For general bipartite mixed states, a sufficient and necessary mathematical condition for certifying entanglement and/or (Bell) nonlocality remains unknown. In this paper, we examine this question for a broad and physically relevant class of bipartite systems, specifically those possessing an additive observable with a definite value. Such systems include, for example, final states of particle decays or bipartitions of spin chains with well-defined magnetization. We derive very simple, handy criteria for detecting entanglement or nonlocality in many cases. For instance, if ${\rho }_{(mp)(nq)}\ne 0$, where the eigenstates $|np⟩$ or $|mq⟩$ do not correspond to the given definite value of the additive observable, then the state is necessarily entangled—this condition is very easy to check in practice. If, in addition, the partitioned Hilbert space has dimension $2\times d$, the condition becomes necessary. Furthermore, if the sectors associated with the eigenstates $|mp⟩$ or $|nq⟩$ are nondegenerate, there exists a Clauser–Horne–Shimony–Holt inequality that is violated. We illustrate these results by analyzing the potential detection of entanglement and nonlocality in $\mathrm{Higgs}\to ZZ$ decays at the LHC.

The analysis of RHIC hydrogen gas jet target polarimeter measurements of transverse analyzing powers $A_{\mathrm{N}}(t)$ in proton-nucleus scattering requires accurate Coulomb corrections to both spin-flip and nonflip amplitudes. These corrections must cover a wide range of nuclear charges $Z$ and form factor slopes, with flexibility to vary form factors during data fitting. To avoid technically challenging calculations involving a small but finite fictitious photon mass, the Coulomb correction to the nonflip electromagnetic amplitude with an exponential form factor was related to the corresponding correction for the spin-flip amplitude. This approach allows soft photon contributions to all amplitudes, including those with nonexponential form factors, to be calculated in the massless photon limit using only analytical expressions and numerically stable integrals with nonsingular integrands and finite integration limits. In addition, an absorptive correction to the spin-flip electromagnetic amplitude, which plays a critical role in spin effects in forward polarized proton-nucleus scattering, was accurately evaluated.

The gravitational wave (GW) spectrum from the first-order phase transition can be characterized by a few phenomenological parameters but with high degeneracies in model/data distinguishments. In this paper, we look into the high-frequency power law of the GW spectrum with preliminary numerical simulations for both quantum and semiclassical pictures of vacuum decay. We first reveal an anticorrelation of the high-frequency power law to a certain power of the ratio between the wall thickness and bubble radius at the onset of bubble collisions, which can be further approximated analytically by some other phenomenological model characteristics to break the model degeneracy.

High energy collision experiments provide a suitable environment where Lorentz symmetry breaking can be tested. This motivates us to study the effect of Lorentz-violating (LV) terms on the hadron production process from pair annihilation in the case correspondent to vectorial nonminimal couplings between the fermions and gauge fields. To be specific, we study the effect of LV terms on B-meson production through pair annihilation: $e^{+}{e}^{-}\to q\overline{q}\to B+\mathrm{Jets}$. To this aim, we first discuss the LV modifications on the quantum electrodynamics part of the process, i.e., $e^{+}{e}^{-}\to q\overline{q}$, due to the inclusion of a vectorial nonminimal coupling between the fermions and vector gauge field (photon in the case $s\ll m_Z^2$). In the following, we study the modifications on the quantum chromodynamics part of the process which is described by the fragmentation functions of $q/\overline{q}\to B$. Considering the available data and the analytical result for the leading order (LO) cross section $\sigma (e^{+}{e}^{-}\to B+\mathrm{Jets})$ in the presence of LV terms, we determine a limit on the corresponding Lorentz violation coefficients which are consistent with other analyses resulting from different processes.

We study the chiral condensate at finite temperature in AdS/QCD in a time-dependent background, in which the position of the black hole horizon $z_h$ changes with time, producing an increasing or decreasing temperature. Conformal invariance is broken, as in the soft-wall model, by a static quadratic dilaton. Two different scenarios are analyzed; in the first a general power-law time dependence is assumed for $z_h$, while in the second the energy-momentum tensor at late times reproduces the one found in viscous hydrodynamics. Depending on the rate at which the system evolves, the transition shifts toward lower temperatures. If the chiral condensate is far from equilibrium at low temperatures, oscillations around its equilibrium value are observed before thermalization. A prethermalization stage is found in the chiral limit if the initial condition is set at a temperature close to the critical one. In the hydrodynamic setup the evolution of the medium is slow enough, and the chiral condensate soon matches the equilibrium curve.

We present an algorithm to extract the Coulomb branch Hasse diagram of orthosymplectic three-dimensional (3D) $\mathcal{N}=4$ quiver gauge theories. The algorithm systematically predicts all descendant theories arising from Coulomb branch Higgsing, thereby detailing the stratification of the symplectic singularity defined by the initial Coulomb branch. Leveraging the Lie algebra isomorphism $\mathfrak{su}(4)\cong \mathfrak{so}(6)$, we validate our algorithm via the 3D mirror of the 4D theories of class $\mathcal{S}$ of such type. This comparison involves moduli spaces that admit both orthosymplectic and unitary quiver realizations, the latter being well understood via standard techniques such as decay and fission. Higgsing on the Coulomb branch of the 3D mirror or the magnetic quiver translates to Higgs branch renormalization group flows of the corresponding higher-dimensional superconformal field theories. Thus, we benchmark our method via Higgsing 6D $\mathcal{N}=(1,0)$ D-type orbi-instanton theories, predicting novel Higgsing patterns involving products of interacting fixed points, and class $\mathcal{S}$ theories of type $\mathfrak{so}(2N)$, demonstrating Higgsing to products of theories of types specified by Levi subalgebras of $\mathfrak{so}(2N)$.

We investigate the stability of quasinormal mode (QNM) spectra and graybody factors in the Schwarzschild black hole by approximating the Regge-Wheeler (R-W) potential with a piecewise parabolic form and treating the deviation as a perturbation. We find that QNM spectra are sensitive to small perturbations, while graybody factors remain stable. This piecewise parabolic approximated potential gives rise to the long-lived modes whose imaginary parts remain close to zero and decrease slowly with overtone number increasing. The reflection coefficient shows distinct resonance feature in the high-frequency regime that are absent in the original R-W case. For the calculation of graybody factors, we employ an analytic method based on transfer matrix technique, and this approach can also be effectively used in other effective potential cases.

In the recent sixth data release (DR6) of the Atacama Cosmology Telescope (ACT) collaboration, the value of $n_{\mathrm{s}}=0.9743\pm 0.0034$ for the scalar spectral index is reported, which excludes the Starobinsky and Higgs inflationary models at $2\sigma$ level. In this paper, we perform a Bayesian inference of the parameters of the Starobinsky or Higgs inflationary model with noninstantaneous reheating using the Markov chain Monte Carlo method. For the analysis, we use observational data on the cosmic microwave background collected by the Planck and ACT collaborations and on baryonic acoustic oscillations from the Dark Energy Spectroscopic Instrument (DESI) collaboration. The reheating stage is modeled by a single parameter $R_{\mathrm{reh}}$, which contains a combination of the reheating temperature $T_{\mathrm{reh}}$ and the effective equation of state parameter during reheating ${\overline{\omega }}_{\mathrm{reh}}$. Using the modified Boltzmann code class and the cobaya software with the getdist package, we perform a direct inference of the model parameter space and obtain their posterior distributions. Using the Kullback-Leibler divergence, we estimate the information gain obtained from the observed data: In the proposed parametrization, we get 8.48 bits of information about the amplitude of the inflaton potential and 2.37 bits of information about the reheating parameter. Inclusion of the ACT DR6 data provides 63% more information about the reheating stage compared to analysis without ACT data. In addition, we draw constraints on the reheating temperature and the average equation of state. While the former can vary within 12 orders of magnitude, values in the 95% credible interval indicate a sufficiently low reheating temperature; for the latter there is a clear preference for values greater than 0.5, which means that the conventional equations of state for dust $\omega =0$ and relativistic matter $\omega =1/3$ are excluded with more than $2\sigma$ level of significance. Nevertheless, there is still a big part of parameter space where Starobinsky and Higgs inflationary models exhibit a high degree of consistency with the latest observational data, particularly from ACT DR6. Therefore, it is premature to reject these models.

The vanilla power law inflation is plagued with two severe drawbacks, the one being the issue of graceful exit, and the other being its compatibility with the existing data. There is yet another daunting problem generic to any inflationary model, and not particular to the power law inflation, is the issue of classicalization of the primordial quantum perturbation. This issue is often treated as an isolated problem primarily because decoherence is often invoked to tackle such problems and decoherence, in principle, does not leaves any observational imprints. However, that is not the case if one invokes the collapse models of quantum mechanics to resolve such a problem, because the collapse models do modify the Schrödinger evolution of the quantum system and the modified dynamics is bound to leave imprints. We show that collapsed modified power law inflation can indeed circumvent the issue with observations and can be made compatible with all the current data coming from Planck, ACT, DESI, and Baryon acoustic oscillations while resolving the classicalization issue associated with the quantum primordial fluctuations. Such an inflationary model also produces a more red-tilted tensor spectrum and no running for both the scalar and tensor spectral indices, which can be a litmus test for this model.

We investigate the impact of inhomogeneous inflaton perturbations on primordial magnetic fields within the framework of generalized inflationary magnetogenesis models. Extending the Ratra model to general spacetime backgrounds, we analyze the constraint structure of the electromagnetic field and demonstrate that the standard Coulomb gauge must be generalized to accommodate spatial inhomogeneities. Instead of the vector potential, we solve the conjugate momentum with the modified initial conditions introduced by the coupling function, which become dominant during the late stages of inflation. These change the conditions under which scale-invariant electromagnetic spectra are achieved. Furthermore, we address the challenge of evaluating convolutions between vector potentials and inflaton perturbations by employing separate large- and small-scale approximations. The resulting influence on the electric and magnetic power spectra is quantified using ${\mathrm{\Delta }}_E$ and ${\mathrm{\Delta }}_B$, revealing a scale-dependent influence of inhomogeneities. We also find that the spectrum index evolution is sensitive to the sign of $V_{\varphi }$, with distinctive behaviors for electric and magnetic fields under different scale-invariance conditions. Notably, for nearly scale-invariant magnetic fields, the perturbative effects shift the spectral index towards the red and migrate toward smaller scales as inflation progresses. We have also compared the obtained results with observational data; these offer a potential observational probe to differentiate between large-field and small-field inflation scenarios.

In this work, we present a set of binary neutron star (BNS) merger simulations including the net muon fraction as an additional degree of freedom in the equation of state (EOS) and hydrodynamics evolution using the numerical-relativity code BAM. Neutrino cooling is modeled via a neutrinos leakage scheme, including in-medium corrections to the opacities and emission rates of semileptonic charged-current reactions, although within the elastic approximation. We show that, for our particular choice of baseline baryonic EOS, the presence of muons delays the gravitational collapse of the remnant compared to the case where muons are neglected. Furthermore, when muons and muonic weak reactions are considered, no gravitational collapse occurs within our simulation time and muons are confined in the densest portions of the remnant, while the disk is effectively colder, less protonized and demuonized. Accordingly, ejecta properties are affected; e.g., ejecta masses are systematically smaller for the muonic setups and exhibit a larger fraction of neutron-rich, small velocity material. Overall, our results suggest that the inclusion of muons and muon-flavored neutrino reactions in the context of BNS merger simulations should not be neglected, thus representing an important step toward more realistic modeling of such systems.

Gravitational waves undergo redshift as they propagate through the expanding Universe, and the redshift may exhibit time-dependent drift. Consequently, for any isolated gravitational wave sources, the mass parameter $\mathcal{M}$ and the redshift $z$ exhibit an observational degeneracy, typically manifesting in the waveform as the redshifted mass $\mathcal{M}(1+z)$. Matching together the wave propagation and the wave generation solutions, we show that dimensionless source parameters depending on mass $\mathcal{M}$ can break this degeneracy. Notably, the postmerger signal from binary neutron stars contains several dimensionless parameters that satisfy this condition, including the quality factors of different frequency components and their frequency ratios. Considering the observations of solely the postmerger signal by the Neutron star Extreme Matter Observatory or the Einstein Telescope, based on the Fisher analysis, we find that the redshift can be measured with fractional uncertainties of $\sim 30\%$ for sources at $0.01<z<0.09$. Additionally, we present a corrected derivation of the waveform phase correction due to the redshift drift effect, rectifying a sign error in previous studies.

The Einstein Telescope (ET) is a proposed next-generation gravitational wave (GW) interferometer designed to detect a large number of astrophysical and cosmological sources with unprecedented sensitivity. A key target for ET is the detection of a stochastic gravitational-wave background (SGWB), a faint signal from unresolved GW sources. In its proposed triangular configuration, correlated Newtonian noise of seismic origin poses some challenges for the SGWB detection. We study the impact of correlated noise on the SGWB detection and relative parameter estimation for ET in the triangular configuration, comparing it to a 2L configuration with two separated L-shaped detectors. We perform a Bayesian analysis on simulated data, which shows that accurate reconstruction of the SGWB parameters and instrumental noise is achievable if the noise is properly modeled. We illustrate that neglecting correlated noise leads to significant biases in the parameter reconstruction. Our results show that, while the 2L configuration provides slightly better parameter estimation precision, mainly due to its longer arm length, the triangular configuration remains competitive when accurate noise modeling is provided.

One of the key concepts in loop quantum gravity is the quantization of spacetime geometry, with discrete observables such as the quantum area and volume. The quantum state of the gravitational field is encoded in so-called spin networks, and the conventional quantum-mechanical dynamics is substituted by a description in terms of constrained quantum states, in which several constraints define the physical subspace of the Hilbert space. One of these constraints, commonly called the Hamiltonian constraint, remains an elusive object in loop quantum gravity because its action on spin networks leads to changes in their corresponding graphs. As a result, calculations in loop quantum gravity are often considered unpractical, and neither the eigenstates of the Hamiltonian constraint, which form the physical space of states, nor the concrete effect of this graph-changing character on observables are entirely known. Much worse, there is no reference value to judge whether the commonly adopted graph-preserving approximations lead to results anywhere close to the nonapproximated dynamics. Our work sheds light on several of these issues, by devising a new numerical tool that allows us to implement the action of the Hamiltonian constraint without the need for approximations and to calculate expectation values for the geometric observables. To achieve that, we fill the theoretical gap left in the derivations of the action of the Hamiltonian constraint on spin networks: we provide the first complete derivation of such action for the case of 4-valent spin networks, while updating the corresponding derivation for 3-valent spin networks. Our derivations also include the action of the volume operator. By proposing a new approach to encode spin networks into functions of lists and the derived formulas into functionals, we implement both the Hamiltonian constraint and the volume operator numerically. We are able to transform spin networks with graph-changing dynamics perturbatively and verify that the expectation values for the volume have rather different behavior from the approximated, graph-preserving results. Furthermore, using our tool we find a family of potentially relevant solutions of the Hamiltonian constraint. Our work paves the way to a new generation of calculations in loop quantum gravity, in which graph-changing results and their phenomenology can finally be accounted for and understood.

We compute various averages over bulk geometries of quantum states prepared by the Chern-Simons path integral, for any level $k$ and compact simple gauge group $G$. We do so by carefully summing over all topologically distinct bulk geometries which have $n$ disjoint boundary tori and a decomposition into $\mathrm{space}\times \mathrm{time}$ of fixed spatial topology. We find that to leading order in the complexity of the state, the typical state contains many types of multiparty entanglement, proving a conjecture of Balasubramanian et al. Combined with the fact that periodic link states are Greenberger–Horne–Zeilinger (GHZ)-like, this result implies that a generic fibered link state contains non-GHZ entanglement if and only if its link complement is hyperbolic. Additionally, we compute an averaged wave function which captures the leading order statistics of boundary observables in the $n$ torus Chern-Simons Hilbert space.

We compute the quasinormal mode (QNM) frequencies of slowly rotating black holes in dynamical Chern-Simons (dCS) gravity, including corrections up to second order in the black hole’s dimensionless spin parameter $\chi$ (which is defined as $J/M^2$, where $J$, $M$ are the angular momentum and mass of the black hole) and second order in the dCS coupling parameter ($\alpha$). Due to the complexities of constructing a Newman-Penrose tetrad at this order, we employ a metric perturbation approach. We derive a system of coupled ordinary differential equations for the primary axial $l$ mode and the polar $l\pm 1$ modes, which is then solved numerically using the Runge-Kutta-Fehlberg method with appropriate ingoing and outgoing wave boundary conditions. Our numerical framework is validated in the general relativistic limit against known Schwarzschild QNMs and highly accurate Kerr QNM results for $\chi \le 0.15$. For the fundamental $n=0$, $l=m=2$ axial mode, we present detailed numerical results illustrating the dependence of QNM frequencies on both $\chi$ and $\alpha$. We observe that while rotation generally increases the damping time, increasing the dCS coupling parameter significantly reduces the damping time of the axial mode. This finding contrasts with previous analytical work on polar modes, which suggested an increase in damping time due to dCS effects, highlighting a crucial parity-dependent difference in how dCS gravity impacts black hole ringdowns. Furthermore, we provide an analytical fitting formula for this mode: $M\omega ={\omega }_{00}+(\alpha /M^2{)}^2{\omega }_{02}+\chi ({\omega }_{10}+(\alpha /M^2{)}^2{\omega }_{12})+{\chi }^2({\omega }_{20}+(\alpha /M^2{)}^2{\omega }_{22})$. The coefficients ${\omega }_{00}$, ${\omega }_{10}$, and ${\omega }_{20}$ accurately reproduce Kerr QNM frequencies (in the limit $\alpha =0$) for $\chi \le 0.4$. These results, incorporating coupled spin and dCS effects at second order, provide more accurate theoretical predictions for testing dCS gravity with gravitational wave observations of black hole ringdowns. The refined QNM calculations are particularly relevant for lower-mass black hole merger events, such as GW230529, where dCS corrections may be more prominent and their distinct damping signatures could be observable by next-generation gravitational wave detectors.

Every emission of radiation in gravity also includes a nonwavelike component that leaves a permanent change in proper distances of the spacetime it travels through. This phenomenon is known as gravitational displacement memory. Building up on a recently developed computation framework that harnesses Isaacson’s insights on a fundamental definition of gravitational waves, we compute the leading displacement memory formula in Einstein-Æther gravity. Our analysis represents the first direct calculation of gravitational memory in a metric theory with nontrivial asymptotic vector field value. We find that an emission of scalar and vector æther waves at a propagation speed greater than the speed of tensor radiation features unprotected causal directions with a priori unbound memory buildup. Based on the results and the existing constraint of luminally propagating tensor waves, we conjecture a stringent exclusion of the superluminal parameter space of Einstein-Æther gravity.

We study exact static spherically symmetric vacuum solutions in generic six-derivative gravity (i.e., without assuming specific relations between the coupling constants). Using modified Schwarzschild coordinates, we systematically classify solutions through Frobenius expansions, determining their number of free parameters and confirming previously known cases, such as the regular solutions at the origin. Importantly, we identify novel solutions absent in four-derivative gravity, including those with (double-degenerate) extreme horizons (and their near-horizon limits) that exist without matter sources, which may indicate the existence of regular black holes. We also find asymptotically (anti–)de Sitter spacetimes, giving rise to an effective cosmological constant. The solutions can be classified into six main classes, and, when possible, we provide the description in standard Schwarzschild coordinates, in which they split into 13 main solution classes.

In this paper we consider a new approach to unify inflation and the late universe with dark energy and dark matter formulated in a model that includes a non-Riemannian metric independent measure and a scalar field with spontaneously broken scale symmetry. Here first of all inflation is possible, which is then followed by a reheating oscillating period and this leads to the formation of all kinds of particles, including fermions, which as the universe expands can contribute to the dark energy and the to the dark matter of the universe. During the inflationary epoch, we find different constraints on the parameter space associated to the effective potential of the scalar field from the observational data. After reheating the scalar field retraces its trajectory in field space but now the scalar field potential can be drastically modified by the effect of the fermions. In this sense, the present dark energy characterized by its very small value compared to the inflationary phase can be explained by appropriately choosing the parameter space of couplings between the Riemannian and non-Riemannian measures to the fermions.