We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry $\mathrm{Diff}(M,\mathcal{F})$ to include a local $U(1)$ symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a scalar field, we find that the scalar field is not only stable in both the ultraviolet and infrared, but also free of the strong coupling problem, because of the presence of high-order spatial derivative terms of the scalar field. Furthermore, applying the theory to cosmology, we find that due to the additional $U(1)$ symmetry, the Friedmann-Robertson-Walker (FRW) universe is necessarily flat. We also investigate the scalar, vector, and tensor perturbations of the flat FRW universe, and derive the general linearized field equations for each kind of the perturbations.

We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the $\delta$-function singularity coming from the Zeeman spin interaction with the magnetic flux tube is solved through the self-adjoint extension method. Using two different approaches already known in the literature, both based on the self-adjoint extension method, we obtain the self-adjoint extension parameter to the bound state and scattering scenarios in terms of the physics of the problem. It is shown that such a parameter is the same for both situations. The method is general and is suitable for any quantum system with a singular Hamiltonian that has bound and scattering states.

Universal extra dimension (UED) models tend to favor a distinctively heavier Higgs mass than in the standard model and its supersymmetric extensions when the Kaluza-Klein (KK) scale is not much higher than the electroweak one, which we call the weak scale UED, in order to cancel the KK-top contributions to the $T$ parameter. Such a heavy Higgs, whose production through the gluon fusion process is enhanced by the KK-top loops, is a fairly model independent prediction of the weak scale UED models regardless of the brane-localized mass structure at the ultraviolet cutoff scale. We study its cleanest possible signature, the Higgs decay into a $Z$ boson pair and subsequently into four electrons and/or muons, in which all the four-momenta of the final states can be measured and both the $Z$ boson masses can be checked. We have studied the Higgs mass, 500 GeV (and also 700 GeV with $\sqrt{s}=14\mathrm{TeV}$), and have found that we can observe significant resonance with the integrated luminosity $10{\mathrm{fb}}^{-1}$ for six-dimensional UED models.

We study out-of-equilibrium dynamics of intense non-Abelian gauge fields. Generalizing the well-known Nielsen-Olesen instabilities for constant initial color-magnetic fields, we investigate the impact of temporal modulations and fluctuations in the initial conditions. This leads to a remarkable coexistence of the original Nielsen-Olesen instability and the subdominant phenomenon of parametric resonance. Taking into account that the fields may be correlated only over a limited transverse size, we model characteristic aspects of the dynamics of color flux tubes relevant in the context of heavy-ion collisions.

The mixing mechanism of axial-vectors $D_{s1}(2460)$ and $D_{s1}(2536)$ is studied via intermediate hadron loops, e.g., $D^{*}K$, to which both states have strong couplings. By constructing the two-state mixing propagator matrix that respects the unitarity constraint and calculating the vertex coupling form factors in a chiral quark model, we can extract the masses, widths, and mixing angles of the physical states. Two poles can be identified in the propagator matrix. One is at $\sqrt{s}=2454.5\mathrm{MeV}$ corresponding to $D_{s1}(2460)$ and the other at $\sqrt{s}=(2544.9-1.0i)\mathrm{MeV}$ corresponding to $D_{s1}(2536)$. For $D_{s1}(2460)$, a large mixing angle $\theta =47.5°$ between ${}^{3}P_1$ and ${}^{1}P_1$ is obtained. It is driven by the real part of the mixing matrix element and corresponds to ${\theta }^{\prime }=12.3°$ between the $j=1/2$ and $j=3/2$ state mixing in the heavy quark limit. For $D_{s1}(2536)$, a mixing angle $\theta =39.7°$, which corresponds to ${\theta }^{\prime }=4.4°$ in the heavy quark limit, is found. An additional phase angle $\varphi =-6.9°\sim 6.9°$ is needed at the pole mass of $D_{s1}(2536)$ since the mixing matrix elements are complex numbers. Both the real and imaginary parts are found important for the large mixing angle. We show that the new experimental data from BABAR provide a strong constraint on the mixing angle at the mass of $D_{s1}(2536)$, from which two values can be extracted, i.e., ${\theta }_1=32.1°$ or ${\theta }_2=38.4°$. Our study agrees well with the latter one. Detailed analysis of the mass-shift procedure due to the coupled channel effects is also presented.

The NLO generalization of the dipole factorization formula for the structure functions $F_2$ and $F_L$ at low $x$ is calculated using light-front perturbation theory. That result gives some interesting insight into the kinematics of initial state parton showers in mixed-space.

We propose a new method to detect short-range $P$- and $T$-violating interactions between nucleons, based on measuring the precession frequency shift of polarized ${}^3\mathrm{He}$ nuclei in the presence of an unpolarized mass. To maximize the sensitivity, a high-pressure ${}^3\mathrm{He}$ cell with thin glass windows ($250\mu \mathrm{m}$) is used to minimize the distance between the mass and ${}^3\mathrm{He}$. The magnetic field fluctuation is suppressed by using the ${}^3\mathrm{He}$ gas in a different region of the cell as a magnetometer. Systematic uncertainties from the magnetic properties of the mass are suppressed by flipping both the magnetic field and spin directions. Without any magnetic shielding, our result has already reached the sensitivity of the current best limit. With improvement in uniformity and stability of the field, we can further improve the sensitivity by 2 orders of magnitude over the force range from ${10}^{-4}-{10}^{-2}\mathrm{m}$.

We study the behavior of a scalar field coupled to a noncommutative black hole which is described by a $\kappa$-cylinder Hopf algebra. We introduce a new class of realizations of this algebra which has a smooth limit as the deformation parameter vanishes. The twisted flip operator is independent of the choice of realization within this class. We demonstrate that the $R$-matrix is quasi-triangular up to the first order in the deformation parameter. Our results indicate how a scalar field might behave in the vicinity of a black hole at the Planck scale.

A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [R. Banerjee, P. Mukherjee, and B. Paul, J. High Energy Phys. 08 (2011) 085.], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons model as an example. A new Hamiltonian analysis of the model is provided. This Hamiltonian analysis has been used to construct the independent gauge generator. An exact mapping between the Hamiltonian gauge transformations and the U(1) symmetries of the action has been established.

We study the equivalence principle and its violations by quantum effects in scalar-tensor theories that admit a conformal frame in which matter only couples to the spacetime metric. These theories possess Ward identities that guarantee the validity of the weak equivalence principle to all orders in the matter coupling constants. These Ward identities originate from a broken Weyl symmetry under which the scalar field transforms by a shift, and from the symmetry required to couple a massless spin two particle to matter (diffeomorphism invariance). But the same identities also predict violations of the weak equivalence principle relatively suppressed by at least two powers of the gravitational couplings, and imply that quantum corrections do not preserve the structure of the action of these theories. We illustrate our analysis with a set of specific examples for spin zero and spin half matter fields that show why matter couplings do respect the equivalence principle, and how the couplings to the gravitational scalar lead to the weak equivalence principle violations predicted by the Ward identities.

We analyze the viscous damping of r-mode oscillations of compact stars, taking into account nonlinear viscous effects in the large-amplitude regime. The qualitatively different cases of hadronic stars, strange quark stars, and hybrid stars are studied. We calculate the viscous damping times of r-modes, obtaining numerical results and also general approximate analytic expressions that explicitly exhibit the dependence on the parameters that are relevant for a future spin-down evolution calculation. The strongly enhanced damping of large-amplitude oscillations leads to damping times that are considerably lower than those obtained when the amplitude dependence of the viscosity is neglected. Consequently, large-amplitude viscous damping competes with the gravitational instability at all physical frequencies and could stop the r-mode growth in case this is not done before by nonlinear hydrodynamic mechanisms.

The concept of gravitational pressure is naturally defined in the context of the teleparallel equivalent of general relativity. Together with the definition of gravitational energy, we investigate the thermodynamics of rotating black holes in the teleparallel framework. We obtain the value of the gravitational pressure over the external event horizon of the Kerr black hole, and write an expression for the thermodynamic relation $TdS=dE+pdV$, where the variations refer to the Penrose process for the Kerr black hole. We employ only the notions of gravitational energy and pressure that arise in teleparallel gravity, and do not make any consideration of the area or the variation of the area of the event horizon. However, our results are qualitatively similar to the standard expression of the literature.

The periastron shift and the Lense-Thirring effect of bound orbital motion in a general axially symmetric space-time given by Plebański and Demiański are analyzed. We also define a measure for the conicity of the orbit and give analytic expressions for the observables in terms of hyperelliptic integrals and Lauricella’s $F_D$ function. For an interpretation of these analytical expressions, we perform a post-Schwarzschild and a post-Newton expansion of these quantities. This clearly shows the influence of the different space-time parameters on the considered observables and allows one to characterize Kerr, Taub-NUT, Schwarzschild–de Sitter, or other space-times.

A point particle of small mass $m$ moves in free fall through a background vacuum spacetime metric $g_{ab}^0$ and creates a first-order metric perturbation $h_{ab}^{1\mathrm{ret}}$ that diverges at the particle. Elementary expressions are known for the singular $m/r$ part of $h_{ab}^{1\mathrm{ret}}$ and for its tidal distortion determined by the Riemann tensor in a neighborhood of $m$. Subtracting this singular part $h_{ab}^{1\mathrm{S}}$ from $h_{ab}^{1\mathrm{ret}}$ leaves a regular remainder $h_{ab}^{1\mathrm{R}}$. The self-force on the particle from its own gravitational field adjusts the world line at $O(m)$ to be a geodesic of $g_{ab}^0+h_{ab}^{1\mathrm{R}}$. The generalization of this description to second-order perturbations is developed and results in a wave equation governing the second-order $h_{ab}^{2\mathrm{ret}}$ with a source that has an $O(m^2)$ contribution from the stress-energy tensor of $m$ added to a term quadratic in $h_{ab}^{1\mathrm{ret}}$. Second-order self-force analysis is similar to that at first order: The second-order singular field $h_{ab}^{2\mathrm{S}}$ subtracted from $h_{ab}^{2\mathrm{ret}}$ yields the regular remainder $h_{ab}^{2\mathrm{R}}$, and the second-order self-force is then revealed as geodesic motion of $m$ in the metric $g_{ab}^0+h^{1\mathrm{R}}+h^{2\mathrm{R}}$.

Proposed space-based gravitational-wave (GW) detectors such as DECIGO and BBO will detect $\sim {10}^6$ neutron-star (NS) binaries and determine the luminosity distances to the binaries with high precision. Combining the luminosity distances with cosmologically induced phase corrections on the GWs, cosmological expansion out to high redshift can be measured without the redshift determinations of host galaxies by electromagnetic observation and be a unique probe for dark energy. On the other hand, such a NS-binary foreground should be subtracted to detect primordial GWs produced during inflation. Thus, the constraining power on dark energy and the detectability of the primordial gravitational waves strongly depend on the detector sensitivity and are in close relation with one another. In this paper, we investigate the constraints on the equation of state of dark energy with future space-based GW detectors with/without identifying the redshifts of host galaxies. We also study the sensitivity to the primordial GWs, properly dealing with the residual of the NS-binary foreground. Based on the results, we discuss the detector sensitivity required to achieve the forementioned targeted study of cosmology.

A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, falloff of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region.

We develop a semianalytical approach, based on the post-Newtonian expansion and on the affine approximation, to model the tidal deformation of neutron stars in the coalescence of black hole-neutron star or neutron star-neutron star binaries. Our equations describe, in a unified framework, both the system orbital evolution, and the neutron star deformations. These are driven by the tidal tensor, which we expand at $1/c^3$ post-Newtonian order, including spin terms. We test the theoretical framework by simulating black hole-neutron star coalescence up to the onset of mass shedding, which we determine by comparing the shape of the star with the Roche lobe. We validate our approach by comparing our results with those of fully relativistic, numerical simulations.

Modified Newtonian dynamics is an empirical modification to Poisson’s equation which has had success in accounting for the “gravitational field” $\Phi$ in a variety of astrophysical systems. The field $\Phi$ may be interpreted in terms of the weak-field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the aquadratic Lagrangian (AQUAL) theory, tensor-vector-scalar (TeVeS) theory and generalized Einstein-aether theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit TeVeS solid angle akin to the case of a Barriola-Vilenkin global monopole. In the case of generalized Einstein-aether, a disformal symmetry of the action emerges in the limit of $\overrightarrow{\nabla }\Phi \to 0$. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.

We study the propagation of a massive vector or Proca field on the Schwarzschild spacetime. The field equations are reduced to a one-dimensional wave equation for the odd-parity part of the field and two coupled equations for the even-parity part of the field. We use numerical techniques based on solving (scalar or matrix-valued) three-term recurrence relations to compute the spectra of both quasinormal modes and quasibound states, which have no massless analogue, complemented in the latter case by a forward-integration method. We study the radial equations analytically in both the near-horizon and far-field regions and use a matching procedure to compute the associated spectra in the small-mass limit. Finally, we comment on extending our results to the Kerr geometry and its phenomenological relevance for hidden photons arising, e.g., in string theory compactifications.