The low-energy spectrum relevant to the lattice calculation of the hadronic vacuum polarization contribution to muon anomalous magnetic moment $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}$ is dominantly given by two-pion states satisfying Lüscher’s finite-volume quantization condition. Finite-volume effects from those states may exhibit power-law dependence on the volume, contrary to an exponential suppression as suggested by chiral effective theory. Employing the finite-volume state decomposition of Euclidean correlators, we systematically investigate the volume dependence and identify the different volume scalings depending on the volume and Euclidean-time region. Using phenomenological inputs for $\pi \pi$ phase shift and the timelike pion form factor, we obtain an estimate for the finite-volume effects on $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}$, which is consistent with previous works. Numerical results are given for the “window” observables of $a_{\mu }$.

We investigate spatial two-point correlation functions of mesonic operators in two-flavor lattice QCD at high temperatures. The simulated temperatures cover the range $T\in [147,330]\mathrm{MeV}$, where the critical temperature is estimated around 165 MeV. To ensure a good control of the chiral symmetry we employ the Möbius domain-wall fermion action for two degenerate flavors of quarks. With a lattice cutoff $a^{-1}\sim 2.6\mathrm{GeV}$, the residual mass is reduced to 0.14 MeV. With the energy spectrum obtained from the screening mass at incremental values of the temperature range, we examine the $SU(2{)}_L\times SU(2{)}_R$ chiral symmetry, the anomalous axial $U(1)$, as well as an enhanced symmetry which exchanges the spin degrees of freedom. We also study how the data approaches the perturbative prediction given by twice the Matsubara frequency of free quarks.

We revisit the definition of the leading-twist chiral-even generalized parton distributions (GPDs) for $N\to \mathrm{\Delta }$ baryon transitions. We identify and address deficiencies in previous definitions of the transition GPDs inspired by the transition form factors of the vector and axial vector currents. Through systematic analysis of all possible covariant structures, respecting discrete symmetries and the baryon spinor equations of motion, we derive complete sets of independent structures for the transition matrix elements of the vector and axial vector partonic operators. They contain additional structures proportional to the light-cone vector, corresponding to transition GPDs of vanishing first moment, which were not included in previous parametrizations. Their presence is confirmed independently by the light-front multipole expansion and the cross-channel SO(3) partial-wave analysis of the transition matrix elements. Our analysis provides a complete definition of the $N\to \mathrm{\Delta }$ transition GPDs for use in theoretical and phenomenological studies.

We show that the dynamics of the Diósi-Penrose (DP) model of classical gravity can entangle the mechanical degrees of freedom of two separate particles. For standard experiments of gravitationally induced entanglement (GIE), we find that entanglement can be generated if and only if the particles are separated by a distance smaller than some limiting value $d_c$, proportional to the only free parameter of the DP model. Greater distances can be achieved through new experimental configurations, where the initial wave functions of the particles are allowed to spread perpendicularly to the separation axis. Although the DP dynamics asymptotically drives the system to a separable state, we observe that, for reasonable experimental parameters, GIE can survive for more than a day. Our results therefore imply that GIE detection is not enough to validate quantum gravity. Experimental tests of GIE dynamics have nonetheless the potential to falsify the DP model.

In this work, we critically reanalyze the explicit breaking of the Peccei-Quinn global symmetry—and the corresponding corrections to the QCD axion potential—induced by gravity. Specifically, we examine the role of gravitational instantons, which are nonperturbative, finite-action solutions to the Euclidean Einstein equations. These instantons represent topologically nontrivial configurations of spacetime and are analogous to instantons in gauge theory. The amount of symmetry breaking induced by gravitational instantons can be computed in a controlled way within the framework of semiclassical gravity, using ’t Hooft operators, in full analogy to the computation of the axion potential arising from QCD small instanton effects. Contrary to previous results in the literature, we find that the effects of gravitational instantons are extremely small and therefore do not give rise to a significant quality problem for the axion solution to the strong $CP$ problem, both within the Standard Model and in beyond-the-Standard-Model scenarios that involve multiple copies of the Standard Model. In conclusion, we argue that, assuming the ultraviolet completion of gravity is weakly coupled, the axion solution to the strong $CP$ problem remains free from any quality issues due to gravity. Along the way, we derive the effective Lagrangian of the QCD axion, including its gravitational coupling.

One of the theoretical motivations behind the belief that black holes as described by general relativity exist in nature is that it is hard to find matter configurations that mimic their properties, especially their compactness. One of the classic results that go in this direction is the so-called Buchdahl limit: a bound for the maximum compactness that spherically symmetric isotropic fluid spheres in hydrostatic equilibrium can possibly achieve with an outward-decreasing energy density. However, physically realistic situations could violate both isotropy and the monotonicity of the density profile. Notably, Bondi already showed that if the density profile is allowed to be arbitrary (but remains non-negative), a less restrictive compactness bound emerges. Furthermore, if negative energy densities are permitted, configurations can approach the black hole compactness limit arbitrarily closely. In this work we introduce a set of simple bilayered and thin-shell toy models designed to illustrate the effect of relaxing separately the assumptions of Buchdahl’s theorem. Within these models we highlight the existence of two special examples that we have called anti–de Sitter stars and Einstein static stars. We also discuss how these toy models may represent some of the main features of realistic systems and how they could be extended to find more refined models.

Recent results from the Atacama Cosmology Telescope (ACT) indicate a scalar spectral index $n_s\simeq 0.9743$, in excellent agreement with the prediction of linear inflation. However, the corresponding tensor-to-scalar ratio $r\simeq 0.0667$ is in tension with current observational bounds. In this work, we investigate how this tension can be alleviated in the Palatini formulation of gravity. We consider two classes of models based on simple monomial potentials: (i) models with a nonminimal coupling between the inflaton and gravity, and (ii) models including an $\alpha R^2$ term. In the first case, we find that a quadratic potential with a linear nonminimal coupling leads to the linear inflation attractor, with $r$ suppressed as $\xi$ increases. In the second case, we show that a linear potential can yield values of $r$ consistent with observations for sufficiently large $\alpha$. Our results demonstrate that simple monomial models can remain compatible with current observational constraints when embedded in the Palatini framework.

The next generation of cosmological surveys is expected to generate unprecedented high-quality data, consequently increasing the already substantial computational costs of Bayesian statistical methods. This will pose a significant challenge to analyzing theoretical models of cosmology. Additionally, new mitigation techniques of baryonic effects, intrinsic alignment, and other systematic effects will inevitably introduce more parameters, slowing down the convergence of Bayesian analyses. In this scenario, machine-learning-based accelerators are a promising solution, capable of reducing the computational costs and execution time of such tools by order of thousands. Yet, they have not been able to provide accurate predictions over the wide prior ranges in parameter space adopted by Stage III/IV collaborations in studies employing real-space two-point correlation functions. This paper offers a leap in this direction by carefully investigating the modern transformer-based neural network (NN) architectures in realistic simulated Rubin Observatory year one cosmic shear $\mathrm{\Lambda }$ cold dark matter inferences. Building on the framework introduced in Part I, we generalize the transformer block and incorporate additional layer types to develop a more versatile architecture. We present a scalable method to efficiently generate an extensive training dataset that significantly exceeds the scope of prior volumes considered in Part I, while still meeting strict accuracy standards. Through our meticulous architecture comparison and comprehensive hyperparameter optimization, we establish that the attention-based architecture performs an order of magnitude better in accuracy than widely adopted NN designs. Finally, we test and apply our emulators to calibrate tension metrics.

We present a new class of machine-learning emulators that accurately model the cosmic shear, galaxy-galaxy lensing, and galaxy clustering real space correlation functions in the context of Rubin Observatory year one simulated data. To illustrate its capabilities in forecasting models beyond the standard $\mathrm{\Lambda }\mathrm{CDM}$, we forecast how well LSST Year 1 data will be able to probe the consistency between geometry ${\mathrm{\Omega }}_{\mathrm{m}}^{\mathrm{geo}}$ and growth ${\mathrm{\Omega }}_{\mathrm{m}}^{\text{growth}}$ dark matter densities in the so-called split $\mathrm{\Lambda }\mathrm{CDM}$ parametrization. When trained with a few million samples, our emulator shows uniform accuracy across a wide range in an 18-dimensional parameter space. We provide a detailed comparison of three neural network designs, illustrating the importance of adopting state-of-the-art transformer blocks. Our study also details their performance when computing Bayesian evidence for cosmic shear on three fiducial cosmologies. The transformers-based emulator is always accurate within polychord’s precision. As an application, we use our emulator to study the degeneracies between dark energy models and growth geometry split parametrizations. We find that the growth-geometry split remains a meaningful test of the smooth dark energy assumption.

In a Universe with nearly Gaussian initial curvature perturbations, the abundance of primordial black holes can be derived from the curvature power spectrum. When the latter is enhanced within a narrow range around a characteristic scale, the resulting mass function has a single distinct peak, corresponding to Schwarzschild radii set by the horizon entry time of that scale. In contrast, we show (both numerically and by providing an analytic estimation) that a broad enhancement—such as a plateau bounded by infrared and ultraviolet scales—produces a bimodal mass function, with a primary peak close to the infrared scale. We find that the typical initial gravitational potential (compaction function), conditioned on meeting the threshold for critical collapse, is generated by a thin spherical shell with infrared radius and a thickness comparable to the ultraviolet scale. This suggests a higher-than-expected abundance of primordial black holes originating from Type II initial fluctuations. Our results significantly impact overproduction bounds on the amplitude of the power spectrum and tighten the viable mass range for primordial black holes as dark matter.

We study rotating hybrid stars, with a particular emphasis on the effect of a deconfinement phase transition on their properties at high spin. Our analysis is based on a hybrid equation of state with a phase transition from hypernuclear matter to color-superconducting quark matter, where both phases are described within a relativistic density functional approach. By varying the vector meson and diquark couplings in the quark matter phase, we obtain different hybrid star sequences with varying extension of the quark matter core, ensuring consistency with astrophysical constraints from mass, radius, and tidal deformability measurements. As a result, we demonstrate the impact of an increasing rotational frequency on the maximum gravitational mass, the central energy density of compact stars, the appearance of the quasiradial oscillations, and nonaxisymmetric instabilities. We demonstrate that for the most favorable parameter sets with a strong vector coupling, hybrid star configurations with a color superconducting quark matter core can describe the fastest spinning and heaviest galactic neutron star PSR J0952-0607, while it is out of reach for the purely hadronic hypernuclear star configuration. We also revise the previously proposed empirical relation between the Kepler frequency, gravitational mass, and radius of nonrotating neutron stars, obtained based on the assumption that all neutron stars, up to the heaviest, are hadronic. We show how the phase transition to quark matter alters this relation and, consequently, the constraints on the dense matter equation of state. Our findings reveal that incorporating the hybrid equation of state has significant implications for the constraints on the properties of strongly interacting matter and neutron stars, placing the upper limit on $R_{1.4}\le 14.90$ and $R_{0.7}<11.49\mathrm{km}$ (considering 716 Hz frequency limit from PSR $\mathrm{J}1748+2446\mathrm{ad}$) and $R_{1.4}\le 11.90\mathrm{km}$ (for 1000 Hz).

In this work, we study the mass spectrum of the hidden-charm hybrid states with the $J^{PC}=0^{-+}$, $0^{++}$, $0^{--}$, $1^{++}$, $1^{+-}$, $1^{-+}$, $1^{--}$, $2^{-+}$ and $2^{++}$ via the quantum chromodynamics (QCD) sum rules in a consistent way. We calculate the vacuum condensates up to dimensions-6 by taking account of both the leading order and next-to-leading order contributions, and take the energy scale formula $\mu =\sqrt{M_{X/Y/Z}^2-(2{\mathbb{M}}_c{)}^2}$ to choose the suitable energy scales of the QCD spectral densities, it is the first time to explore the energy scale dependence of the QCD sum rules for the hidden-charm hybrid states.

A recent proposal reinterprets the eikonal as the scattering generator, which computes scattering observables through an action as a symmetry generator. The aim of this study is to incorporate dissipative effects from radiation into this framework, where the eikonal is generalized to the radiation eikonal by including mediator field degrees of freedom. The proposed generalization is tested through several post-Minkowskian scattering observables; scattering waveform, radiated momentum, and (time-asymmetric) radiation loss in the impulse.

Black holes have long served as a testing ground for probing theories of gravity and quantum mechanics. Notably, fundamental fields in the neighborhood of black holes exhibit rich phenomena that could yield astrophysically observable signatures. However, exploring these structures typically requires computationally intensive numerical calculations. In this work, the dynamics of a massive Dirac field outside a Schwarzschild black hole are revisited. We propose a novel matching scheme that enables the analytical solution of the coupled first-order Dirac equation, as opposed to the conventional second-order approach. This method yields a compact and unified analytical expression for the energy spectrum, which shows improved agreement with the numerical results. The improvement comes from the higher-order correction of the angular parameter that was ignored previously.

We consider Lovelock gravity in arbitrary, even dimensions. We find a large class of new gravitational instantons by considering extended nontrivial circle bundles over Kähler manifolds. Concretely, we generalize the Page-Pope metric in the presence of higher-curvature corrections of the Lovelock class. A subset of these spaces admits analytic continuation into the Lorentzian sector, producing new stationary solutions in Lovelock gravity. The geometries are fully determined by a single algebraic equation. We also obtain necessary and sufficient conditions for Lovelock-constant Kähler manifolds to exist in Lovelock gravity. Finally, we find a wide class of Lovelock-Maxwell solutions beyond staticity, allowing us to obtain the electrovacuum extension of these instantons.

The characteristic initial boundary problem is discussed in spherical symmetry for the Einstein-Maxwell-scalar field equations. It is formulated for an affine-null metric, and the resulting field equations are cast into a hierarchical system of partial differential equations. The initial boundary value problem for a family of null hypersurfaces is specified for a timelike-null foliation at the central geodesic of spherical symmetry as well as for a double-null foliation where the corresponding boundary is a null hypersurface. For the latter, two distinct boundary value formulations arise: one where the null boundary has zero Misner-Sharp mass, and another one where the corresponding Misner-Sharp mass is nonzero. As an application, the nonextremal and the extremal Reissner-Nordström solution in null coordinates for a charged black hole and the Fisher-Janis-Newman-Winicour solution are derived.

Recently, several papers have claimed that superhorizon curvature perturbations are not conserved at the one-loop level in single-field inflation models if there is a transient ultraslow-roll period. In this work, we point out that the contributions from the counterterms were overlooked in the recent papers. We show that the counterterm contributions play a crucial role in canceling the one-loop power spectrum of superhorizon curvature perturbations in the comoving gauge.

The convergence of the third-order general cosmographic expansion of the luminosity distance is examined using several versions of a semirealistic model of our local cosmic neighborhood, based on publicly available density and velocity fields from CosmicFlows-4. The study supports earlier findings that the general cosmographic expansion diverges at surprisingly low redshifts, often well before $z\sim 0.1$. By being based on a realistically placed observer within a data-informed cosmic environment, the results underscore that convergence must be a central concern when applying the general cosmographic expansion. By showing all-sky maps of kinematic parameters, the study also highlights the substantial information we lose when relying solely on standard Friedmann-Lemaitre-Robertson-Walker-based cosmography. Poor convergence does not necessarily render the information extracted by fitting data to the general cosmographic expansion meaningless. Rather, it calls for caution in interpreting this information, particularly regarding the physical meaning of the fitting coefficients, the physical scales they probe, and the implicit smoothing introduced by the fit.

In this work, we develop a simulation-based model to predict the excess surface mass density (ESD) depending on the local density environment. Using a conditional stellar mass function, our foreground galaxies are tailored toward the bright galaxy sample of the early data release of the Dark Energy Spectroscopic Instrument (DESI). Due to the nature of the ESD measurement, our derived model is directly applicable to all DESI data. To build this model, we use the abacussummit $N$—body simulation suite from which we measure all necessary statistics and train an emulator based on cosmopower. Finally, we present a cosmological parameter forecast for a possible combined analysis of DESI and the Ultraviolet Near Infrared Optical Northern Survey.

In dimensional regularization with $D=D_0-2\epsilon$, the minimal subtraction (MS) scheme is characterized by counterterms that only consist of singular terms in $\epsilon$. We develop a general method to compute the infinite sums of massless ladder or rainbow Feynman integrals in MS at $D_0$. Our method is based on relating the MS-solution to a kinematic solution at a coupling-dependent renormalization point. If the $\epsilon$-dependent Mellin transform of the kernel diagram of the insertions can be computed in closed form, we typically obtain a closed form expression for the all-order solution in MS. As examples, we consider Yukawa theory and ${\varphi }^4$ theory in $D_0=4$, and ${\varphi }^3$ theory in $D_0=6$.