Although quasi-dilaton massive gravity is a well-defined gravitational theory, it exhibits instabilities and suffers from the strong coupling problem. In this work we construct an extension of the theory through the inclusion of the aether field. Focusing on flat Friedmann-Lemaître-Robertson-Walker geometry, we show the existence of exact, self-accelerating solutions at the background level, characterized by an effective cosmological constant arising from the graviton mass. Additionally, we perform a detailed perturbation analysis, investigating separately the tensor, vector, and scalar perturbations, extracting the dispersion relation of gravitational waves, and determining the stability conditions for vector and scalar sectors. As we show, there are always regions in the parameter space in which the obtained solutions are free from ghost instabilities, as well as from the strong coupling problem. Hence, although the aether field does not play an important role in the background self-accelerating solutions, it does play a crucial role in the alleviation of the perturbation-related problems of the simple quasi-dilaton massive gravity.

The centers of the core-collapse supernovae are one of the densest environments in the Universe. Under such conditions, it is conceivable that a first-order phase transition from ordinary nuclear matter to the quark-gluon plasma occurs. This transition releases a large amount of latent heat that can drive a supernova explosion and may imprint a sharp signature in the neutrino signal. We show how this snap feature, if observed at large-scale neutrino detectors, can set competitive limits on the neutrino masses and assist the localization of the supernova via triangulation. The 95% C.L. limit on the neutrino mass can reach 0.16 eV in Ice-Cube, 0.22 eV in Hyper-Kamiokande, and 0.58 eV in DUNE, for a supernova at a distance of 10 kpc. For the same distance and in the most optimistic neutrino conversion case, the triangulation method can constrain the $1\sigma$ angular uncertainty of the supernova localization within $\sim 0.3°–9.0°$ in the considered pairs of the detectors, leading to an improvement up to an order of magnitude with respect to the often considered in the literature rise time of the neutronization burst.

We reanalyze the binary-neutron-star signals, GW170817 and GW190425, focusing on the inspiral regime. We use post-Newtonian waveform models as templates, which are theoretically rigid and efficiently describe the inspiral regime. We study potential systematic difference in estimates of the binary tidal deformability $\tilde{\mathrm{\Lambda }}$ by using different descriptions for the point-particle dynamics and tidal effects. We find that the estimates of $\tilde{\mathrm{\Lambda }}$ show no significant systematic difference among three models for the point-particle parts: TF2, TF2g, and $\mathrm{TF}2+$, when they employ the same tidal model. We compare different tidal descriptions given by different post-Newtonian orders in the tidal phase. Our results indicate that the estimates of $\tilde{\mathrm{\Lambda }}$ slightly depend on the post-Newtonian order in the tidal phase and an increase in the tidal post-Newtonian order does not lead to a monotonic change in the estimate of $\tilde{\mathrm{\Lambda }}$. We also compare the estimate of $\tilde{\mathrm{\Lambda }}$ obtained by the post-Newtonian tidal model and numerical-relativity calibrated tidal models. We find that the post-Newtonian model gives slightly larger estimate of $\tilde{\mathrm{\Lambda }}$ and wider posterior distribution than the numerical-relativity calibrated models. According to Bayesian model comparison, it is difficult to identify a preference among the post-Newtonian orders by relying on the GW170817 and GW190425 data. Our results indicate no preference among numerical-relativity calibrated tidal models over the post-Newtonian model. Additionally, we present constraints on equation-of-state models for neutron stars with the post-Newtonian model, which show that the GW170817 data disfavor less compact models, though they are slightly weaker constraints than the numerical-relativity calibrated tidal models.

Low-mass neutron stars are directly associated with the nuclear saturation parameters because their central density is definitely low. We have already found a suitable combination of nuclear saturation parameters for expressing the neutron star mass and gravitational redshift, i.e., $\eta \equiv (K_0{L}^2{)}^{1/3}$ with the incompressibility for symmetric nuclear matter, $K_0$, and the density-dependent nuclear symmetry energy, $L$. In this study, we newly find another suitable combination given by ${\eta }_{\tau }\equiv (-K_{\tau }{L}^5{)}^{1/6}$ with the isospin dependence of incompressibility for asymmetric nuclear matter, $K_{\tau }$, and derive the empirical relations for the neutron star mass and gravitational redshift as a function of ${\eta }_{\tau }$ and the normalized central number density. With these empirical relations, one can evaluate the mass and gravitational redshift of the neutron star, whose central number density is less than threefold the saturation density, within $\sim 10\%$ accuracy, and the radius within a few percent accuracy. In addition, we discuss the neutron star mass and radius constraints from the terrestrial experiments, using the empirical relations, together with those from the astronomical observations. Furthermore, we find a tight correlation between ${\eta }_{\tau }$ and $\eta$. With this correlation, we derive the constraint on $K_{\tau }$ as $-348\le K_{\tau }\le -237\mathrm{MeV}$, assuming that $L=60\pm 20$ and $K_0=240\pm 20\mathrm{MeV}$.

In the paper, we propose a scheme to constrain the axion-to-nucleon interaction and non-Newtonian gravity. Here, we consider a levitated optomechanical system consisting of a silica nanosphere and an optical cavity. The total force gradient exerted on this nanosphere modifies its resonance frequency. Based on this, we have developed a quantum optical method to detect and constrain the two exotic forces. Also, we have established prospective constraints on axion-neucleon coupling constants and the Yukawa interaction constant. In addition, these constraints significantly improve the existing bounds.

It has been found that at a high luminosity $e^{+}{e}^{-}$ collider, sizable ${\eta }_c+c\overline{c}X$, and ${\eta }_b+b\overline{b}X$ events can be produced when it works around the $Z$ peak. In this paper, we calculate the decay widths of $Z\to {\eta }_c+c+\overline{c}+X$ and $Z\to {\eta }_b+b+\overline{b}+X$ up to next-to-leading order (NLO) accuracy. We find that the NLO corrections are significant in these two processes. After including the NLO corrections, the decay widths of $Z\to {\eta }_c+c+\overline{c}+X$ and $Z\to {\eta }_b+b+\overline{b}+X$ are enhanced by about 34% and 28% for the case of ${\mu }_R=2m_Q$, and are enhanced by about 112% and 83% for the case of ${\mu }_R=m_Z$, respectively. The differential decay widths $d\mathrm{\Gamma }/dz$, $d\mathrm{\Gamma }/d{m}_{12}$, and $d\mathrm{\Gamma }/d{m}_{23}$ for these two decay processes are also analyzed.

The linear- and quadratic-in-spin contributions to the binding potential and gravitational-wave flux from binary systems are derived to next-to-next-to-leading order in the post-Newtonian (PN) expansion of general relativity, including finite-size and tail effects. The calculation is carried out through the worldline effective field theory framework. We find agreement in the overlap with the available PN and self-force literature. As a direct application, we complete the knowledge of spin effects in the evolution of the orbital phase for aligned-spin circular orbits to fourth PN order. We estimate the impact in the number of accumulated gravitational-wave cycles and find they make a significant contribution for next-generation observatories. The results presented here will therefore play an important role in providing reliable physical interpretation of gravitational-wave signals from spinning binaries with future gravitational-wave detectors such as LISA and the Einstein Telescope.

The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for $U(1)$ gauge theories regularized via finite-dimensional Hilbert spaces of quantum spin-$S$ operators, known as quantum link models. For quantum electrodynamics (QED) in one spatial dimension, we numerically demonstrate the continuum limit by extrapolating the ground state energy, the scalar, and the vector meson masses to large spin lengths $S$, large volume $N$, and vanishing lattice spacing $a$. By exactly solving Gauss’s law for arbitrary $S$, we obtain a generalized PXP spin model and count the physical Hilbert space dimension analytically. This allows us to quantify the required resources for reliable extrapolations to the continuum limit on quantum devices. We use a functional integral approach to relate the model with large values of half-integer spins to the physics at topological angle $\mathrm{\Theta }=\pi$. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.

The commutator $[x(t),p]$ in an inverted harmonic oscillator (IHO) in one-dimensional quantum mechanics exhibits remarkable properties. It reduces to a c-number and does not show any quantum fluctuations for arbitrary states. Related to this nature, the quantum Lyapunov exponent computed through the out-of-time-order correlator (OTOC) $⟨[x(t),p{]}^2⟩$ precisely agrees with the classical one. Hence, the OTOC may be regarded as an ideal indicator of the butterfly effect in the IHO. Since IHOs are ubiquitous in physics, these properties of the commutator $[x(t),p]$ and the OTOCs might be seen in various situations, too. In order to clarify this point, as a first step, we investigate OTOCs in one-dimensional quantum mechanics with polynomial potentials, which exhibit butterfly effects around the peak of the potential in classical mechanics. We find two situations in which the OTOCs show exponential growth reproducing the classical Lyapunov exponent of the peak. The first one, which is obvious, is using a suitably localized wave packet near the peak, and the second one is taking a limit akin to the large-$N$ limit in the noncritical string theories.

Nambu-Goldstone (NG) modes for 0-form and higher-form symmetries can become unstable in the presence of background fields. Examples include the instability of a photon with a time-dependent axion background or with a chirality imbalance, known as the chiral plasma instability, and the instability of a dynamical axion with a background electric field. We show that all these phenomena can be universally described by a symmetry algebra for 0-form and higher-form symmetries. We prove a counting rule for the number of unstable NG modes in terms of correlation functions of broken symmetry generators. Based on our unified description, we further give a simple new example where one of the NG modes associated with the spontaneous 0-form symmetry breaking $U(1)\times U(1)\to \{1\}$ becomes unstable.

We study the decay of the false vacuum in the scaling Ising and tricritical Ising field theories using the truncated conformal space approach and compare the numerical results to theoretical predictions in the thin wall limit. In the Ising case, the results are consistent with previous studies on the quantum spin chain and the ${\phi }^4$ quantum field theory; in particular, we confirm that while the theoretical predictions get the dependence of the bubble nucleation rate on the latent heat right, they are off by a model-dependent overall coefficient. The tricritical Ising model allows us on the other hand to examine more exotic vacuum degeneracy structures, such as three vacua or two asymmetric vacua, which leads us to study several novel scenarios of false vacuum decay by lifting the vacuum degeneracy using different perturbations.

Scattering amplitudes mediated by graviton exchange display IR singularities in the forward limit. This obstructs standard application of positivity bounds based on twice-subtracted dispersion relations. Such divergences can be canceled only if the UV limit of the scattering amplitude behaves in a specific way, which implies a very nontrivial connection between the UV and IR behaviors of the amplitude. We show that this relation can be expressed in terms of an integral transform, obtaining analytic results when $t\log s\to 0$. Carefully applying this limit to dispersion relations, we find that infinite arc integrals, which are usually taken to vanish, can give a nontrivial contribution in the presence of gravity, unlike in the case of finite negative $t$. This implies that gravitational positivity bounds cannot be trusted unless the size of this contribution is estimated in some way, which implies assumptions on the UV completion of gravitational interactions. We discuss the relevance of these findings in the particular case of QED coupled to gravity.

We analyze entanglement harvesting for arbitrary initial states of particle detectors and arbitrary quasifree states of the field. Despite the fact that spatially smeared particle detectors are known to break covariance for arbitrary initial states, we show that the entanglement harvested by a pair of detectors from a quasifree state of a scalar field is a covariant quantity up to second order in perturbation theory.

We compute the metric fluctuations induced by a turbulent energy-matter tensor within the first order post-Minkowskian approximation. It is found that the turbulent energy cascade can in principle interfere with the process of black hole formation, leading to a potentially strong coupling between these two highly nonlinear phenomena. It is further found that a power-law turbulent energy spectrum $E(k)\sim k^{-n}$ generates metric fluctuations scaling as $x^{n-2}$, where $x$ is the four-dimensional spacelike distance from an arbitrary origin in Minkowski spacetime, highlighting the onset of metric singularities whenever $n<2$. Finally, the effect of metric fluctuations on the geodesic motion of test particles is also discussed as a potential technique to extract information on the spectral characteristics of fluctuating spacetime.

We study the Einstein-Euler-Heisenberg theory in the presence of a self interacting scalar field, minimally coupled to gravity. We solve analytically the field equations for the magnetically charged case and we obtain novel magnetically charged hairy black holes. The scalar field dresses the black hole with a secondary scalar hair. The hairy black hole develops three horizons when the Euler-Heisenberg parameter and the magnetic charge are small and the horizon radius is getting large when the scalar charge and the gravitational mass are large. The presence of matter and the magnetic field outside the horizon of the black hole increases the temperature only for small black holes. Calculating the heat capacity we show that the asymptotically anti–de Sitter (AdS) Euler-Heisenberg hairy black hole undergoes a second order phase transition and then it is stabilized. Also the weak energy condition is violated for the asymptotically AdS Euler-Heisenberg hairy black hole.

The dynamical evolution of the Hajicek 1-form is derived in the Einstein-Cartan (EC) theory. We find that like the Einstein theory of gravity, the evolution equation is related to a projected part of the Einstein tensor (${\widehat{G}}_{ab}$) on a generic null surface $\mathcal{H}$, particularly ${\widehat{G}}_{ab}{l}^a{q^b}_c$, where $l^a$ and ${q^a}_c$ are the outgoing null generators of $\mathcal{H}$ and the induced metric to a transverse spatial cross section of $\mathcal{H}$, respectively. Under the geodesic constraint, a possible fluid interpretation of this evolution equation is then proposed. We find that it has the structure which is reminiscent to the Cosserat generalization of the Navier-Stokes fluid provided we express the dynamical evolution equation of the Hajicek 1-form in a set of coordinates adapted to $\mathcal{H}$ and in a local inertial frame. An analogous viewpoint can also be built under the motive that the usual material derivative for fluids should be replaced by the Lie derivative. Finally, the tidal force equation in EC theory on the null surface is also derived.

Some sixty years ago Buchdahl pioneered a program in search of static spherically symmetric metrics for pure ${\mathcal{R}}^2$ gravity in vacuo [H. A. Buchdahl, Nuovo Cimento 23, 141 (1962).]. Surpassing several obstacles, his work culminated in a nonlinear second-order ordinary differential equation (ODE) which required being solved. However, Buchdahl deemed the ODE intractable and abandoned his pursuit for an analytical solution. We have finally managed to overcome this remaining hurdle and bring his program to fruition. Reformulating Buchdahl’s ODE, we obtain a novel class of metrics (which we shall call the Buchdahl-inspired metrics hereafter) in a compact and transparent expression: ${ds}^2=e^{k\int \frac{dr}{rq(r)}}\{p(r)[-\frac{q(r)}{r}d{t}^2+\frac{r}{q(r)}d{r}^2]+r^{2}d{\mathrm{\Omega }}^2\},$ in which the pair $\{p,q\}$ are two functions of the radial coordinate $r$ obeying the evolution rules $\frac{dp}{dr}=\frac{3k^2}{4r}\frac{p}{q^2},\frac{dq}{dr}=(1-\mathrm{\Lambda }{r}^2)p$, and the Ricci scalar is $\mathcal{R}(r)=4\mathrm{\Lambda }{e}^{-k\int \frac{dr}{rq(r)}}$. We are able to verify ex post, via direct inspection, that the metric given above satisfies the ${\mathcal{R}}^2$ vacuo field equation $\mathcal{R}({\mathcal{R}}_{\mu \nu }-\frac{1}{4}{g}_{\mu \nu }\mathcal{R})+(g_{\mu \nu }\square -{\nabla }_{\mu }{\nabla }_{\nu })\mathcal{R}=0,$ hence establishing its validity. The compact form above casts the Buchdahl-inspired metric in a parallel resemblance with the classic Schwarzschild–de Sitter (SdS) metric, with the case $k=0$ corresponding to the SdS metric. We show why the Buchdahl-inspired metric, which exhibits nonconstant scalar curvature when $k\ne 0$, defeats a “no-go” theorem proved in Kehagias et al. [J. High Energy Phys. 05 (2015) 143.], which posits that pure ${\mathcal{R}}^2$ gravity vacua are restricted to the Einstein spaces, ${\mathcal{R}}_{\mu \nu }=\mathrm{\Lambda }{g}_{\mu \nu }$, and the vanishing Ricci scalar spaces, $\mathcal{R}=0$. The aforementioned “no-go” theorem assumes a rapid asymptotic falloff for the metric as $r\to \infty$. However, we find that the Buchdahl-inspired metric evades that central assumption, which is overly restrictive. A product of a fourth-derivative gravity, a Buchdahl-inspired metric is specified by four parameters: $\mathrm{\Lambda }$ measuring the scalar curvature at largest distances, $k$ effecting the variation of the curvature on the manifold, and $\{p_0,q_0\}$ initiating the “evolution” of $\{p(r),q(r)\}$ along the radial direction, forming a two-dimensional phase space. The class of Buchdahl-inspired metrics is exhaustive as it covers all “nontrivial” static spherically symmetric metrics admissible for pure ${\mathcal{R}}^2$ gravity in vacuo, with the SdS metric being a special case, $k=0$. Transparently, the quartet $\{\mathrm{\Lambda },k,p_0,q_0\}$ spans a topological space with all members in the class of Buchdahl-inspired metrics being smoothly connected to the SdS metrics when $k$ is continuously tuned to 0. In this respect, the Buchdahl-inspired metrics constitute a natural enlargement suitably regarded as a framework “beyond Schwarzschild–de Sitter.” Our novel solution thereby completes Buchdahl’s six-decades-old program. We also explore the mathematical properties of the Buchdahl-inspired metric in the limit of small $k$ and in the region around the coordinate origin.

The mechanical tidal effects of gravitational waves (GWs) in the low- and middle-frequency bands, typically from dozens to hundreds of Hz, have been detected by the LIGO-Virgo-KAGRA ground laser interferometers. To implement the detection of the GWs in the higher-frequency bands (such as the MHz band and the higher ones), predicted by a series of theoretical models in astrophysics and cosmology, we propose here an experimental system to probe their electromagnetic (EM) responses (EMRs). The system mainly consists of a modulated high magnetic field and the weak-light detection techniques (such as single-photon detectors). Physically, when the high-frequency GWs pass through such a modulated high magnetic field, the first-order EMR signals, rather than the second-order ones generated by the inverse Gertsenshtein effects, are induced and can be detected by the current weak-light detection techniques. Interestingly, by considering the influences from the main noises, i.e., the thermal and shot ones, we show that the sensitivity of the proposed system could be utilized to implement the detection of the relic GWs (predicted by the well-known Big Bang model) in the MHz and GHz bands, depending on the frequency of the applied alternating magnetic field. Hopefully, such an experimental system can be built to detect the EMRs of the GWs for testing the relevant gravitational models.

We introduce a class of relativistic fluid states satisfying the relativistic local thermodynamical equilibrium postulate [abbreviated as relativistic (LTE) postulate]. States satisfying this postulate are states “near equilibrium” (a term defined precisely in the course of the paper), and, they permit one to attach a fictitious “local thermodynamical equilibrium” state that fits event by event the actual fluid state. States within this class allow one to single out an admissible class of rest frames relative to which thermodynamical variables like the energy density, thermodynamical pressure, stresses, and particle number density (or densities) measured by observers at rest relative to these frames are becoming frame independent provided second (or higher) order deviations from the fictitious state of local thermodynamical equilibrium are ignored. We have verified this property for a large class of theories of relativistic dissipation that include the Hiscock-Lindblom class of first-order theories, the Eckart and Landau-Lifshitz theories, the Israel-Stewart transient thermodynamics, the Liu-Müller-Ruggeri theory, fluids of divergence type, and the latest developed (BDNK) theory. Moreover, for states that are compatible with the relativistic (LTE) postulate, we show that the phenomenological equations describing first-order deviations from any fictitious local thermodynamical equilibrium state satisfy equations that remain form invariant under change of frame within the admissible class of frames. We proved this property for the Hiscock-Lindblom class of first-order theories, the Eckart and Landau-Lifshitz theories, the Israel-Stewart transient thermodynamics, the Liu-Müller-Ruggeri theory of relativistic dissipation, and the (BDNK) theory, and we expect the same property to hold for the class of relativistic fluids of divergence type.