Einstein equations can be written in the so-called fully constrained formulation (FCF). This formulation has two different sectors: the elliptic sector, formed by the Hamiltonian and momentum constraints together with the equations derived from the gauge choice; and the hyperbolic sector, formed by the evolution of the rest of the spacetime metric variables, which encodes the gravitational radiation. In this work, we present a modification of both sectors that keeps local uniqueness properties of the elliptic system of equations and includes a hierarchical post-Newtonian structure of all the elliptic and hyperbolic equations. This reformulation can have potential applications in cosmology and relativistic astrophysics. Moreover, we show how initial stationary data can be computed numerically using this formulation without assuming a conformally flat spatial metric, with the illustrative example of a rotating neutron star.

In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the “infinities” (spacelike, timelike, and null infinity) of general relativity. However, in numerical calculations often compactified coordinates in the physical space are used to reach these infinities. In this note, we discuss the conformal Einstein equations in spherical symmetry coupled to a massless scalar field and compare them with corresponding equations using a compactified coordinate in physical spacetime. The derivation of the field equations is based on metrics, in which the radial coordinate is an affine parameter along outgoing null rays. We show that the conformal equations within an affine-null metric formulation can be cast in a natural hierarchical form after the introduction of suitable auxiliary fields. The system of partial differential equations associated with the resulting (unphysical) conformal field equations proves to be identical to a system that employs a compactified coordinate in physical space along with well-constructed regularized fields. The reason for this equivalence is the introduction of new regularized fields in the physical spacetime after coordinate compactification to obtain a regular system of equations on the complete domain of the compactified coordinate. As part of this work, we also present the solution of the conformal field equations in affine-null coordinates near the conformal boundary, where the Bondi mass loss formula for a massless scalar field is recovered. The validity of the balance law of the mass loss at null infinity is demonstrated numerically.

The study investigates orbital motion of test particles near compact objects described by solutions involving massless scalar fields, electromagnetic fields, and nonlinear electrodynamics. Specifically, we analyze orbital dynamics in the Janis-Newman-Winicour, Janis-Newman-Winicour-Maxwell, Schwarzschild-Melvin, and Bonnor-Melvin spacetimes, comparing the results with those obtained for the Schwarzschild and Reissner-Nordström solutions. We examine the stability of circular orbits and the behavior of epicyclic frequencies under varying physical parameters. Our analysis shows that in certain cases the central object transitions into a naked singularity. Deviations from classical Schwarzschild and Reissner-Nordström solutions reveal conditions for the existence of multiple photon orbits or marginally stable orbits. In some instances, the geometry allows the presence of two photon orbits—one stable and one unstable—with an interesting connection to the region of stable orbits. We find that at lower intensities, the effects of the scalar field and electromagnetic fields are comparable and seemingly interchangeable. However, for a sufficiently strong scalar field, its influence becomes dominant, leading to the emergence of a distinct region of stable orbits near the naked singularity. These effects are illustrated within the framework of optical geometry using embedding diagrams.

Next-generation gravitational-wave observatories will reach farther into the Universe than currently possible, revealing black-hole mergers from early stellar binary systems such as Population III stars, whose properties are currently poorly constrained. We develop a method to infer the properties of their progenitor populations from gravitational-wave catalogs. Using Bayesian deep learning, we train an emulator for population-synthesis predictions of black-hole merger properties across redshift as a function of the initial stellar mass function, crucially accounting for systematic uncertainty due to the finite number of training simulations. Combined with a nonparametric model for star formation history, we analyze catalogs containing both Population I/II and III sources simulated with full Bayesian parameter estimation for a detector network of Cosmic Explorer and Einstein Telescope with one year of observing time. We demonstrate our ability to separate these two populations at high redshifts where both make comparable contributions to the black-hole merger rate, excluding a Population III merger rate of zero at nearly 100% credibility. Moreover, we can place meaningful constraints on the Population III progenitor distributions; in particular, we constrain the spectral index of the initial mass function to within roughly $\pm 0.5$ of the true value and the log of the star formation rate density to within $\sim 25\%$ over redshifts 10 to 20. By leveraging astrophysics-informed and astrophysics-agnostic models, we demonstrate the discriminative power of our combined inference approach and highlight the potential of next-generation gravitational-wave observatories to uncover the details of high-redshift stellar populations.

Extrasolar planetary systems commonly exhibit planets on eccentric orbits, with many systems located near or within mean-motion resonances, showcasing a wide diversity of orbital architectures. Such complex systems challenge traditional secular theories, which are limited to first-order approximations in planetary masses or rely on expansions in orbital elements—eccentricities, inclinations, and semimajor axis ratios—that are subject to convergence issues, especially in highly eccentric, inclined, or tightly packed systems. To overcome these limitations, we develop a numerical approach to second-order perturbation theory based on the Lie transform formalism. Our method avoids the need for expansions in orbital elements, ensuring broader applicability and more robust convergence. We first outline the Hamiltonian framework for the 3-body planetary problem and apply a canonical transformation to eliminate fast angle dependencies, deriving the secular Hamiltonian up to second order in the mass ratio. We then use the fast Fourier transform algorithm to numerically simulate, in an accurate way, the long-term evolution of planetary systems near or away from mean-motion resonances. Finally, we validate our methods against well-known planetary configurations, such as the Sun-Jupiter-Saturn system, as well as to exoplanetary systems like WASP-148, TIC 279401253, and GJ 876, demonstrating the applicability of our models across a wide range of planetary configurations.

We discuss a novel mechanism for the proto-neutron star acceleration assisted by the chiral separation effect, which induces an axial vector current in a dense medium. We consider the process of neutrinos scattering off the background axial vector current of electrons. We show that anisotropy of either magnetic field or density in momentum space is essential for nonzero recoil, and we call this mechanism the chiral anisotropy conversion. Assuming a strong magnetic field $B\simeq {10}^{12}\mathrm{T}$ and anisotropy by $\sim 10\%$, we find that the chiral anisotropy conversion can yield the velocity of order of typical pulsar kicks, i.e., $v_{\mathrm{kick}}\gtrsim 1000\mathrm{km}/\mathrm{s}$.

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.