We study the dynamical formation of scalar monopole and dipole hair in scalar Gauss-Bonnet theory and dynamical Chern-Simons theory. We prove that the spherically symmetric mode of the dipole hair is completely determined by the product of the mass of the spacetime and the value of the monopole hair. We then show that the dynamics of the $\ell =1$ mode of the dipole hair is intimately tied to the appearance of the event horizon during axisymmetric collapse, which results in the radiation of certain modes that could have been divergent in the future of the collapse. We confirm these analytical predictions by simulating the gravitational collapse of a rapidly rotating neutron star in the decoupling limit, both in scalar Gauss-Bonnet and dynamical Chern-Simons theory. Our results, combined with those in Hegade K. R. et al. [Phys. Rev. D 105, 064041 (2022)], provide a clear physical picture of the dynamics of scalar monopole and dipole radiation in axisymmetric and spherical gravitational collapse in these theories.

The Gibbons-Werner method for the gravitational deflection angle of unbound particles in static spherically symmetric spacetimes is based on the Jacobi metric and Gauss-Bonnet theorem. When it is extended to bound massive particles, there exist two difficulties: (a) Bound orbits may overlap with themselves azimuthally. To extend the definition of deflection angle for unbound orbits to bound orbits, we divide the bound orbit into multiple segments such that each segment does not overlap with itself azimuthally and can be regarded as an unbound orbit. (b) The infinite region constructed for unbound orbits in the Gibbons-Werner method is invalid for bound orbits, since the Jacobi metric of bound massive particles is singular at the far region. To construct a suitable region for bound orbits, we adopt the generalized Gibbons-Werner method proposed in our last work [Huang and Cao, Phys. Rev. D 106, 104043 (2022)], so that the unphysical region in Jacobi space is avoided. What is more, taking the Schwarzschild spacetime as an example, we show the details of the calculation and obtain an analytical expression of the deflection angle between two arbitrary points on the orbit.

We study the linear stability of black holes in Maxwell-Horndeski theories where a $U(1)$ gauge-invariant vector field is coupled to a scalar field with the Lagrangian of full Horndeski theories. The perturbations on a static and spherically symmetric background can be decomposed into odd- and even-parity modes under the expansion of spherical harmonics with multipoles $l$. For $l\ge 2$, the odd-parity sector contains two propagating degrees of freedom associated with the gravitational and vector field perturbations. In the even-parity sector, there are three dynamical perturbations arising from the scalar field besides the gravitational and vector field perturbations. For these five propagating degrees of freedom, we derive conditions for the absence of ghost/Laplacian stabilities along the radial and angular directions. We also discuss the stability of black holes for $l=0$ and $l=1$, in which case no additional conditions are imposed to those obtained for $l\ge 2$. We apply our general results to Einstein-Maxwell-dilaton-Gauss-Bonnet theory and Einstein-Born-Infeld-dilaton gravity and show that hairy black hole solutions present in these theories can be consistent with all the linear stability conditions. In regularized four-dimensional Einstein-Gauss-Bonnet gravity with a Maxwell field, however, exact charged black hole solutions known in the literature are prone to instabilities of even-parity perturbations besides a strong coupling problem with a vanishing kinetic term of the radion mode.

Using numerical methods, we examine the dynamics of nonlinear perturbations in the expanding time direction, under a Gowdy symmetry assumption, of Friedmann-Lemaître-Robertson-Walker (FLRW) fluid solutions to the Einstein-Euler equations with a positive cosmological constant $\mathrm{\Lambda }>0$ and a linear equation of state $p=K\rho$ for the parameter values $1/3<K<1$. This paper builds upon the numerical work in [arXiv:2209.06982] in which the simpler case of a fluid on a fixed FLRW background spacetime was studied. The numerical results presented here confirm that the instabilities observed in [arXiv:2209.06982] are also present when coupling to gravity is included as was previously conjectured in [A. D. Rendall, Asymptotics of solutions of the Einstein equations with positive cosmological constant, Ann. Henri Poincaré 5, 1041 (2004); J. Speck, The stabilizing effect of spacetime expansion on relativistic fluids with sharp results for the radiation equation of state, Arch. Ration. Mech. Anal. 210, 535 (2013)]. In particular, for the full parameter range $1/3<K<1$, we find that the fractional density gradient of the nonlinear perturbations develop steep gradients near a finite number of spatial points and becomes unbounded there at future timelike infinity.

The origin of our Universe’s cosmological magnetic fields remains a mystery. In this study, we consider whether these magnetic fields could have been generated in the early Universe by a population of charged, spinning primordial black holes. To this end, we calculate the strength and correlation length of the magnetic fields generated by this population, and describe their evolution up to the current epoch. We find that near-extremal black holes in the mass range $M\sim {10}^{28}–{10}^{36}\mathrm{g}$ could potentially generate magnetic fields with present day values as large as $B\sim {10}^{-20}–{10}^{-15}\mathrm{G}$; those with $M\gtrsim {10}^{38}\mathrm{g}$ could have produced even larger fields $B\gtrsim {10}^{-14}\mathrm{G}$. To motivate this scenario, we briefly discuss how new physics may have induced a chemical potential which could have briefly maintained the black holes in an electrically charged state in the early Universe. Finally, we comment on a correlation between the parameters of the cosmological magnetic field and the stochastic gravitational wave background coming from the merger of primordial black hole binaries as the primary observable signature of this scenario.

Early dark energy (EDE), whose cosmological role is localized in time around the epoch of matter-radiation equality in order to resolve the Hubble tension, introduces a new coincidence problem: Why should the EDE dynamics occur near equality if EDE is decoupled from both matter and radiation? The resolution of this problem may lie in an early dark sector (EDS), wherein the dark matter mass is dependent on the EDE scalar field. Concretely, we consider a Planck-suppressed coupling of EDE to dark matter, as would naturally arise from breaking of the global $U(1)$ shift symmetry of the former by quantum gravity effects. With a sufficiently flat potential, the rise to dominance of dark matter at matter-radiation equality itself triggers the rolling and subsequent decay of the EDE. We show that this trigger EDS model can naturally resolve the EDE coincidence problem at the background level without any fine-tuning of the coupling to dark matter or of the initial conditions. When fitting to current cosmological data, including that from the local distance ladder and the low-redshift amplitude of fluctuations, the trigger EDS maximum-likelihood model performs comparably to EDE for resolving the Hubble tension, achieving $H_0=71.2\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. However, fitting the Planck cosmic microwave background data requires a specific range of initial field positions to balance the scalar field fluctuations that drive acoustic oscillations, providing testable differences with other EDE models.

We examine effective field theories (EFTs) with a continuum sector in the presence of gravity. We first explain, via arguments based on central charge and species scale, that an EFT with a free continuum cannot consistently couple to standard (i.e., 4D Einstein) gravity. It follows that EFTs with a free or nearly free continuum must have either a finite number of degrees of freedom or nonstandard gravity. The latter claim is realized for holographically defined continuum models. We demonstrate this by computing the deviations from standard gravity in a specific 5D scalar-gravity system that gives rise to a gapped continuum (i.e., the linear dilaton background). We find an $R^{-2}$ deviation from the Newtonian potential. At finite temperature, we find an energy density with matterlike behavior in the brane Friedmann equation, holographically induced from the bulk geometry. Thus, remarkably, a braneworld living in the linear dilaton background automatically contains dark matter. We also present a slightly more evolved asymptotically AdS linear dilaton model, for which the deviations exhibit a transition between AdS and linear dilaton behaviors.

We detail the construction of electric string solutions in $SU(2)$ Yang-Mills-Higgs theory with a scalar in the fundamental representation and discuss the properties of the solution. We show that Schwinger gluon pair production in the electric string background is absent. A similar construction in other models, such as with an adjoint scalar field and the electroweak model, does not yield solutions.

The scalar sector of the 3-3-1 model with an axionlike particle is studied in detail. In the model under consideration, there are two kinds of scalar fields: the bilepton scalars carrying lepton number two and the ordinary ones without lepton number. We show that there is no mixing among these two kinds of scalar fields. We analyze in detail the $CP$-odd scalar sector of the model to find the physical fields of the axionlike particle and a pseudoscalar with mass in the range 100 GeV to 1 TeV. The results are different from others which have been published before. The $CP$-even scalar sector of the model is analyzed as well. The results of our analysis of the scalar sector allow us to accommodate scalar masses in the 100 GeV–1 TeV region. Furthermore we analyze the implications of the model in several flavor changing neutral decays of the top quark as well as in rare top quark decays. Besides that, the leptonic decays of the SM like Higgs boson as well as the meson oscillations are also analyzed. Our numerical analysis show that the model under consideration is consistent with the experimental constraints imposed by these processes.

We study possible current and future low-energy signals of the gauge leptoquark in quark-lepton $SU(4)$ unification à la Pati-Salam. Taking fully into account the freedom in the generation mixing between quarks and leptons, we compile a catalog of observables which currently form a border of the excluded part of the parameter space—hot candidates for first signals of new physics. We also determine the sensitivity needed in order to inspect a currently allowed part of the parameter space for several other measurements which are not included in this catalog. We improve older similar works on this topic by taking into account more (and more recent) experimental measurements and by scanning the parameter space more densely. Furthermore, we study in a similar manner the $SU(4)$ models with a small number of generations of extra leptons. We also discuss the minimal number of leptons needed in order to alleviate the contemporary discrepancies in the neutral-current $B$-meson decays.

We apply the tensor renormalization group method to the ($1+1$)-dimensional SU(2) principal chiral model at finite chemical potential with the use of the Gauss-Legendre quadrature to discretize the SU(2) Lie group. The internal energy at vanishing chemical potential $\mu =0$ shows good consistency with the prediction of the strong and weak coupling expansions. This indicates an effectiveness of the Gauss-Legendre quadrature for the partitioning of the SU(2) Lie group. In the finite density region with $\mu \ne 0$ at the strong coupling we observe the Silver-Blaze phenomenon for the number density.

Using a set of field equations in the null surface formulation we obtain the linearized coupling between the gravitational and matter fields. We first derive a formula for the metric of the space time and then we use this formula to study the scattering of incoming gravitational waves when matter is present, obtaining explicit formulae relating the radiation modes at past and future null infinity for a general asymptotically flat spacetime. An example application is made at the end of this work when the matter field is a massless real scalar field. The relevance of this result for a perturbation procedure is discussed.

We consider quantum field theory with self-interactions in various patches of Minkowski and de Sitter spacetimes. Namely, in Minkowski spacetime we consider separately the right (left) Rindler wedge, past wedge, and future wedge. In de Sitter spacetime we consider expanding the Poincaré patch, the static patch, the contracting Poincaré patch, and the global de Sitter itself. In all cases we restrict our considerations to the isometry invariant states leading to maximally analytic propagators. We prove that loop corrections in the right (left) Rindler wedge, in the past wedge (of Minkowski spacetime), in the static patch and in the expanding Poincaré patch (of de Sitter spacetime) respect the isometries of the corresponding symmetric spacetimes. All these facts are related to the causality and analyticity properties of the propagators for the states that we consider. At the same time in the future wedge, in the contracting Poincaré patch and in the global de Sitter spacetime infrared effects violate the isometries.

The UV cutoff on a quantum field theory (QFT) can explicitly break or conserve the Poincaré (translation) symmetry. And the very same cutoff can explicitly break or conserve the gauge symmetry. In the present work, we perform a systematic study of the UV cutoff in regard to its gauge and Poincaré properties and construct UV completions restoring the broken gauge symmetry. In the case of the Poincaré-conserving UV cutoff, we find that the gauge symmetry gets restored via the Higgs mechanism. In the case of Poincaré-breaking UV cutoff, however, we find that the flat spacetime affine curvature takes the place of the Higgs field and, when taken to curved spacetime, gauge symmetry gets restored at the extremum of the metric-affine action. We also find that gravity emerges at the extremum if the QFT under concern consists of new particles beyond the known ones. The resulting emergent gravity plus renormalized QFT setup has the potential to reveal itself in various astrophysical, cosmological, and collider phenomena.

This study examines on-shell supersymmetry breaking in the Abelian $\mathcal{N}=1$ Chern-Simons-matter model within a three-dimensional spacetime. The classical Lagrangian is scale invariant, but two-loop radiative corrections to the effective potential break this symmetry, along with gauge and on-shell supersymmetry. To investigate this issue, the renormalization group equation is used to calculate the two-loop effective potential.

We build an effective-one-body (EOB) Hamiltonian at third post-Newtonian (3PN) order in scalar-tensor (ST) and Einstein-scalar-Gauss-Bonnet (ESGB) theories of gravity. The latter is an extension of general relativity that predicts scalar hair for black holes. We start from the known two-body Lagrangian at 3PN order, and use order-reduction methods to construct its ordinary Hamiltonian counterpart. We then reduce the conservative two-body dynamics to the (nongeodesic) motion of a test particle in an effective metric by means of canonical transformations. The resulting EOB Hamiltonian is a modification of the general relativistic Hamiltonian, and already at 3PN order, it must account for nonlocal-in-time tail contributions. We include the latter beyond circular orbits and up to sixth order in the binary’s orbital eccentricity. We finally calculate the orbital frequency at the innermost stable circular orbit of binary black holes in the shift-symmetric ESGB model. Our work extends the work of Julié and Deruelle [Phys. Rev. D 95, 124054 (2017)], and it is an essential step toward the accurate modeling of gravitational waveforms beyond general relativity.

When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code bamps in the form of fully adaptive, physics-agnostic hp refinement. We describe the foundations of mesh refinement in the context of spectral element methods, the precise algorithm used to perform refinement in bamps, as well as several indicator functions used to drive it. Finally, we test the performance, scaling, and the accuracy of the code in treating several 1D and 2D example problems, showing clear improvements over static mesh configurations. In particular, we consider a simple nonlinear wave equation, the evolution of a real scalar field minimally coupled to gravity, as well as nonlinear gravitational waves.

We study the axial anomaly of Dirac spinors on gravitational instanton backgrounds in the context of nonlinear electrodynamics. In order to do so, we consider Einstein gravity minimally coupled to a recently proposed conformal electrodynamics that enjoys duality transformation invariance. These symmetries allow us to generalize the Eguchi-Hanson configuration while preserving its geometry. We then compute the Dirac index of the nonlinearly charged Eguchi-Hanson and Taub-NUT configurations. We find that there is an excess of positive chiral Dirac fermions over the negative ones which triggers the anomaly.

The possibility of obtaining symbolic expressions for cosmic backreaction is explored through a case study of so-called 2-region models. By using the publicly available symbolic regression algorithm AI Feynman, it is shown that the kinematical backreaction from a single 2-region model can be well described as a function of the mean redshift (or, equivalently, the volume averaged scale factor). A single expression depending on the redshift/scale factor as well as a model parameter, $f$, that can accurately describe the backreaction for a significant range of models is naturally more complicated but is also achieved with percent-level accuracy. Datasets of redshift drift in the 2-region models are also considered. Again utilizing AI Feynman, expressions for the redshift drift are found. In particular, an expression for the difference between the mean redshift drift and the drift of the mean redshift in terms of the kinematical backreaction is easily obtained for a single 2-region model. An accurate symbolic expression that describes this difference for an array of 2-region models is achieved by using the redshift as a feature instead of the kinematical backreaction.

OJ 287 is a blazar thought to be a binary system containing a $\simeq 18\mathrm{billion}$ solar mass primary black hole accompanied by a $\simeq 150\mathrm{million}$ solar mass secondary black hole in an eccentric orbit, which triggers electromagnetic flares twice in every $\simeq 12\mathrm{year}$ orbital period when it traverses the accretion disk of the primary. The times of these emissions are consistent with the predictions of general relativity calculated to the 4.5th post-Newtonian order. The orbit of the secondary black hole samples the gravitational field at distances between $\mathcal{O}(10)$ and $\mathcal{O}(50)$ Schwarzschild radii around the primary, and hence is sensitive to the possible presence of a dark matter spike around it. We find that the agreement of general-relativistic calculations with the measured timings of flares from OJ 287 constrains the mass of such a spike to $\lesssim 3\%$ of the primary mass.