We study the interaction of two massive particles with a quantized gravitational field in its vacuum state using two different position observables: (i) a frame-dependent coordinate separation and (ii) a frame-independent geodesic separation. For free particles, (i) leads to purely unitary dynamics but (ii) leads to dissipation. For two particles coupled through a linear spring, (i) and (ii) lead to different cutoff dependences in the frequency shift harmonic ladder of the differential motional mode. Our findings highlight the observable consequences of choosing different position observables at the interface of quantum mechanics and gravity.

We present a new method for embedding a causal set into Minkowski spacetime. The method is similar to a previously presented method, but is simpler and provides better embedding results. The method uses spacetime volumes to define causal set analogs of time coordinates for all elements, and spatial distances for pairs of causally related elements. The spatial distances for causally related pairs are then used to derive spatial distances for spacelike separated pairs by applying the triangle inequality. The result is a matrix of spatial distances for all pairs of elements in the causal set. This distance matrix can be decomposed to give coordinates in Minkowski spacetime. Results are presented showing good quality embeddings into Minkowski spacetime for dimensions $d=2,3,4$.

In this short paper we want to generalize some recent concepts related to stubs in open string field theory. First, we modify the auxiliary field method by Erbin and Firat [Open string stub as an auxiliary string field, 2023.] to sliver frame stubs which are not even with respect to the Belavin-Polyakov-Zamolodchikov (BPZ) product. We then also show that the construction is consistent at the full quantum level without any additional assumptions. Finally, we apply the method explicitly to the tachyon vacuum and the simplest identitylike solution.

Loop quantum gravitational effects can resolve the central singularity of black holes, while potentially leaving tiny traces of quantization in the exterior spacetime. We show the way these residues can, in principle, be explored using tidal Love numbers (TLNs). We consider loop quantized Schwarzschild black hole, in particular the Ashtekar-Olmedo-Singh (AOS) model, and study the static response to external tidal fields of spin zero (scalar field), spin one (vector field), and spin two (axial gravitational field) types. We find that, in contrast to the classical theory, where TLNs vanish, they are nonvanishing and negative for all three responses and for all multipoles. Besides, the magnitude of TLNs decreases as the black hole mass increases, and TLNs, in response to the axial gravitational field, have the largest magnitude among these three responses. Our results show that for black holes of mass $M\gtrsim 4.3\times {10}^4{M}_{\mathrm{Pl}}$, the AOS model is consistent with current and next-generation detection limits for TLNs. Our findings suggest that the quantum deformability of loop-quantized black holes, arising from the inherent fuzziness of spacetime geometry, reveals a fundamentally distinct internal structure compared to their classical counterparts. This unique feature manifests as quantum hair, which, in principle, can be detected by future observations.

In this work, we investigated the off-shell expansion relation of the Yang-Mills scalar theory. We explicitly showed that the single-trace Berends-Giele currents in the Yang-Mills scalar theory can be decomposed into a term expressed by a linear combination of bi-adjoint scalar Berends-Giele currents and one that vanishes under the on-shell limit. We proved that the bi-adjoint scalar currents, as well as the corresponding coefficients, can be characterized by a graphic approach that was originally studied in the Einstein-Yang-Mills expansion. Furthermore, we generalized the decomposition to the multitrace case through unifying relations and established the connection both in single-trace and multitrace graphic descriptions. Finally, we established the relations between the Yang-Mills currents and the single-trace Yang-Mills scalar currents, choosing special reference orders of the Yang-Mills graphs.

In this paper we consider a massive self-interacting scalar quantum field in a Lorentz-violation scenario based on a Hořava-Lifshitz model. Specifically, we investigate the vacuum energy density and its loop correction, up to first order in the self-interaction coupling constant, and also the topological mass generation. These quantities are also analyzed in the case where the field is massless. The scalar vacuum state is perturbed by the presence of two large parallel plates, placed at a distance $L$ from each other, due to the imposition of the Dirichlet boundary condition on the two plates. To perform this study, the effective potential approach in quantum field theory is applied.

Fractonic matter with dipole symmetry can be coupled to a two-index symmetric tensor gauge field. In this work, we show that this symmetric tensor field, along with other related generalized Maxwell theories, can be consistently coupled to curved backgrounds in a covariant and gauge-invariant way by reformulating dipole symmetry using conventional vector gauge fields. We identify a family of curved geometries where global dipole symmetry is preserved and derive energy-momentum conservation laws as Ward identities associated with background diffeomorphisms. Our results pave the way for future extensions, including generalizations to higher-order multipole theories.

We initiate an investigation into features of vacuum entanglement as probed by accelerated quantum probes in curved spacetime. Focusing specifically on de Sitter (dS) spacetime with curvature $\mathrm{\Lambda }$, we obtain several exact results corresponding to different kinematical setups of the probes. The interaction with the quantum field creates a nonlocal correlation between initially uncorrelated probes accelerating in different directions. It is well known that a single quantum probe in dS spacetime with uniform acceleration $a$ responds exactly as a quantum probe in Minkowski spacetime with “effective” acceleration $q\equiv \sqrt{a^2+\mathrm{\Lambda }}$. However, no such mapping generically exists for the entanglement between probes. Our results suggest that entanglement exhibits independent variations with changes in acceleration and curvature depending on different configurations of detector motion.

We analyze the dynamics of Bogomol’nyi-Prasad-Sommerfield three-vortex solutions. First, for unexcited vortices, we study the two-dimensional moduli space of centered vortices with $y\to -y$ symmetry, and its metric. We identify the one-dimensional subspaces describing the head-on collisions of equidistant collinear and equilateral triangle configurations, where geodesic motion results in 90° and 60° scattering, respectively. Second, by studying the frequency spectrum of vibrational shape modes along these subspaces, we explain how the force-free, geodesic motion is modified by shape mode excitations into a pattern of chaotic multibounce collisions.

We study propagation of high-frequency electromagnetic and gravitational waves in the gravitational field of a rotating black hole. Due to the interaction of the spin of the field with the spacetime curvature, the standard geometric optics approximation that is used for obtaining the approximate high-frequency solutions of the wave equation should be modified. The corresponding modified spinoptics equations show that the worldline of the spinning massless particle is still null, but no longer a geodesic. We demonstrate that using the hidden symmetries of the Kerr metric, one can obtain the corresponding spinoptics equations in the leading order of a $1/\omega$ expansion in an explicit form. We focus on the case of the spinning massless fields scattering in the region near the equatorial plane. We demonstrate that the asymptotic planes of the corresponding null ray’s motion are slightly tilted. We study this effect and its dependence on the spin of the black hole.

The quantum nature of gravity remains an open question in fundamental physics, lacking experimental verification. Gravitational waves (GWs) provide a potential avenue for detecting gravitons, the hypothetical quantum carriers of gravity. However, by analogy with quantum optics, distinguishing gravitons from classical GWs requires the preservation of quantum coherence, which may be lost due to interactions with the cosmic environment causing decoherence. We investigate whether GWs retain their quantum state by deriving the reduced density matrix and evaluating decoherence, using an environmental model where a scalar field is conformally coupled to gravity. Our results show that quantum decoherence of GWs is stronger at lower frequencies and higher reheating temperatures. We identify a model-independent amplitude threshold below which decoherence is negligible, providing a fundamental limit for directly probing the quantum nature of gravity. In the standard cosmological scenario, the low-energy density of the universe at the end of inflation leads to complete decoherence at the classical amplitude level of inflationary GWs. However, for higher-energy densities, decoherence is negligible within a frequency window in the range $100\mathrm{Hz}-{10}^8\mathrm{Hz}$, which depends on the reheating temperature. In a kinetic-dominated scenario, the dependence on reheating temperature weakens, allowing GWs to maintain quantum coherence above ${10}^7\mathrm{Hz}$.

Gravitational waves from asymmetric mass-ratio black-hole binaries carry unique information about their astrophysical environment. For instance, the Laser Interferometer Space Antenna (LISA) could potentially measure the amplitude and slope of gas torques in binaries embedded in the accretion disks of active Galactic nuclei, helping differentiate competing accretion disk models. However, this relies on simplified analytic models, which do not account for the stochastic variability of torques seen in hydrodynamic simulations. In this work, we use hydrodynamic simulations to create gravitational waveforms for extreme and intermediate mass-ratio inspirals in the LISA band. We then analyze these simulated waveforms using simpler templates that assume analytic torques, without stochastic time variability. By performing realistic Bayesian parameter estimation, we find no bias at 90% confidence in the binary parameters; however, estimates of accretion disk parameters, such as torque amplitude and slope, may be biased. Typically, the posterior distribution is centered around the average value of the torques, but when stochastic variability is large, the posterior can indicate no torques, even though they are present in the simulation. Our results suggest that while simplified analytic torque models work well for estimating binary parameters, caution is needed when using them to infer properties of the accretion disk. This work moves towards a more realistic assessment of one of the LISA science objectives, i.e., probing the properties of the astrophysical environments of black holes.

Hořava-Lifshitz gravity (to be precise, its projectable version) is recognized as a renormalizable, unitary, and asymptotically free quantum field theory of gravity. Notably, one of its cosmological predictions is that it can produce scale-invariant primordial density fluctuations and primordial gravitational waves without relying on inflation. In this paper, we investigate the quantum nature of the primordial gravitational waves generated in Hořava-Lifshitz gravity. It has been suggested that, for some inflationary models, the non-classicality of primordial gravitational waves in the squeezed coherent quantum state can be detected using the Hanbury Brown—Twiss (HBT) interferometry. We show that in Hořava-Lifshitz gravity, scale-invariant primordial gravitational waves can be generated during both the radiation-dominated and matter-dominated eras of the Universe. Moreover, the frequency range of their quantum signatures is shown to extend beyond that of inflationary models.

In this paper, we investigate the cosmological dynamics of teleparallel dark energy in the presence of nonzero spatial geometry. Extending previous analyses of nonminimal scalar-tensor theories in the torsion-based framework, we consider different scalar field potentials and examine the resulting background evolution and linear perturbations. Adopting a dynamical systems approach, we reformulate the field equations and constrain the model parameters via a Markov chain Monte Carlo analysis combining updated datasets from $\mathrm{Pantheon}+\mathrm{SH}0\mathrm{ES}$ supernovae, cosmic chronometers, and growth rate measurements. Our results suggest a mild preference for an open geometry, although all models remain consistent with a flat universe at the $1\sigma$ level. Notably, Bayesian information criteria indicate that the nonflat teleparallel scenario with a vanishing potential is strongly favored over the standard $\mathrm{\Lambda }\mathrm{CDM}$ model. Furthermore, all teleparallel scenarios are compatible with local determinations of the Hubble constant and exhibit better agreement with low-redshift structure formation data compared to $\mathrm{\Lambda }\mathrm{CDM}$. These findings highlight the potential of nonflat teleparallel gravity to address current observational tensions and motivate its further investigation as a viable alternative to standard cosmology.

During the postmerger regime of a binary black hole merger, the gravitational wave signal consists of a superposition of quasinormal modes (QNMs) of the remnant black hole. It has been observed empirically, primarily through numerical simulations and heuristic arguments, that the infalling radiation at the horizon is also composed of a superposition of QNMs. In this paper we provide an analytic explanation for this observation in the perturbative regime. Our analysis is based on a characteristic initial value formulation where data is prescribed on the horizon (modeled as a perturbed isolated horizon), and on a transversal null hypersurface which registers the outgoing radiation. This allows us to reformulate the traditional QNM problem in a fully four-dimensional setting. Using a mode decomposition, we demonstrate that the radiation modes crossing $\mathcal{H}$ are highly correlated with the outgoing modes crossing $\mathcal{I}$, and provide explicit expressions linking ${\tilde{\mathrm{\Psi }}}_0$ at the horizon with ${\tilde{\mathrm{\Psi }}}_4$ at null infinity. Hence, we analytically demonstrate that measuring the ringdown signal at null infinity allows us to probe the dynamics of the horizon.

We explore the universal symmetries of the black hole photon ring in a wide range of non-Kerr spacetimes, including the Kerr-Newman, Kerr-Sen, Kerr-Bardeen, and Kerr-Hayward metrics. The demagnification exponent ($\gamma$) controls the size and flux scaling of higher-order images, which appear in the photon ring, the time delay ($\tau$) determines the timing of their appearance, and the rotation parameter ($\delta$) relates their relative orientations on the image plane. Our investigation reveals that these critical parameters respond distinctly to variations in black hole spin, generalized charge, and observer inclination, establishing them as complementary probes of spacetime geometry: $\gamma$ is predominantly influenced by charge and spin, $\tau$ is strongly affected by inclination, especially for near-extremal black holes, and $\delta$ is highly sensitive to spin. Notably, we find that the time delay provides an independent constraint on shadow size for polar observers, while the rotation parameter facilitates metric-independent spin measurements. Specifically, for Kerr black holes, the total variation in $\gamma$, $\tau$, and $\delta$ across all possible inclinations and spins is $\lesssim 20\%$, $\lesssim 10\%$, and $\lesssim 60\%$, respectively. By contrast, the Kerr shadow radius varies by only $\lesssim 8\%$. A future joint measurement of these critical parameters—along with the black hole shadow size—will enable precise spacetime characterization, including measurements of the spin, inclination, and generalized charge.

This study explores the impact of cosmic curvature on structure formation through general relativistic first-order perturbation theory. We analyze continuity and Euler equations, incorporating cosmic curvature into Einstein equations. Emphasizing late-time dynamics, we investigate matter density contrast evolution in the presence of cosmic curvature, with a specific focus on sub-Hubble scales. Solving the evolution equation, we conduct data analysis using cosmic chronometers, baryon acoustic oscillations from Dark Energy Spectroscopic Instrument Data Release 2 (including $r_d$ constraint from cosmic microwave background), type Ia supernova observations from $\mathrm{Pantheon}+$ sample, logarithmic growth rate $f$ data, and $f{\sigma }_8$ data. While constraints on some parameters remain consistent, inclusion of cosmic curvature loosens constraints on ${\mathrm{\Omega }}_{\mathrm{m}0}$ and ${\sigma }_{8,0}$ in $\mathrm{\Lambda }$ cold dark matter (CDM) and $w_0\mathrm{CDM}$ models. The nonphantom behavior of dark energy proves more favorable in the $w_0\mathrm{CDM}$ model, whereas in the Chevallier-Polarski-Linder (CPL) model, there is certain evidence for nonphantom behavior at lower redshift and phantom behavior at higher redshift. Interestingly, we find certain evidence for nonzero cosmic curvature in the $\mathrm{\Lambda }\mathrm{CDM}$ model, but no evidence for it in both the $w_0\mathrm{CDM}$ and CPL models, which indirectly proves the nondegeneracy between dynamical dark energy and cosmic curvature.

We systematically analyze the implications of statistical noise within numerical derivatives on simulation-based Fisher forecasts for large scale structure surveys. Noisy numerical derivatives resulting from a finite number of simulations, $N_{\mathrm{sims}}$, act to bias the associated Fisher forecast such that the resulting marginalized constraints can be significantly tighter than the noise-free limit. We show the source of this effect can be traced to the influence of the noise on the marginalization process. Parameters such as the neutrino mass, $M_{\nu }$, for which higher-order forward differentiation schemes are commonly used, are more prone to noise; the predicted constraints can be akin to those purely from a random instance of statistical noise even using $(1\mathrm{Gpc}/h{)}^3$ simulations with $N_{\mathrm{sims}}=500$ realizations. We demonstrate how derivative noise can artificially reduce parameter degeneracies and seemingly null the effects of adding nuisance parameters to the forecast, such as halo occupation distribution fitting parameters. We mathematically characterize these effects through a full statistical analysis, and demonstrate how confidence intervals for the true noise-free, $N_{\mathrm{sims}}\to \infty$, Fisher constraints can be recovered even when noise comprises a consequential component of the measured signal. The findings and approaches developed here are important for ensuring simulation-based analyses can be accurately used to assess upcoming survey capabilities.

In the millihertz frequency band, the stochastic gravitational-wave background can be composed of both astronomical and cosmological sources, both can be anisotropic. Numerically depicting these anisotropies can be critical in revealing the underlying properties of their origins. For the first time, we perform a theoretical analysis of the constraining ability of TianQin on multiple moments of the stochastic background. First, we find that with a one year operation, for a background with a signal-to-noise ratio of 16, TianQin can recover the multiple moments up to $l=4$. We also identified a unique feature of the stochastic background sky map, which is the mirror symmetry along the fixed orbital plane of TianQin. Finally, we explain the difference in anisotropy recovering ability between TianQin and LISA, by employing the criteria of the singularity of the covariance matrix (which is the condition number). We believe that the findings of this work can provide an important reference to future stochastic background analysis pipelines. It can also serve as a guideline for designing better gravitational-wave detectors aiming to decipher anisotropies in the stochastic background.

We study the low energy dynamics of a system of two coupled real scalar fields in $1+1$ dimensions using the flow equation approach of the similarity renormalization group in a wavelet basis. This paper presents an extension of the work by Michlin et al. [Multiresolution decomposition of quantum field theories using wavelet bases, Phys. Rev. D 95, 094501 (2017).] at one resolution higher. We also present the analysis of a model of two scalar fields coupled through a generally quadratic interaction in $1+1$ dimensions using wavelet-based flow equations. We demonstrate that the specifically chosen generator flows the Hamiltonian into a block diagonal form with each diagonal block being associated with a fixed resolution. The wavelet basis is known to transform the scalar field theory into a model of coupled localized oscillators, each of which is labeled by location and resolution indices. The chosen interaction represents the coupling between two types of oscillators at the same location and resolution index. There is no coupling between oscillators across locations and resolutions. We show that wavelet-based flow equations carry out scale separation while maintaining the interactions between the two scalar fields at each resolution. The effective Hamiltonian associated with the coarsest resolution is shown to correctly reproduce the normal mode frequencies of the model.