective on the problem.

We propose a gauge-symmetry origin of a rank-two Dirac neutrino mass matrix that enforces one exactly massless neutrino, while being consistent with the oscillation data, as well as cosmological constraints. The mechanism relies on a minimal dark $SU(2{)}_D$ gauge symmetry under which one right-handed neutrinolike Weyl fermion is charged, thereby forbidding its Standard Model Yukawa coupling. Quantum consistency then fixes the minimal dark-sector completion: Cancellation of the Witten anomaly requires a second fermionic $SU(2{)}_D$ doublet, while a discrete $Z_4$ symmetry that forbids Majorana masses allows the two dark doublets to form a vectorlike pair. This anomaly-free completion gives rise to a secluded, confining dark sector that can contain a potential dark matter candidate, linking the protected neutrino texture to dark infrared dynamics.

A modified version of loop quantum cosmology model, the so-called mLQC-I, motivated by Thiemann’s regularization of the Hamiltonian constraint, leads to the resolution of the big bang singularity and a bounce in the isotropic setting, where either the pre- or postbounce epoch is necessarily characterized by an emergent Planckian de Sitter phase. In this work we explore the Planckian physics of this mLQC-I prescription for the Bianchi-I spacetimes. We show that, as in the isotropic model, there exists an emergent de Sitter phase which naturally dampens anisotropic shear and removes cosmic hair. However, this isotropization comes at a steep price: although a macroscopic postbounce regime is achieved, the universe does not become classical. As is well known from the Kasner solution, the classical evolution of a contracting Bianchi-I universe toward the singularity can in general be either point- or cigarlike. However, cigarlike evolution is prevalent unless the matter content dominates over the anisotropic shear. For a class of physically admissible initial conditions corresponding to cigarlike evolution, we further demonstrate that this isotropization mechanism is nongeneric. These results clarify and reinterpret recent claims by Gan et al. [Phys. Rev. Lett. 136, 251501 (2026)] that, in anisotropic mLQC-I, quantum gravity effects generically damp anisotropic shear in a manner independent of initial conditions and matter content, and that this damping arises from a novel quantum gravity effect. Our work explains the origin of this mechanism and its limitations in the mLQC-I model.

In gravitational physics, matter does not merely move within spacetime; it also determines the light cones that define causal relations. What happens when the matter that determines these light cones is itself in a quantum state? We address this question in a controlled low-energy setting: a massless scalar field propagating in the spacetime with the Newtonian gravitational potential sourced by a nonrelativistic quantum particle. We show that the light cones are affected by an operator-valued Shapiro delay, with the three consequences: (i) causal-boundary shifts are promoted to noncommuting observables, giving the causal structure an irreducible quantum uncertainty; (ii) the causal relation between two fixed spacetime points can become a superposition of timelike and spacelike configurations; and (iii) tracing out the source smears the Wightman light cone singularity, producing an effective UV cutoff. Thus, quantum matter does not merely fluctuate within spacetime; it makes the causal structure itself quantum, even without including propagating graviton modes.

This study explores the nonlinear interactions between gravitational waves in an expanding universe. Random ensembles of gravitational waves are evolved numerically in cosmological models whose spatial volumes increase by more than an order of magnitude during these simulations. These evolutions show the spectra of the gravitational waves evolving as energy cascades away from the wavelengths at the peak of the initial spectra toward both longer and shorter wavelengths. Evolutions performed at different gravitational-wave amplitudes are shown to produce cascades that scale with amplitude in the way predicted by the four-wave scattering models of gravitational-wave turbulence.

The effect of deflection of a light signal that propagates through the gravitational field of a solar system body at rest is considered in the case that the source and the observer are at a finite distance from the body. The observer is assumed to be located somewhere nearby the Earth, for instance at Lagrange point $L_2$ of the Sun-Earth system, while the spatial position of the celestial light source is arbitrary. The gravitational fields in the exterior of the bodies are described by the full set of time-dependent mass-multipoles and spin-multipoles of these bodies. So the gravitating bodies can be of arbitrary shape, inner structure, and rotational motion. The unit tangent vector of the light trajectory at the position of the observer is determined in the 1PN and 1.5PN approximation of the post-Newtonian (PN) scheme. A simplified expression for the unit tangent vector is obtained, where all terms are neglected that together contribute less than 10 nano-arcseconds in light deflection for all astrometric configurations between source, body, and observer. It is shown that in the case of an axisymmetric body the unit tangent vector of the light ray as well as the light deflection are given in terms of Chebyshev polynomials. This fact allows for determining the effect of light deflection in the gravitational fields of the bodies up to any order of the mass-multipoles and spin-multipoles. It is shown that the total light deflection, that is the angle of light deflection where source and observer are located at infinite spatial distance from the body, represents an upper limit of the effect of light deflection. These investigations are aiming at astrometric measurements on the sub-micro-arcsecond level of accuracy.

In this work, the strong lensing effect of the memory signal was considered. In the geometric optics limit, the lensed memory signal becomes oscillatory, while the unlensed is basically monotonic. This is because only the high frequency Fourier modes contribute strongly to the lensed signal. Because of the step-function-like behavior of the unlensed memory waveform, the lensed waveform possesses characteristic morphology that is dependent on the type of the image, but independent of the lens model and the binary system. That is, for each type of the lensed image, the lensed memory waveform has an approximate reflection symmetry about a symmetrical axis in the time domain. More specifically, for the type I and type III images, the lensed memory signals are nearly odd under the reflection, while the type II signal is roughly even. In addition, at the symmetrical axis, the sign of the slope for the type I image is different from that for the type III image. These universal characteristic features would help determine the type of the lensed image. This is particularly because the memory waveform can be well approximated by a suitable step function, which involves just two parameters, the overall amplitude and the time of arrival. It is fast and cheap to simulate this approximated waveform. Once the type of the lensed image is determined with the approximated memory waveform, one can use the appropriate waveform template for the oscillatory component of the gravitational wave to perform the parameter estimation.

We present a fast Bayesian inference framework to address the growing computational cost of gravitational-wave parameter estimation. The increased cost is driven by improved broadband detector sensitivity, particularly at low frequencies, due to advances in detector commissioning, resulting in longer in-band signals and a higher detection rate. Waveform models now incorporate features like higher-order modes, further increasing the complexity of standard inference methods. Our framework employs meshfree likelihood interpolation with radial basis functions to accelerate Bayesian inference using the IMRPhenomXHM waveform model that incorporates higher modes of the gravitational wave signal. In the initial start-up stage, interpolation nodes are placed within a constant-match metric ellipsoid in the intrinsic parameter space. During sampling, likelihood is evaluated directly using the precomputed interpolants, bypassing the costly steps of on-the-fly waveform generation and overlap-integral computation. We speed-up sampler convergence by sampling in a rotated parameter space aligned with the eigenbasis of the metric ellipsoid, where the parameters are uncorrelated by construction. This method yields unbiased parameter recovery when applied to 104 simulated neutron-star–black-hole signals (NSBH) in LIGO–Virgo data, while reducing computational cost by up to an order of magnitude for the longest-duration signal. The meshfree framework equally applies to symmetric compact binary systems dominated by the quadrupole mode, supporting parameter estimation across a broad range of sources. Applied to a simulated NSBH signal in Einstein Telescope data where the effects of Earth’s rotation are neglected for simplicity, our method achieves an $\mathcal{O}({10}^4)$ speed-up, demonstrating its potential use in the 3G era.

We propose gravitational caloric theory (GCT)—an extension of general relativity that features a vector field $S_{\mu }$ sourced by and nonminimally coupled to the fluid sector while preserving covariant conservation of the standard fluid energy-momentum tensor. Our initial motivation is to trigger early dark energy (EDE) using the total fluid equation of state that encodes the cosmic radiation-matter transition. This mechanism provides a natural resolution of the EDE coincidence problem. The cosmological background dynamics are analyzed in detail by casting the evolution equations into dynamical-system form and, in relevant reduced cases, using Poincaré compactification to uncover the corresponding global phase-space structure. Beyond EDE, GCT admits two novel cosmological applications associated with critical points at infinity. Both arise from a class of energy-canceling solutions in which conventional energy components preferentially excite $S_{\mu }$ rather than source spacetime curvature. One is a $\mathrm{\Lambda }$-canceling solution that realizes the self-tuning mechanism for the old cosmological constant problem. However, the present realization does not reenter the standard hot Big Bang phase and is therefore incomplete. The other is a fluid-canceling solution that serves as the basis for our proposed early static hot Universe. In this scenario, $S_{\mu }$ offsets the gravitational effect of ordinary hot gas, yielding quasi-static expansion with a decreasing comoving Hubble radius that can address the horizon problem. This offers an alternative to inflation. Furthermore, its hot ingredient distinguishes this scenario from other quasi-static early Universe models and may leave observable signatures in primordial fluctuations. To probe the viability of GCT beyond cosmology, we further analyze linear perturbations about Minkowski spacetime and investigate static spherically symmetric (strong-field) systems. The perturbative analysis singles out a special parameter point at which the theory is free from instabilities and, under standard asymptotically flat boundary conditions, recovers Newtonian gravity in the Solar System regime and admits six independent luminal gravitational-wave polarizations in the radiative sector. For static spherically symmetric configurations, the solution space exhibits rich structures, including wormholes, naked singularities, and effective $\mathrm{\Lambda }$-like behavior, whereas no black hole solution other than Schwarzschild is found in the cases analyzed. Our findings reveal a wide variety of nontrivial gravitational phenomena in GCT, underscoring its promise for future investigations.

The thermal Sunyaev–Zel’dovich (tSZ) power spectrum is a sensitive probe of cosmology and cluster astrophysics, but its statistics are non-Gaussian because the signal receives a significant contribution from rare, massive, low-redshift galaxy clusters. As a result, a Gaussian likelihood fails to describe the statistics of its power spectrum on large scales. We use simulation-based inference (SBI) to test the accuracy of the standard Gaussian power-spectrum likelihood for a Planck-like tSZ analysis. Using halo-based simulations of full-sky Compton-$y$ maps, we train neural posterior and likelihood estimators and compare the resulting constraints with those from a Gaussian likelihood assumption. Using only multipoles $\ell <1000$, we find that the Gaussian likelihood assumption gives unbiased cosmological constraints, while the SBI-based inference shows a mild broadening of the posterior distributions for the amplitudes of residual foregrounds. This suggests that the Gaussian likelihood assumption is sufficiently accurate for cosmological inference for a Planck-like tSZ analysis, while SBI provides a useful validation tool to model non-Gaussian likelihoods beyond analytic approximations.

DESI DR2 data have been widely interpreted as evidence for late-time evolving dark energy (DE) with an apparent phantom crossing. Here we investigate an alternative explanation, based on early-Universe physics. If dark acoustic oscillations (DAOs) are close in scale to baryon acoustic oscillations (BAOs), they can bias the extraction of the BAO scale from the peak in the galaxy correlation function. This leads to an apparent shift in the inferred distance if the superposition of BAO and DAO features is misinterpreted as being due to BAOs only. Taking this shift into account, we find that a DAO with percent-level amplitude can reconcile DESI DR2 with Planck 2018 as well as $\mathrm{Pantheon}+\text{supernovae}$ data, with fit improvement at a similar level compared to evolving DE. Notably, a DAO feature with the required properties has been predicted in a previously proposed scenario that resolves the Hubble tension via a prerecombination decoupling of dark matter and dark radiation. The presence of a DAO feature close to the BAO peak can be scrutinized with future full-shape galaxy clustering data from DESI and Euclid.

Core-collapse supernovae (CCSNe) are powerful sources of gravitational waves (GWs). These signals propagate essentially unobstructed, providing a unique probe of the supernova central engine. In this work, we investigate parameter estimation from the bounce and early ring-down GW signal of rotating CCSNe using machine learning. We infer the peak frequency and peak amplitude of the signal as well as the rotation of the core. We extend previous studies in several directions. We consider a range of progenitor models and nuclear equations of state, and we assess the impact of key physical uncertainties, including bounce time uncertainty and source inclination. We incorporate both current detector noise and the projected sensitivities of next-generation observatories. We find that uncertainty in the bounce time does not significantly affect parameter estimation when the analysis is performed in the Fourier domain. In contrast, orientations when the rotation axis is near the line of sight substantially degrade performance. For optimal orientations, next-generation detectors can constrain rotation out to distances exceeding 100 kpc.

We use the two-flavor linear sigma model with quarks as an effective description of QCD to investigate the nature of the chiral phase transition at finite baryon chemical potential and zero temperature. We work at one-loop order to set up and solve the system of self-consistent coupled equations for the particle pole masses. The chemical potential-dependent value of the chiral order parameter is obtained by minimizing the one-loop effective potential. This treatment goes beyond the conventional ring-diagram approximation and provides a description valid for arbitrary values of the chemical potential. We find that the phase transition is of first order and occurs when the quark chemical potential reaches the value of the vacuum quark mass for the chosen set of parameters. The first order nature of the transition is signaled by the discontinuous behavior of the chiral condensate, the masses, and the couplings. The thermodynamics of the system is readily implemented and in particular, we find that the square of the speed of sound exhibits a discontinuity at the phase transition and then smoothly approaches the conformal limit from below.

We present the one-loop computation of the quark propagator of the Curci-Ferrari model, extending previous analyses to include dynamical quarks. This model contains a mass for the gluons and ghosts that tame the infrared behavior of the theory. Using the infrared-safe renormalization scheme, we study how finite gauge parameters affect the infrared behavior of the correlation functions. The coupling, gluon mass, and gauge parameter are found to freeze below a finite energy scale, confirming the infrared stability of the framework. The quark dressing function $Z(p)$ shows a change in concavity between the Landau and finite-$\xi$ cases, suggesting that nonvanishing gauges may better reproduce lattice trends at one-loop order. These results establish the CFDJ gauge as a possible infrared-safe setting candidate for perturbative QCD with massive gluons. This work may provide a basis for future lattice studies of the quark-gluon vertex and related observables in this gauge.

We calculate the spin density matrix of a back-to-back quark-antiquark pair inclusively produced in electron-nucleus scattering, taking into account the gluon saturation effect and the linearly polarized gluon distribution. We then investigate concurrence and stabilizer Rényi entropy, quantifying entanglement, Bell nonlocality, and nonstabilizerness. We find that the linearly polarized gluon distribution tends to enhance the entanglement of a heavy quark pair when the total and relative transverse momenta of the pair are orthogonal.

We perform a global Bayesian analysis of coherent and incoherent diffractive $\mathrm{J}/\psi$ photoproduction in $\gamma +p$ and $\gamma +\mathrm{Pb}$ collisions using a color glass condensate (CGC)-based framework and ultraperipheral collision data from the Large Hadron Collider (LHC), corrected for the expected effect of electromagnetic dissociation (EMD). Using Gaussian-process emulators of the underlying CGC calculations, we infer model parameters from a combined set of HERA and LHC measurements. We find that the $\gamma +\mathrm{Pb}$ data with EMD correction substantially reduce the previously observed tension between proton and nuclear datasets, enabling a consistent simultaneous description of diffractive $\mathrm{J}/\psi$ production in $\gamma +p$ and $\gamma +\mathrm{Pb}$ collisions within the CGC framework.

We study diffractive photo- and electroproduction of the $S$-wave heavy quarkonia $J/\psi$, $\psi (2S)$, and $\mathrm{\Upsilon }(nS)$ at energies relevant for the Electron Ion Collider (EIC). The production amplitude is evaluated while retaining the full transverse-momentum (${\ell }_t$) dependence of the hard two-gluon kernel, that is, without expanding the impact-parameter Bessel kernel as is done in the small-size color-dipole limit. The quarkonia light-cone wave functions are built from Cornell-potential solutions of the Schrödinger equation, normalized to the measured leptonic widths, and combined with a modern collinear gluon distribution. After benchmarking the framework against the full set of HERA charmonium cross-section ratio data, we provide a consistent set of bottomonium cross-section ratio predictions in EIC kinematics. We find that the full ${\ell }_t$-resolved treatment systematically improves the description of the radially excited states relative to the leading dipole limit, and we identify the kinematic windows where this difference is largest.

Motivated by the first observation of $CP$ violation in $b$-baryon decays, the search for baryonic decays exhibiting large $CP$ violation will be a primary focus in the coming years. We propose that significant $CP$-violating effects exist in the decay ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }D$, where $D$ denotes a $CP$ eigenstate of the $D^0\text{−}{\overline{D}}^0$ system. The predicted $CP$ asymmetries for both the $CP$-even and $CP$-odd modes can reach magnitudes as large as 50%, making these decays promising targets for measurement at the LHCb experiment. Additionally, we predict for the first time several nonzero $CP$-violating observables associated with angular distribution parameters, providing valuable complementary information in the search for $CP$ violation in baryon decays. Furthermore, we propose a novel strategy to extract the Cabibbo-Kobayashi-Maskawa angle $\gamma$ by combining data on angular distribution parameters and decay rates from the relevant channels. We emphasize that ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }D$ decays are among the most promising candidates for determining $\gamma$ in the baryon sector. Our findings may offer new insights for future theoretical and experimental investigations.

We study the analytic properties and three equivalent representations of the Toller matrices $T^{(\pm )}$, which appear in the causal formulation of spinfoam transition amplitudes for 4D Lorentzian quantum gravity. These are polynomially bounded functions on the Lorentz group that satisfy the relation $T^{(+)}+T^{(-)}=D$, where the Wigner matrix $D$ provides a unitary irreducible representation of $SL(2,\mathbb{C})$. Rühl’s definition of $T^{(\pm )}$ in terms of analyticity and asymptotic properties is shown to be equivalent to the recently introduced Feynman $\mathrm{i}ϵ$ prescription in spinfoams. We show that, equivalently, they can be represented as an integral over eigenvalues of the boost operator, which results in a sum over residues. The latter reproduces the Wick rotation relating Euclidean Spin(4) to Lorentzian $SL(2,\mathbb{C})$ spinfoams studied by Donà, Gozzini, and Nicotra. We provide explicit expressions in terms of hypergeometric functions and specialize them to the $\gamma$-simple representations relevant for spinfoams.