The gravitational wave (GW) interferometers Laser Interferometer Space Antenna (LISA) and the Einstein Telescope (ET) are expected to be functional in the next decade(s), possibly around the same time. They will operate over different frequency ranges, with similar integrated sensitivities to the amplitude of a stochastic GW background (SGWB). We investigate the synergies between these two detectors, in terms of a multiband detection of a cosmological SGWB characterized by a large amplitude, and a broad frequency spectrum. We develop the notion of integrated sensitivity and propose a novel signal-to-noise ratio optimal for characterization of the geometrical properties of the interferometer systems of LISA and the ET operating simultaneously. By investigating various examples of SGWBs, such as those arising from cosmological phase transition, cosmic string, and primordial inflation, we show that LISA and the ET operating together will have the opportunity to assess more effectively the characteristics of the GW spectrum produced by the same cosmological source, but at separate frequency scales. Moreover, the two experiments in tandem can be sensitive to features of early Universe cosmic expansion before big bang nucleosynthesis (BBN), which affects the SGWB frequency profile and which would not be possible to detect otherwise, since two different frequency ranges correspond to two different pre-BBN (or postinflationary) epochs. Besides considering the GW spectrum, we additionally undertake a preliminary study of the sensitivity of LISA and the ET to soft limits of higher-order tensor correlation functions. Given that these experiments operate at different frequency bands, their synergy constitutes an ideal direct probe of squeezed limits of higher-order GW correlators, which cannot be measured operating with a single instrument only.

Quark and gluon jets provide one of the best ways to probe the matter produced in ultrarelativistic high-energy collisions, from cold nuclear matter to hot quark-gluon plasma. In this work, we propose a unified framework for efficient quantum simulation of many-body dynamics using the ($3+1$)-dimensional QCD Hamiltonian on the light front, particularly suited for studying the scattering of quark and gluon jets on nuclear matter in heavy-ion collisions. We describe scalable methods for mapping physical degrees of freedom onto qubits and for simulating in-medium jet evolution. We then validate our framework by implementing an algorithm that directly maps second-quantized Fock states onto qubits and uses Trotterized simulation for simulating time dynamics. Using a classical emulator, we investigate the evolution of quark and gluon jets with up to three particles in Fock states, extending prior studies. These calculations enable the study of key observables, including jet momentum broadening, particle production, and parton distribution functions.

We investigate the radiative decays of the $X(3872)$ to $\gamma V(V={\rho }^0,\omega )$ in the molecule scenario, where the $X(3872)$ is regarded as a pure hadronic molecule of the $D{\overline{D}}^{*}+\mathrm{c}\mathrm{.}\mathrm{c}\mathrm{.}$ in an $S$-wave with the quantum numbers $J^{PC}=1^{++}$. The radiative processes were assumed to occur via the triangle hadronic loops, and the relevant calculations were conducted using an effective Lagrangian approach. It is found that the absolute decay widths are model-dependent, but the relative width ratio is rather independent of the model parameter. Moreover, the calculated results indicate that the radiative decays of the $X(3872)$ are strongly influenced by the molecular configuration characterized by the proportion of the charged and neutral constituents. We hope that the present calculations could be tested by the experimental measurements.

We present a measurement of the branching fraction and fraction of longitudinal polarization of $B^0\to {\rho }^{+}{\rho }^{-}$ decays, which have two ${\pi }^0$’s in the final state. We also measure time-dependent $CP$ violation parameters for decays into longitudinally polarized ${\rho }^{+}{\rho }^{-}$ pairs. This analysis is based on a data sample containing $(387\pm 6)\times {10}^6$ $\mathrm{\Upsilon }(4S)$ mesons collected with the Belle II detector at the SuperKEKB asymmetric-energy $e^{+}{e}^{-}$ collider in 2019–2022. We obtain $\mathcal{B}(B^0\to {\rho }^{+}{\rho }^{-})=(2.89_{-0.22}^{+0.23}{}_{-0.27}^{+0.29})\times {10}^{-5}$, $f_L=0.921_{-0.025}^{+0.024}{}_{-0.015}^{+0.017}$, $S=-0.26\pm 0.19\pm 0.08$, and $C=-0.02\pm 0.12_{-0.05}^{+0.06}$, where the first uncertainties are statistical and the second are systematic. We use these results to perform an isospin analysis to constrain the Cabibbo-Kobayashi-Maskawa angle ${\varphi }_2$ and obtain two solutions; the result consistent with other Standard Model constraints is ${\varphi }_2=({92.6}_{-4.7}^{+4.5})°$.

We present a first two-dimensional general relativistic analysis of superconducting regions in axially symmetric highly magnetized neutron star (magnetar) models with toroidal magnetic fields. We investigate the topology and distribution of type-II and type-I superconducting regions for varying toroidal magnetic field strengths and stellar masses by solving the Einstein-Maxwell equations using the xns code. Our results reveal that the outer cores of low- to intermediate-mass magnetars sustain superconductivity over larger regions compared to higher-mass stars with nontrivial distribution of type-II and type-I regions. Consistent with previous one-dimensional (1D) models, we find that regardless of the gravitational mass, the inner cores of magnetars with toroidal magnetic fields are devoid of $S$-wave proton superconductivity. Furthermore, these models contain nonsuperconducting, torus-shaped regions; a novel feature absent in previous 1D studies. Finally, we speculate on the potential indirect effects of superconductivity on continuous gravitational wave emissions from millisecond pulsars, such as PSR J1843-1113, highlighting their relevance for future gravitational wave detectors.

The scattering amplitudes of string theory exhibit many extraordinary properties. But are they the unique mathematical objects to do so? Recently, it has been shown how the spectrum and amplitudes of open string theory follow directly from the assumptions of faster than power-law falloff at high energies and a property dubbed level truncation. At present there is no analogous principle for closed string scattering, which is famously rigid and naively impervious to modification. In this paper we analytically bootstrap the spectrum and four-point amplitudes of the closed string—together with a parametrized space of deformations—from conditions on high-energy falloff and level truncation. While these deformations exhibit the same Regge scaling as pure gravity, in the tensionless limit they reproduce remarkable extremal amplitudes that have appeared in bottom-up studies of positivity.

As the criterion for the applicability of the background subtraction method, not only the finiteness condition of the resulting Hamiltonian but also the condition for the validity of the first law of black hole thermodynamics can be reduced to the form amenable to much simpler analysis at infinity by using the covariant phase space formalism. With this, we further establish that the background subtraction method is as applicable as the covariant counterterm method not only to Einstein’s gravity, but also to its higher derivative corrections for black hole thermodynamics in both asymptotically flat and anti–de Sitter spacetimes. In addition, our framework also provides us with the first derivation of the universal expression of the Gibbs free energy in terms of the Euclidean on-shell action beyond Einstein’s gravity. Among others, our findings have a far reaching impact on the shift in methodology for the Euclidean approach to black hole thermodynamics, where the well justified background subtraction method by our wieldy criterion is supposed to be the favored choice compared to the covariant counterterm method.

Neutron stars (NSs) offer an exceptional opportunity to investigate gravitational physics in extreme environments. In the context of alternative theories of general relativity (GR), a scalar field nonminimally coupled to gravity can lead to “hairy” NS solutions with a nonzero scalar charge. As a result, binary systems containing at least one hairy NS can serve as probes for testing GR through observations. In this work, we analyze the gravitational wave signals from four neutron star-black hole merger events: GW190814, GW200115, GW200105, and GW230529 examine the hairy NS hypothesis predicted by the luminal Horndeski theories. Our analysis constrains the scalar charge to be on the order of ${10}^{-3}-{10}^{-4}$, with the most stringent limit arising from the recent GW230529 event. In addition, we discuss the implications of our results in relation to the scalarized NS solutions found in the literature.

The effective field theory (EFT) of dark energy predicts a possible time variation of the propagation speed of gravitational waves (GW) which could be tested with multimessenger astronomy. For this purpose we derive the relation between the redshift dependence of the propagation speed of GWs and the time delay between the detection of GWs and electromagnetic waves (EMWs) emitted by the same source. According to the EFT the friction term of the GW propagation equation depends on the effective Planck mass and GW speed time variation, affecting the GW-EMW luminosity distance ratio. We compute the general form of the GW-EMW luminosity distance ratio in terms of the effective GW speed and effective Planck mass, and then focus on theories with constant Planck mass (CPM) and time varying GW speed. For CPM theories the GW speed can be jointly constrained by the GW-EMW detection time delay and luminosity distance ratio, allowing one to derive a consistency relation between these two observables. The event GW170817 and its EM counterpart satisfy the CPM consistency condition, and this allows one to set constraints on the time variation of the GW speed, and consequently on the coefficients of the effective theory.

We study the imaging of a hairy black hole (HBH) in the Einstein-Klein-Gordon theory, where Einstein gravity is minimally coupled to a scalar potential $V(\varphi )=-\mathrm{\Lambda }{\varphi }^4+\mu {\varphi }^2$ with $\mathrm{\Lambda }$ and $\mu$ are constants. As a consequence, a nontrivial scalar field at the event horizon ${\varphi }_H$ allows the HBH to evade the no-hair theorem, bifurcate from the Schwarzschild black hole by acquiring some new properties, which can affect the shadow of the HBH received by a distant observer. The framework of ray-tracing is adopted to investigate the optical appearance of the HBH, thus the trajectories of light rays around the HBH can be classified into three emissions: direct, lensed, and photon ring. Employing three models of optically and geometrically thin accretion disk, we compare the differences between the Schwarzschild black hole and HBH with both having the same horizon radius, and find that the size of the shadow and accretion disk increases as ${\varphi }_H$ increases, but the brightness of the rings remain nearly unaffected. This implies our HBH can potentially mimic the Schwarzschild black hole if we vary the horizon radius of the HBH. Finally, we also constraint the parameter $\mathrm{\Lambda }$ from the observations of supermassive black holes in the galactic center of M87 and Sgr ${\mathrm{A}}^{*}$, which could offer new insights for imaging of black holes and astrophysical observations.

In bimetric gravity, nonbidiagonal solutions describing a static, spherically symmetric, and asymptotically flat black hole are given by a pair of Schwarzschild geometries, one in each metric sector. The two geometries are linked by a nontrivial diffeomorphism, which can be fully determined analytically if the two geometries possess the same isometries. This exact solution depends on four free parameters: the mass parameters of the two black holes, the ratio between the areal radii of the two metrics, and the proportionality constant between their (appropriately normalized) time-translation invariance Killing vector fields. We study the dynamics of axial dipolar perturbations on such a background and obtain general analytical solutions for their evolution. We show that, in general, the characteristic curves followed by dipolar gravitational waves are spacelike with respect to both metrics, and thus the propagation is superluminal. In fact, the velocity of a pulse, as measured by a static observer, turns out to increase with the distance to the black hole. The only exception to this general behavior corresponds to the special case where the two proportionality constants linking the areal radii and the Killing vectors coincide, for which waves travel at the speed of light. Therefore, we conclude that this is the only physically reasonable background, and thus our results restrict the class of viable black-hole solutions in bimetric gravity.

One of the major differences that lies between Finsler geometry and Riemannian geometry is Finsler spaces with constant curvature that are not equivalent to each other. It is important to test the difference by physical observations. In this paper, we investigate stellar motion around Sagittarius ${\mathrm{A}}^{\star }$ in axially symmetric Finslerian extensions of a Schwarzschild black hole. Specifically, we investigate two nonequivalent Finsler spacetimes, namely, Randers type and Bryant type, that are characterized by unique Finslerian parameters $\epsilon$ and $\alpha$, respectively. The two Finslerian parameters quantify deviations from the Schwarzschild black hole. We have shown that orbital motion of the Finslerian extension of Schwarzschild spacetime with Bryant type is confined to a single plane which is the same with the one in Schwarzschild spacetime. It is a distinct feature between the Randers type and Bryant type. In our previous researches, we have shown that orbital plane precession exists in the Finslerian extension of Schwarzschild spacetime with Randers type. Using publicly available astronomical measurements and spectroscopic data of the S2 star orbiting Sagittarius ${\mathrm{A}}^{\star }$, we employ an Markov chain Monte Carlo algorithm to explore the potential effects of Finslerian gravity. For the Finslerian extension of Schwarzschild spacetime with Randers type, the posterior distribution of the Finslerian parameter $\epsilon$ exhibits two distinct peaks, each corresponds to 85.41% and 14.59% probability, respectively. Gaussian fits to these peaks estimate $\epsilon =(-0.868\pm 2.460)\times {10}^{-4}$ for the dominant peak and $\epsilon =(11.92\pm 2.453)\times {10}^{-4}$ for the subdominant peak, both at the $1\sigma$ confidence level. This result manifests a feature of parity violation of the axially symmetric Finslerian extension of Schwarzschild spacetime. It indicates that no significant deviation from Schwarzschild black hole with large probability and a preference for the axially symmetric Finslerian extension of a Schwarzschild black hole of positive $\epsilon$ with small probability. In the case of the axially symmetric Finslerian extension of a Schwarzschild black hole with Bryant type, the posterior distribution of the Finslerian parameter $\alpha$ shows a single peak, estimating $\alpha =-0.631_{-8.222}^{+8.546}\times {10}^{-4}$ at $1\sigma$ confidence level. We have shown that the parameter $\alpha$ will dramatically affect the distance between perihelion and aphelion of orbit. Therefore, it is the reason that there is no significant deviation from a Schwarzschild black hole by the numerical result.

Detection of gravitational waves in the kilohertz (kHz) frequency range is crucial for understanding the physical processes of binary neutron star mergers. In Ref. [Phys. Rev. X 13, 021019 (2023)], a new interferometric configuration has been proposed, employing an L-shaped optical resonant cavity as the arm cavity. This alteration enhances the detector response to kHz signals. However, the departure from the conventional Michelson configuration necessitates a redesign of its sensing and control scheme, which is currently under study. In this article, we consider replacing linear arm cavities in the conventional Michelson interferometer with the L-shaped resonator, which was first considered in [Phys. Rev. D 77, 022002 (2008)] for detecting MHz gravitational waves. This hybrid configuration, with an arm length of tens of kilometers, features an enhanced response at kilohertz while retaining the same sensing and control scheme as the Michelson setup. At the conceptual level, it exhibits a higher sensitivity in the 2–4 kHz range compared to existing configurations.

According to the von Laue condition, the volume integral of the proper pressure inside isolated particles with a fixed structure and finite mass vanishes in the Minkowski limit of general relativity. In this work, we consider a simple illustrative example: nonstandard static global monopoles with finite energy, for which the von Laue condition is satisfied when the proper pressure is integrated over the whole space. We demonstrate, however, that the absolute value of this integral, when calculated up to a finite distance from the center of the global monopole, generally deviates from zero by no more than the energy located outside the specified volume (under the assumption of the dominant energy condition). Furthermore, we find that the maximum deviation from unity of the ratio between the volume averages of the on-shell Lagrangian and the trace of the energy-momentum tensor cannot exceed three times the outer energy fraction. Extending these results to real particles, we demonstrate that these constraints generally hold for finite-mass systems with fixed structure, including stable atomic nuclei, provided the dominant energy condition is satisfied. Specifically, we show that, except in extremely dense environments with energy densities comparable to that of the particles themselves, the volume average of the aforementioned ratio must be extremely close to unity. Finally, we discuss the broader implications of our findings for the form of the on-shell Lagrangian of real fluids, which is often a crucial element for accurately modeling the dynamics of the gravity and matter, especially in scenarios involving nonminimal couplings to other matter fields or gravity. We find that, in general, the ideal gas on-shell Lagrangian provides an accurate approximation of the true on-shell Lagrangian, even for nonideal gases with significant interparticle interactions.

We explore the impact of the reionization history on examining the shape of the power spectrum of the primordial gravitational waves (PGWs) with the cosmic microwave background (CMB) polarization. The large-scale CMB generated from the reionization epoch is important in probing the PGWs from all-sky experiments, such as LiteBIRD. The reionization model has been constrained by several astrophysical observations. However, its uncertainty could impact constraining models of the PGWs if we use large-scale CMB polarization. Here, by expanding the analysis of Mortonson and Hu (2007), we estimate how reionization uncertainty impacts constraints on a generic primordial tensor power spectrum. We assume that CMB polarization is measured by a LiteBIRD-like experiment and the tanh model is adopted for a theoretical template when we fit data. We show that constraints are almost unchanged even if the true reionization history is described by an exponential model, where all parameters are within 68% confidence level (CL). We also show an example of the reionization history that the constraints on the PGWs are biased more than 68% CL. Even in that case, using $E$-mode power spectrum on large scales would exclude such a scenario and make the PGW constraints robust against the reionization uncertainties.

We explore bounce scenarios in the framework of homogeneous and isotropic cosmological models with arbitrary spatial curvature in the theory of gravity with nonminimal derivative coupling of a scalar field to the curvature given by the term $(\zeta /H_0^2)G^{\mu \nu }{\nabla }_{\mu }\varphi {\nabla }_{\nu }\varphi$ in the Lagrangian. In general, a cosmological model is determined by six dimensionless parameters: the coupling parameter $\zeta$, and density parameters ${\mathrm{\Omega }}_0$ (cosmological constant), ${\mathrm{\Omega }}_2$ (spatial curvature term), ${\mathrm{\Omega }}_3$ (nonrelativistic matter), ${\mathrm{\Omega }}_4$ (radiation), ${\mathrm{\Omega }}_6$ (scalar field term). As expected, we find that there are no turning points and/or bounces in cosmological models with negative or zero spatial curvature. At the same time, both a turning point and a bounce can exist in the model with positive spatial curvature. In particular, the bounce—when the Universe’s contraction is replaced by expansion—happens at $\tau ={\tau }_{*}$ when $a({\tau }_{*})=a_{\min }=(3\zeta {\mathrm{\Omega }}_2{)}^{1/2}$, where $\tau =H_{0}t$ is a dimensionless cosmic time, and ${\tau }_{*}$ is a moment when the bounce happens. It is important fact that the value $a_{\min }$ depends only on $\zeta$ and ${\mathrm{\Omega }}_2$ and does not depend on ${\mathrm{\Omega }}_0$, ${\mathrm{\Omega }}_3$, and ${\mathrm{\Omega }}_4$. We find that near the bounce $a(\tau )\approx a_{\min }(1+\mathrm{\Delta }{\tau }^2/18\zeta )$ and $h(\tau )\approx \mathrm{\Delta }\tau /9\zeta$, where $\mathrm{\Delta }\tau =\tau -{\tau }_{*}$. Thus, the scale factor $a(\tau )$, the Hubble parameter $h(\tau )$, and all corresponding geometrical invariants have a regular behavior near the bounce. In particular, $a(\tau )\to a_{\min }$, $h(\tau )\to 0$ as $\tau \to {\tau }_{*}$. Additionally, the values characterizing matter energy densities, such as ${\rho }_m\sim a^{-3}$ and ${\rho }_r\sim a^{-4}$, are regular near the bounce. Nevertheless, though the spacetime geometry and energy densities remain to be regular near the bounce, the scalar field has a singular behavior there. Namely, ${\varphi }^{\prime }\propto 1/\mathrm{\Delta }{\tau }^2\to \infty$ as $\mathrm{\Delta }\tau \to 0$. As a result, we conclude that the complete dynamical system describing the cosmological evolution in theory of gravity with nonminimal derivative coupling is singular near the bounce. To our knowledge, such a scenario, when the spacetime geometry and matter energy densities remain to be regular at approaching the Universe evolution to the moment of bounce, while the behavior of scalar field becomes singular, was unknown before. For this reason, we term this scenario as a “singular” bounce.

The Sun is not quite a perfect sphere, and its oblateness, thought to be induced through its rotation, has been measured using optical observations of its radius. Its gravitational quadrupole moment can then be deduced using solar models, or through helioseismology, and it can also be determined from measurements of its gravitational effects on Mercury’s orbit. The various assessments do not appear to agree, with the most complete and precise orbital assessments being in slight excess of other determinations. This may speak to the existence of a nonluminous disk or ring, where we also note evidence for a circumsolar dust ring within Mercury’s orbit from the Solar TErrestrial RElations Observatory (STEREO) mission. Historically, too, a protoplanetary disk may have been key to reconciling the Sun’s metallicity with its neutrino yield. The distribution of the nonluminous mass within Mercury’s orbit can modify the relative size of the optical and orbital quadrupole moments in different ways. We develop how we can use these findings to limit the mass of a dark disk, ring, or halo in the immediate vicinity of the Sun, and we note how future observational studies of the inner Solar System can not only refine these constraints but can also help to identify and to assess the mass of its dark-matter component.

We demonstrate that the scalar-mediator dark-matter scenario is consistent with the experimental data on the decay $B\to K{M}_X$ and provides a good description of the shape of the observed excess. Within this scenario, the interaction with dark-matter particles leads to approximately the same excess in $\mathrm{\Gamma }(B\to K^{*}{M}_X)$ and $\mathrm{\Gamma }(B\to K{M}_X)$ compared to the Standard Model; also the differential distributions of the excess events are similar in shape in the variable $q_{\mathrm{rec}}^2$ measured by experiment.