We give a proof of the equivalence of the electric-magnetic duality on one side and helicity conservation of the tree-level amplitudes on the other side within general models of nonlinear electrodynamics. Using modified Feynman rules derived from a generalized normal ordered Lagrangian, we discuss the interrelation of the above two properties of the theory also at higher loops. As an illustration we present two explicit examples; namely we find the generalized normal ordered Lagrangian for the Born-Infeld theory and derive a semiclosed expression for the Lagrangian of the Bossard-Nicolai model (in terms of the weak field expansion with explicitly known coefficients) from its normal ordered form.

We calculate the divergent part of the one-loop effective action in curved spacetime for a particular class of second-order vector field operators with a degenerate principal part. The principal symbol of these operators has the structure of a longitudinal projector. In this case, standard heat-kernel techniques are not directly applicable. We present a method which reduces the problem to a nondegenerate scalar operator for which standard heat-kernel techniques are available. Interestingly, this method leads to the identification of an effective metric structure in the longitudinal sector. The one-loop divergences are compactly expressed in terms of invariants constructed from this metric.

We study superradiance effect in the ghost-free theory. We consider a scattering of a ghost-free scalar massless field on a rotating cylinder. We assume that cylinder is thin and empty inside, so that its interaction with the field is described by a deltalike potential. This potential besides the real factor, describing its height, contains also imaginary part, responsible for the absorption of the field. By calculating the scattering amplitude we obtained the amplification coefficient both in the local and nonlocal (ghost-free) models and demonstrated that in the both cases it is greater than 1 when the standard superradiance condition is satisfied. We also demonstrated that dependence of the amplification coefficient on the frequency of the scalar field wave may be essentially modified in the nonlocal case.

We extend the class of recently formulated scalar-nonmetricity theories by coupling a five-parameter nonmetricity scalar to a scalar field and considering a mixed kinetic term between the metric and the scalar field. The symmetric teleparallel constraint is invoked by Lagrange multipliers or by inertial variation. The equivalents for the general relativity and ordinary (curvature-based) scalar-tensor theories are obtained as particular cases. We derive the field equations, discuss some technical details, e.g., debraiding, and formulate the Hamilton-like approach.

In this article we construct an extended relativistic $f(R)$ theory of gravity with matter-curvature couplings $F(R,{\mathcal{L}}_{\mathrm{matt}})$ for which its weak-field limit of approximation recovers the simplest version of MOND. We do this by (a) performing an order-of-magnitude calculation and (b) perturbing the resulting field equations of the theory to the weak-field limit. We also compute the geodesic equation of the resulting theory and show that it has an extra force, a fact that commonly appears in general matter-curvature couplings.

The damped harmonic gauge is important for numerical relativity computations based on the generalized harmonic formulation of Einstein’s equations and is used to reduce coordinate distortions near binary black hole mergers. However, currently there is no prescription to construct quasiequilibrium binary black hole initial data in this gauge. Instead, initial data are typically constructed using a superposition of two boosted analytic single black hole solutions as free data in the solution of the constraint equations. Then, a smooth time-dependent gauge transformation is done early in the evolution to move into the damped harmonic gauge. Using this strategy to produce initial data in the damped harmonic gauge would require the solution of a single black hole in this gauge, which is not known analytically. In this work we construct a single boosted, spinning, equilibrium black hole in damped harmonic coordinates as a regular time-independent coordinate transformation from Kerr-Schild coordinates. To do this, we derive and solve a set of four coupled, nonlinear, elliptic equations for this transformation, with appropriate boundary conditions. This solution can now be used in the construction of damped harmonic initial data for binary black holes.

We study the hidden symmetries, the symmetries associated with Killing tensors, of the near-horizon geometry of odd-dimensional Kerr-AdS-NUT black holes in two limits: generic extremal and extremal vanishing horizon (EVH) limits. Starting from a Kerr-AdS-NUT black hole in ellipsoidal coordinates which admit integrable geodesic equations, we obtain the near-horizon extremal and EVH geometries and their principal and Killing tensors by taking the near-horizon limit. We explicitly demonstrate that geodesic equations are separable and integrable on these near-horizon geometries. We also compute the constants of motion and read the Killing tensors of these near-horizon geometries from the constants of motion. As expected, they are the same as the Killing tensors given by taking the near-horizon limit.

We have obtained a Finslerian Reissner-Nordström solution where it is asymptotic to a Finsler spacetime with a constant flag curvature while $r\to \infty$. The covariant derivative of a modified Einstein tensor in a Finslerian gravitational field equation for this solution is conserved. The symmetry of the special Finslerian Reissner-Nordström spacetime, namely, Finsler spacetime with a constant flag curvature, has been investigated. It admits four independent Killing vectors. The Finslerian Reissner-Nordström solution differs from the Reissner-Nordström metric only in two-dimensional subspace, and our solution requires that its two-dimensional subspace has a constant flag curvature. We have obtained the eigenfunction of the Finslerian Laplacian operator of the “Finslerian sphere,” namely, a special subspace with a positive constant flag curvature. The eigenfunction is of the form ${\overline{Y}}_l^m=Y_l^m+{\epsilon }^2(C_{l+2}^m{Y}_{l+2}^m+C_{l-2}^m{Y}_{l-2}^m)$ in powers of the Finslerian parameter $\epsilon$, where $C_{l+2}^m$ and $C_{l-2}^m$ are constant. However, the eigenvalue depends on both $l$ and $m$. The eigenvalues corresponding to $Y_1^0$ remain the same with the Riemannian Laplacian operator and the eigenvalues corresponding to $Y_1^{\pm 1}$ are different. This fact just reflects the symmetry of the Finslerian sphere, which admits a $z$-axis rotational symmetry and breaks other symmetry of the Riemannian sphere. The eigenfunction of the Finslerian Laplacian operator implies that monopolar and dipolar terms of the multipole expansion of gravitational potential are unchanged and other multipole terms are changed.

We study null geodesic congruences (NGCs) in the presence of spacetime torsion, recovering and extending results in the literature. Only the highest spin irreducible component of torsion gives a proper acceleration with respect to metric NGCs, but at the same time obstructs abreastness of the geodesics. This means that it is necessary to follow the evolution of the drift term in the optical equations, and not just shear, twist and expansion. We show how the optical equations depend on the non-Riemannian components of the curvature, and how they reduce to the metric ones when the highest spin component of torsion vanishes.

For the first time, we construct an inspiral-merger-ringdown waveform model within the effective-one-body formalism for spinning, nonprecessing binary black holes that includes gravitational modes beyond the dominant $(\ell ,|m|)=(2,2)$ mode, specifically $(\ell ,|m|)=(2,1),(3,3),(4,4),(5,5)$. Our multipolar waveform model incorporates recent (resummed) post-Newtonian results for the inspiral and information from 157 numerical-relativity simulations, and 13 waveforms from black-hole perturbation theory for the (plunge-)merger and ringdown. We quantify the improvement in accuracy when including higher-order modes by computing the faithfulness of the waveform model against the numerical-relativity waveforms used to construct the model. We define the faithfulness as the match maximized over time, phase of arrival, gravitational-wave polarization and sky position of the waveform model, and averaged over binary orientation, gravitational-wave polarization and sky position of the numerical-relativity waveform. When the waveform model contains only the (2,2) mode, we find that the averaged faithfulness to numerical-relativity waveforms containing all modes with $\ell \le 5$ ranges from 90% to 99.9% for binaries with total mass $20–200M_{\odot }$ (using the Advanced LIGO’s design noise curve). By contrast, when the (2,1), (3,3), (4,4), (5,5) modes are also included in the model, the faithfulness improves to 99% for all but four configurations in the numerical-relativity catalog, for which the faithfulness is greater than 98.5%. Starting from the complete inspiral-merger-ringdown model, we develop also a (stand-alone) waveform model for the merger-ringdown signal, calibrated to numerical-relativity waveforms, which can be used to measure multiple quasi-normal modes. The multipolar waveform model can be extended to include spin-precessional effects, and will be employed in upcoming observing runs of Advanced LIGO and Virgo.

We study the gravitational instability of a general relativistic complex scalar field with a quartic self-interaction in an infinite homogeneous static background. This quantum relativistic Jeans problem provides a simplified framework to study the formation of the large-scale structures of the Universe in the case where dark matter is made of a scalar field. The scalar field may represent the wave function of a relativistic self-gravitating Bose-Einstein condensate. Exact analytical expressions for the dispersion relation and Jeans length ${\lambda }_J$ are obtained from a hydrodynamical representation of the Klein-Gordon-Einstein equations [ and , Phys. Rev. D 92, 023510 (2015)]. We compare our results with those previously obtained with a simplified relativistic model [, , and , Mon. Not. R. Astron. Soc. 215, 575 (1985)]. When relativistic effects are fully accounted for, we find that the perturbations are stabilized at very large scales of the order of the Hubble length ${\lambda }_H$. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with a repulsive self-interaction, and for bosons with an attractive self-interaction (QCD axions and ultralight axions). We show that the Jeans instability is inhibited in the ultrarelativistic regime of the scalar field (early Universe and radiationlike era) because the Jeans length is of the order of the Hubble length (${\lambda }_J\sim {\lambda }_H$), except when the self-interaction of the bosons is attractive. By contrast, structure formation can take place in the nonrelativistic regime of the scalar field (matterlike era) for ${\lambda }_J\le \lambda \le {\lambda }_H$. Since the scalar field has a nonzero Jeans length due to its quantum nature (Heisenberg uncertainty principle or quantum pressure due to the self-interaction of the bosons), it appears that the wave properties of the scalar field can stabilize gravitational collapse at small scales, providing halo cores and suppressing small-scale linear power. This may solve the CDM crisis such as the cusp problem and the missing satellite problem. We also compare our results with those obtained in the case where dark matter is made of fermions instead of bosons.

In this paper, we show how the structure of the landscape potential of the primordial Universe may be probed through the properties of the primordial density perturbations responsible for the origin of the cosmic microwave background anisotropies and the large-scale structure of our Universe. Isocurvature fields—fields orthogonal to the inflationary trajectory—may have fluctuated across the barriers separating local minima of the landscape potential during inflation. We analyze how this process could have impacted the evolution of the primordial curvature perturbations. If the typical distance separating consecutive minima of the landscape potential and the height of the potential barriers are smaller than the Hubble expansion rate parametrizing inflation, the probability distribution function of isocurvature fields becomes non-Gaussian due to the appearance of bumps and dips associated with the structure of the potential. We show that this non-Gaussianity can be transferred to the statistics of primordial curvature perturbations if the isocurvature fields are coupled to the curvature perturbations. The type of non-Gaussian structure that emerges in the distribution of curvature perturbations cannot be fully probed with the standard methods of polyspectra; instead, the probability distribution function is needed. The latter is obtained by summing all the $n$-point correlation functions. To substantiate our claims, we offer a concrete model consisting of an axionlike isocurvature perturbation with a sinusoidal potential and a linear derivative coupling between the isocurvature and curvature field. In this model, the probability distribution function of the curvature perturbations consists of a Gaussian function with small superimposed oscillations reflecting the isocurvature axion potential.

Models of spontaneous baryogenesis have an interaction term ${\partial }_{\mu }\theta j_B^{\mu }$ in the Lagrangian, where $j_B^{\mu }$ is the baryonic current and $\theta$ can be a pseudo-Nambu-Goldstone boson. Since the time component of this term, $\dot{\theta }{j}_B^0$, equals $\dot{\theta }{n}_B$ for a spatially homogeneous current, it is usually argued that this term implies a splitting in the energy of baryons and antibaryons, thereby providing an effective chemical potential for baryon number. In thermal equilibrium, one then obtains $n_B\sim \dot{\theta }{T}^2$. We however argue that a term of this form in the Lagrangian does not contribute to the single particle energies of baryons and antibaryons. We show this for both fermionic and scalar baryons. However, similar to some recent work, we find that despite the above result the baryon number density obtained from a Boltzmann equation analysis can be proportional to $\dot{\theta }{T}^2$. Our arguments are very different from that in the standard literature on spontaneous baryogenesis.

We examine the hypothesis of decaying heavy dark matter (HDM) in the context of the IceCube highest energy neutrino events and recent limits on the diffuse flux of high-energy photons. We consider dark matter (DM) particles $X$ of mass $10^6\le M_X\le {10}^{16}\mathrm{GeV}$ decaying on tree level into $X\to \nu \overline{\nu }$, $X\to e^{+}{e}^{-}$, and $X\to q\overline{q}$. The full simulation of hadronic and electroweak decay cascades and the subsequent propagation of the decay products through the interstellar medium allows us to determine the permitted values of $M_X$. We show that for leptonic decay channels it is possible to explain the IceCube highest energy neutrino signal without overproducing high-energy photons for $M_X\lesssim 5.5\times {10}^7\mathrm{GeV}$ and $1.5\times {10}^8\lesssim M_X\lesssim 1.5\times {10}^9\mathrm{GeV}$, while hadronic decays contradict the gamma-ray limits for almost the whole range of $M_X$ values considered. The leptonic hypothesis can be probed by operating and planned gamma-ray observatories: For instance, the currently upgrading Carpet experiment will be capable to test a significant part of the remaining parameter window within one year of observation.

We study the distribution of dark matter in the nonlinear regime in a model in which the primordial fluctuations include, in addition to the dominant primordial Gaussian fluctuations generated by the standard $\mathrm{\Lambda }\mathrm{CDM}$ cosmological model, the effects of a cosmic string wake set up at the time of equal matter and radiation, making use of cosmological $N$-body simulations. At early times, the string wake leads to a planar overdensity of dark matter. We study how this non-Gaussian pattern of a cosmic string wake evolves in the presence of the Gaussian perturbations, making use of wavelet and ridgeletlike statistics specifically designed to extract string wake signals. At late times, the Gaussian fluctuations disrupt the string wake. We find that for a string tension of $G\mu ={10}^{-7}$, a value just below the current observational limit, the effects of a string wake can be identified in the dark matter distribution, using the current level of the statistical analysis, down to a redshift of $z=10$.

In order to gain deeper insight into the physics of the novel rotating solution of nonideal transverse magnetohydrodynamics (MHD), presented in one of our recent works, we replace the previously considered Maxwell theory with the $\mathcal{CP}$ violating Maxwell-Chern-Simons (MCS) theory. In this way, dissipationless chiral magnetic (CM) and anomalous Hall (AH) currents appear in the MCS equation of motion, that, together with equations of relativistic hydrodynamics, builds the set of constitutive equations of the nonideal transverse Chern-Simons magnetohydrodynamics (CSMHD). We are, in particular, interested in the effect of these currents on the evolution of electromagnetic fields in a uniformly and longitudinally expanding quark-gluon plasma with chirality imbalance. Combining the constitutive equations of CSMHD under these assumptions, we arrive, as expected, at two distinct rotating and nonrotating solutions for electromagnetic fields. The rotation occurs with increasing rapidity and a constant angular velocity ${\omega }_0$. Remarkably, the relative angle between the electric and magnetic fields, $\delta$, turns out to be given by the coefficient of AH current ${\kappa }_E$ and the electric conductivity of the medium $\sigma$, as $\delta ={\tan }^{-1}({\kappa }_E/\sigma )$. Whereas the nonrotating solution implies the AH coefficient to be vanishing, and thus nonrotating electric and magnetic fields to be either parallel or antiparallel, the relative orientation of rotating electric and magnetic fields and the evolution of the CM conductivity ${\kappa }_B$ are strongly affected by nonvanishing ${\kappa }_E$. We explore the effect of positive and negative ${\omega }_0$ on the evolution of the CM current, and show, in particular, that a rotation of electromagnetic fields with negative ${\omega }_0$ implies a sign flip of the CM current in a chiral fluid with nonvanishing AH current.

The effective coupling of the Higgs boson to a gluon pair is one of the most important parameters to test the Standard Model and search for the new physics beyond. In this paper, we propose several new observables based on the jet energy profile to extract the effective coupling. The statistical uncertainties of the effective coupling extracted by using new observables are derived and estimated based on the simulation at the future $e^{+}{e}^{-}$ collider for 250 GeV center-of-mass energy and $5{\mathrm{ab}}^{-1}$ integrated luminosity. We found that the statistical uncertainties of effective coupling via the optimized observable can reach about 1.6% in the channels of a $Z$ boson decaying to lepton pairs and is reduced by 52% compared to the relevant uncertainties in the conventional approach. These new observables potentially can be helpful for the measurement of effective coupling at future $e^{+}{e}^{-}$ colliders.

We derive the equations of motion of relativistic, nonresistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like particles with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. In a first approximation, we assume the fluid to be nonresistive, which allows to express the electric field in terms of the magnetic field. We derive equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local thermodynamical equilibrium. We analyze the Navier-Stokes limit of these equations, reproducing previous results for the structure of the first-order transport coefficients. Finally, we truncate the system of equations for the irreducible moments using the 14-moment approximation, deriving the equations of motion of relativistic, nonresistive, second-order dissipative magnetohydrodynamics. We also give expressions for the new transport coefficients appearing due to the coupling of the magnetic field to the dissipative quantities.

A model for neutrino masses and mixing is presented using the seesaw mechanism. The model combines type-I and type-II seesaw contributions of which the latter dominates. The scalars and the leptons in the model are assigned $A4$ charges suitable to obtain the mass matrices required for the scheme. The type-II seesaw accommodates atmospheric mass splitting and maximal mixing in the atmospheric sector (${\theta }_{23}=\pi /4$). It is characterized by vanishing solar mass splitting and ${\theta }_{13}$ whereas the third neutrino mixing angle can acquire any value, ${\theta }_{12}^0$. Particular alternatives of ${\theta }_{12}^0$ viz. ${\theta }_{12}^0=35.3°$ (tribimaximal), $45.0°$ (bimaximal), $31.7°$ (golden ratio) are accounted for. Another choice of ${\theta }_{12}^0=0°$ (no solar mixing) is also considered. Incorporating the corrections provided by the subdominant type-I seesaw involves degenerate perturbation theory due to vanishing solar splitting in the type-II seesaw enabling the solar mixing angle to receive substantial corrections. Apart from amending the solar sector, the type-I seesaw also tunes all the neutrino oscillation parameters into the allowed ranges, thus interrelating them all. Thus, the model is testable in the light of future experimental data. As an example, ${\theta }_{23}$ emerges in the first (second) octant for normal (inverted) ordering. $CP$-violation is controlled by phases present in the right-handed Majorana neutrino mass matrix, $M_{\nu R}$. Only normal ordering is allowed if these phases are absent. If $M_{\nu R}$ is complex the Dirac $CP$-violating phase $\delta$, can be large, i.e., $\sim \pm \pi /2$, and inverted ordering is also allowed. T2K and NOVA preliminary data favoring normal ordering and $\delta \sim -\pi /2$ predicts lightest neutrino mass to be 0.05 eV or more within the model framework.