We study the radial and nonradial oscillations of Cross stars (CrSs), i.e., stars with a quark matter crust and a hadronic matter core in an inverted order compared to conventional hybrid stars. We draw comparisons of their oscillation modes with those of neutron stars, quark stars, and conventional hybrid stars. We find that the stellar stability analysis from the fundamental mode of radial oscillations, and the $g$, $f$ modes of nonradial oscillations are quite similar to those of conventional hybrid stars. However, due to the inverted stellar structure, the first nonradial $p$-mode of CrSs behaves in an inverted way and sits in a higher-frequency domain compared to that of conventional hybrid stars. These results provide a direct way to discriminate CrSs from other types of compact stars via gravitational wave (GW) probes. Specifically, compact stars emitting $g$-mode GWs within the 0.5–1 kHz range should be CrSs or conventional hybrid stars rather than neutron stars or pure quark stars, and a further GW detection of the first $p$-mode above 8 kHz or an identification of a decreasing trend of frequencies versus star masses associated with it will help identify the compact object to be a CrS rather than a conventional hybrid star.

In this paper, we study the feeble sterile neutrino portal dark matter under the $Z_3$ symmetry. The dark sector consists of one fermion singlet $\chi$ and one scalar singlet $\chi$, which transform as $\chi \to e^{i2\pi /3}\chi ,\varphi \to e^{i2\pi /3}\varphi$ under the $Z_3$ symmetry. Regarding fermion singlet $\chi$ as the dark matter candidate, the new interaction terms $y_{\chi }\varphi \overline{{\chi }^c}\chi$ and $\mu {\varphi }^3/2$ could induce various new production channels. For instance, when $m_{\varphi }>2m_{\chi }$, the pair decay $\varphi \to \chi \chi$ could be the dominant channel, rather than the delayed decay $\varphi \to \chi \nu$. Another appealing scenario is when the dark sector is initially produced through the scattering process as $NN\to \chi \chi ,NN\to \varphi \varphi ,h\nu \to \chi \varphi$, then the semiproduction processes $N\chi \to \varphi \varphi ,N\varphi \to \varphi \chi ,N\chi \to \chi \chi$ could lead to the exponential growth of dark sector abundances. The phenomenology of the sterile neutrino and the cosmological impact of the dark scalar are also considered in the $Z_3$ symmetric model.

According to the preceding studies, the lattice SU(2) gauge-scalar model with a single scalar field in the fundamental representation of the gauge group has a single confinement-Higgs phase where confinement and Higgs regions are subregions of an analytically continued single phase and there are no thermodynamic phase transitions, which is a well-known consequence of the Osterwalder-Seiler-Fradkin-Shenker theorem. In this paper, we show that we can define new types of gauge-invariant operators by combining the original fundamental scalar field and the so-called color-direction field which is obtained by change of field variables based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. By performing the numerical simulations on the lattice without any gauge fixing, we reproduce the conventional thermodynamic transition line in the weak gauge coupling, and moreover we find a new transition line detected by the new gauge-invariant operators which separates the confinement-Higgs phase into two parts, confinement phase and the Higgs phase, in the strong gauge coupling. All results are obtained in the gauge-independent way, since no gauge fixing has been imposed in the numerical simulations. Moreover, we discuss a physical interpretation for the new transition from the viewpoint of the realization of a global symmetry.

Using the full data sample of $980{\mathrm{fb}}^{-1}$ collected with the Belle detector at the KEKB asymmetric energy electron-positron collider, we report the results of the first search for the rare semileptonic decays ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^0{\ell }^{+}{\ell }^{-}$ ($\ell =e$ or $\mu$). No significant signals are observed in the ${\mathrm{\Xi }}^0{\ell }^{+}{\ell }^{-}$ invariant-mass distributions. Taking the decay ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ as the normalization mode, we report 90% credibility upper limits on the branching fraction ratios $\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^0{e}^{+}{e}^{-})/\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+})<6.7\times {10}^{-3}$ and $\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^0{\mu }^{+}{\mu }^{-})/\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+})<4.3\times {10}^{-3}$ based on the phase-space assumption for signal decays. The 90% credibility upper limits on the absolute branching fractions of $\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^0{e}^{+}{e}^{-})$ and $\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^0{\mu }^{+}{\mu }^{-})$ are found to be $9.9\times {10}^{-5}$ and $6.5\times {10}^{-5}$, respectively.

We study information-theoretic properties of scalar models containing two Higgs doublets ${\mathrm{\Phi }}_a$, where $a=1$, 2 is the flavor quantum number. Considering the 2-to-2 scattering ${\mathrm{\Phi }}_a{\mathrm{\Phi }}_b\to {\mathrm{\Phi }}_c{\mathrm{\Phi }}_d$ as a two-qubit system in the flavor subspace and the $S$-matrix as a quantum logic gate, we analyze the entanglement power of the $S$-matrix at the tree level, in the limit the gauge coupling is turned off. Demanding the suppression of flavor entanglement during the scattering, the perturbative $S$-matrix in the broken phase can only be in the equivalent class of the Identity gate and the scalar potential exhibits a maximally enhanced $SO(8)$ symmetry acting on the eight real components of the two doublets. The $SO(8)$ symmetry leads to the alignment limit naturally, giving rise to a Standard-Model-like Higgs boson as a consequence of entanglement suppression.

The quantization of Yang-Mills field theories requires the introduction of a gauge fixing which leads to a violation of the local Gauss law described by the so-called Gauss operator. We discuss the local quantizations of Yang-Mills theories in terms of the possible Gauss operators, which are argued to have a more physical meaning than the gauge fixings. We focus the attention on the local quantizations that leave the global gauge group and a subgroup of local gauge transformations unbroken, such as the Feynman quantization of quantum electrodynamics, and show that in the non-Abelian case such properties cannot be realized together with Lorentz covariance; thus, quite generally, one cannot have the structural properties of the Feynman quantization of quantum electrodynamics. By relaxing the condition of Lorentz covariance, we obtain a classification of Gauss operators, which satisfy gauge covariant conservation laws and generate nontrivial residual subgroups of local gauge transformations.

We highlight some universal features concerning the role of spacetime curvature in the entanglement induced between quantum probes coupled to a quantum field in a suitable vacuum state. The probes are initially causally disconnected and nonentangled. We explore the parameter space $\{\omega ,d_0,{\mathit{v}}_0\}$ spanned by the energy gap $\omega$ of the detectors, and the initial values of separation distance $d_0$ and relative velocity ${\mathit{v}}_0$, both covariantly defined in arbitrary curved spacetime. We also obtain numerical results in de Sitter spacetimes and use these to explore strong curvature regime, while also corroborating our perturbative results in arbitrary curved spacetime. Our analysis shows that curvature can induce entanglement features in certain regions of the above parameter space, in a manner which facilitates using entanglement as a probe of spacetime curvature.

Despite its elegance, the theory of General Relativity (GR) is subject to experimental, observational, and theoretical scrutiny to arrive at tighter constraints or an alternative, more preferred theory. In alternative gravity theories, the macroscopic properties of neutron stars, such as mass, radius, tidal deformability, etc. are modified. This creates a degeneracy between the uncertainties in the equation of state (EOS) and gravity since assuming a different EOS can be mimicked by changing to a different theory of gravity. We formulate a hierarchical Bayesian framework to simultaneously infer the EOS and gravity parameters by combining multiple astrophysical observations. We test this framework for a particular 4D Horndeski scalar-tensor theory originating from higher-dimensional Einstein-Gauss-Bonnet gravity and a set of 20 realistic EOSs and place improved constraints on the coupling constant of the theory with current observations (still inferred assuming General Relativity). Assuming a large number of observations with upgraded or third-generation detectors, we find that the $A+$ upgrade could place interesting bounds on the coupling constant of the theory, whereas with the LIGO Voyager upgrade or the third-generation detectors (Einstein Telescope and Cosmic Explorer), the degeneracy between EOS and gravity could be resolved with high confidence, even for small deviations from GR.

The Gotay-Nester-Hinds method is used in this paper to study the Hamiltonian formulation of the Euclidean self-dual action. This action can be used to arrive at the complex Ashtekar formulation of general relativity or a real connection formulation for Euclidean general relativity. The main result of the paper is a derivation of the Ashtekar formulation for Euclidean gravity without using any gauge fixing. It is interesting to compare this derivation with the one corresponding to the Holst action. In particular it is worth noting that no “tertiary” constraints appear in the case considered in the present paper.

Here we study possible improvements of the existing constraints on the upper bound of the graviton mass by the analysis of the stellar orbits around the supermassive black hole (SMBH) at the Galactic Center (GC) in the framework of Yukawa gravity. A motivation for this study is a recent detection of Schwarzschild precession in the orbit of S2 star around the SMBH at the GC by the GRAVITY Collaboration. The authors indicated that the orbital precession of the S2 star is close to the general relativity (GR) prediction, but with possible small deviation from it, and parametrized this effect by introducing an ad hoc factor in the parametrized post-Newtonian (PPN) equations of motion. Here we use the value of this factor presented by GRAVITY in order to perform two-body simulations of the stellar orbits in massive gravity using equations of motion in the modified PPN formalism, as well as to constrain the range of massive interaction $\mathrm{\Lambda }$. From the obtained values of $\mathrm{\Lambda }$, and assuming that it corresponds to the Compton wavelength of graviton, we then calculated new estimates for the upper bound of graviton mass which are found to be independent, but consistent with the LIGO’s estimate of graviton mass from the first gravitational wave (GW) signal GW150914 (later this graviton mass estimation was significantly improved with consequent observations of GW events). We also performed calculations including numerical simulations in order to constrain the bounds on graviton mass in the case of a small deviation of the stellar orbits from the corresponding GR predictions and showed that our method could further improve previous estimates for the upper bounds on the graviton mass. It is also demonstrated that such an analysis of the observed orbits of S-stars around the GC in the frame of the Yukawa gravity represents a tool for constraining the upper bound for the graviton mass, as well as for probing the predictions of GR or other gravity theories.

In the present paper, we consider a rotating black hole moving in a static homogeneous electromagnetic field. We assume that the field is weak and neglect its backreaction on the geometry, so that the metric at far distance from the black hole is practically flat. We present an exact solution for a stationary electromagnetic field in the presence of the black hole for this problem and use it to calculate fluxes of the energy, momentum and angular momentum into the black hole. Using these results we derive the equations of motion of the rotating black hole in the electromagnetic field and discuss some of the interesting solutions of these equations. In particular, we demonstrate how the interaction of the spin of the black hole with the external magnetic field changes its trajectory.

The time delay of a light signal that propagates in the gravitational field of an isolated body at rest is considered. The gravitational field is given in the post-Newtonian scheme and in terms of the full set of mass multipoles and spin multipoles of the body. The asymptotic configuration is considered, where source and observer are located at spatial infinity from the massive body. It is found that in this asymptotic limit the higher multipole terms of time delay are related to the higher multipole terms of total light deflection. Furthermore, it is shown that the gauge terms vanish in this asymptotic configuration. In case of an axisymmetric body in uniform rotational motion, the higher multipole terms of time delay can be expressed in terms of Chebyshev polynomials. This fact allows one to determine the upper limits of the time delay for higher multipoles. These upper limits represent a criterion to identify those multipoles that contribute significantly to the time delay for a given accuracy of time measurements. It is found that the first mass multipoles with $l\le 8$ and the first spin multipoles with $l\le 3$ are sufficient for an accuracy on the femtosecond scale of accuracy in time measurements.

In this work, we present the environmental effects on wormholes residing in a galaxy. By this, we propose that these wormholes are mimickers of supermassive black holes residing at the galactic centers. In particular, we consider two wormhole spacetimes classes: the Damour-Solodukhin wormhole and the braneworld wormhole. While there is no classical matter model for the Damour-Solodukhin wormhole, the braneworld wormhole, on the other hand, is supported by a scalar-tensor theory on the four-dimensional brane. Intriguingly, it turns out that the presence of a dark matter halo surrounding these wormholes can tame the violations of energy conditions present in generic wormhole spacetimes. Our results also demonstrate that the galactic Damour-Solodukhin wormhole is more stable than its isolated counterpart under linear scalar perturbation, whereas we obtain the opposite behavior for the braneworld wormhole. The perturbation of these wormholes leads to echoes in the ringdown waveform, which are sensitive to the properties of the dark matter halo. To be precise, the time delay between two echoes is affected by the galactic matter environment, and it appears to be a generic effect present for any exotic compact object living in a galaxy. This allows us to identify the galactic parameters, independently from the gravitational wave measurements, if echoes are observed in future generations of gravitational wave detectors. For completeness, we have also analyzed the impact of the galactic environment on the photon sphere, the innermost stable circular orbits, and the shadow radius. It turns out that the dark matter halo indeed affects these locations, with implications for shadow and accretion physics.

We study the geodesic motion in a space-time describing a swirling universe. We show that the geodesic equations can be fully decoupled in the Hamilton-Jacobi formalism leading to an additional constant of motion. The analytical solutions to the geodesic equations can be given in terms of elementary and elliptic functions. We also consider a space-time describing a static black hole immersed in a swirling universe. In this case, full separation of variables is not possible, and the geodesic equations have to be solved numerically.

The normal modes of Proca field perturbations in $d$-dimensional anti–de Sitter spacetime, ${\mathrm{AdS}}_d$ for short, with reflective Dirichlet boundary conditions, are obtained exactly. Within the Ishibashi-Kodama framework, we decompose the Proca field in scalar-type and vector-type components, according to their tensorial behavior on the ($d-2$)-sphere ${\mathcal{S}}^{d-2}$. Two of the degrees of freedom of the Proca field are described by scalar-type components, which in general are coupled due to the mass of the field, but in ${\mathrm{AdS}}_d$ we show that they can be decoupled. The other $d-3$ degrees of freedom of the field are described by a vector-type component that generically decouples completely. The normal modes and their frequencies for both the scalar-type and vector-type components of the Proca field are then obtained analytically. Additionally, we analyze the normal modes of the Maxwell field as the massless limit of the Proca field. We find that for scalar-type perturbations in $d=4$ there is a discontinuity in the massless limit, in $d=5$ the massless limit is well-defined using Dirichlet-Neumann rather than Dirichlet boundary conditions, and in $d>5$ the massless limit is completely well-defined, i.e., it is obtained smoothly from the massless limit of the scalar-type perturbations of the Proca field. For vector-type perturbations the Maxwell field limit is obtained smoothly for all $d$ from the massless limit of the vector-type perturbations of the Proca field.

The images of supermassive black holes in M87 and our galaxy captured by the Event Horizon Telescope (EHT) might open up a new way for exploring black hole physics at the horizon scale. Theoretically, this could provide insights into studying the emission sources around a black hole or the geometries of the black hole itself. This paper investigates the two-point correlations of intensity fluctuations on the photon ring, resulting from the existence of shock waves or gravitational fluctuations around a black hole. Following approaches used in the field of gravitational wave detectors, we introduce response functions of very long baseline interferometry (VLBI) for detecting gravitational fluctuations and study the shape of the overlap reduction functions. It is found that the shape of the correlations here differs from that resulting from stochastic emission sources. By providing an order-of-magnitude estimate for the signal-to-noise ratio (SNR), we obtain sensitivity curves for the detection of gravitational fluctuations. This might reveal the potential for detecting gravitational fluctuations with future VLBI observations in the LIGO frequency band.

Early dark energy is a promising potential resolution of the Hubble tension. Unfortunately, many models suffer from the need to fine-tune their initial conditions to ensure that the epoch of early dark energy coincides with matter-radiation equality. We propose a class of attractive early dark energy models where this coincidence arises naturally as a saddle point of a dynamical system that attracts a large volume of phase-space trajectories regardless of the initial conditions. The system approaches a global dark energy attractor at late-times. Our framework therefore unifies early and late dark energy using a single scalar degree of freedom. We analyze a fiducial attractive early dark energy model and find that it is disfavored by cosmological data due to the presence of a long-lived saddle point in the matter era where the scalar plays the role of an additional component of (nonclustering) dark matter. Our investigations provide lessons for future model-building efforts aimed at constructing viable attractive early dark energy models.

The evolution of linear initial conditions present in the early Universe into extended halos of dark matter at late times can be computed using cosmological simulations. However, a theoretical understanding of this complex process remains elusive; in particular, the role of anisotropic information in the initial conditions in establishing the final mass of dark matter halos remains a long-standing puzzle. Here, we build a deep learning framework to investigate this question. We train a three-dimensional convolutional neural network to predict the mass of dark matter halos from the initial conditions, and quantify in full generality the amounts of information in the isotropic and anisotropic aspects of the initial density field about final halo masses. We find that anisotropies add a small, albeit statistically significant amount of information over that contained within spherical averages of the density field about final halo mass. However, the overall scatter in the final mass predictions does not change qualitatively with this additional information, only decreasing from 0.9 dex to 0.7 dex. Given such a small improvement, our results demonstrate that isotropic aspects of the initial density field essentially saturate the relevant information about final halo mass. Therefore, instead of searching for information directly encoded in initial conditions anisotropies, a more promising route to accurate, fast halo mass predictions is to add approximate dynamical information based e.g. on perturbation theory. More broadly, our results indicate that deep learning frameworks can provide a powerful tool for extracting physical insight into cosmological structure formation.

The $S_8$ tension between low-redshift galaxy surveys and the primary cosmic microwave background (CMB) signals a possible breakdown of the $\mathrm{\Lambda }\mathrm{CDM}$ model. Recently differing results have been obtained using low-redshift galaxy surveys and the higher redshifts probed by CMB lensing, motivating a possible time-dependent modification to the growth of structure. We investigate a simple phenomenological model in which the growth of structure deviates from the $\mathrm{\Lambda }\mathrm{CDM}$ prediction at late times, in particular as a simple function of the dark energy density. Fitting to galaxy lensing, CMB lensing, baryon acoustic oscillations, and supernovae datasets, we find significant evidence—$2.5–3\sigma$, depending on analysis choices—for a nonzero value of the parameter quantifying a deviation from $\mathrm{\Lambda }\mathrm{CDM}$. The preferred model, which has a slower growth of structure below $z\sim 1$, improves the joint fit to the data over $\mathrm{\Lambda }\mathrm{CDM}$. While the overall fit is improved, there is weak evidence for galaxy and CMB lensing favoring different changes in the growth of structure.