Using the covariant formalism developed in a companion paper [F.-Q. Wu, L. E. Qiang, X. Wang, and X. Chen, preceding Article, Phys. Rev. D 82, 083002 (2010)] (paper I), we derive observational constraints on the Brans-Dicke model in a flat Friedmann-Lemaître-Robertson-Walker universe with a cosmological constant and cold dark matter. The CMB observations we use include the Wilkinson Microwave Anisotropy Probe 5 yr data, the Arcminute Cosmology Bolometer Array Receiver 2007 data, the Cosmic Background Imager polarization data, and the Balloon Observations of Millimetric Extragalactic Radiation and Geophysics 2003 flight data. For the large scale structure we use the matter power spectrum data measured with the luminous red galaxy survey of the Sloan Digital Sky Survey Data Release 4. We parametrize the Brans-Dicke parameter $\omega$ with a new parameter $\zeta =\ln (1/\omega +1)$, and use the Markov-Chain Monte Carlo method to explore the parameter space. We find that using CMB data alone, one could place some constraints on positive $\zeta$ or $\omega$, but negative $\zeta$ or $\omega$ could not be constrained effectively. However, with additional large scale structure data, one could break the degeneracy at $\zeta <0$. The $2\sigma$ (95.5%) bound on $\zeta$ is $-0.00837<\zeta <0.01018$ (corresponding to $\omega <-120.0$ or $\omega >97.8$). We also obtained constraints on $\dot{G}/G$, the rate of change of $G$ at present, as $-1.75\times {10}^{-12}{\mathrm{yr}}^{-1}<\dot{G}/G<1.05\times {10}^{-12}{\mathrm{yr}}^{-1}$, and $\delta G/G$, the total variation of $G$ since the epoch of recombination, as $-0.083<\delta G/G<0.095$ at the $2\sigma$ confidence level.

In the covariant cosmological perturbation theory, a $1+3$ decomposition ensures that all variables in the frame-independent equations are covariant and gauge invariant and that they have clear physical interpretations. We develop this formalism in the case of Brans-Dicke gravity, and apply this method to the calculation of CMB anisotropy and large scale structures. We modify the publicly available Boltzmann code CAMB to calculate numerically the evolution of the background and adiabatic perturbations, and obtain the temperature and polarization spectra of Brans-Dicke theory for both scalar and tensor modes; the tensor mode results for Brans-Dicke gravity are obtained numerically for the first time. We first present our theoretical formalism in detail, and then explicitly describe the techniques used in modifying the CAMB code. These techniques are also very useful for other gravity models. Next we compare the CMB and large scale structure spectra in Brans-Dicke theory with those in the standard general relativity theory. At last, we investigate the integrated Sachs-Wolfe effect and the CMB lensing effect in Brans-Dicke theory. Constraints on the Brans-Dicke model with current observational data are presented in a companion paper [F. Wu and X. Chen, following Article, Phys. Rev. D 82, 083003 (2010)] (paper II).

The generalized hidden local symmetry (GHLS) model is the chiral model of pseudoscalar, vector, and axial vector mesons and their interactions. It contains also the couplings of strongly interacting particles with electroweak gauge bosons. Here, GHLS model is confronted with the ALEPH data on the decay ${\tau }^{-}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}{\nu }_{\tau }$. It is shown that the invariant mass spectrum of final pions in this decay calculated in GHLS framework with the single $a_1(1260)$ resonance disagrees with the experimental data at any reasonable number of free GHLS parameters. Two modifications of GHLS model based on inclusion of two additional heavier axial vector mesons are studied. One of them, which gives a good description of the ALEPH data with all the parameters kept free, is shown to result in very large ${\Gamma }_{a_1^{\pm }\to {\pi }^{\pm }\gamma }$ partial width. The other scheme with the GHLS parameters fixed in a way that the universality is preserved and the observed central value of ${\Gamma }_{a_1^{\pm }\to {\pi }^{\pm }\gamma }$ is reached, which results in a good description of the three pion spectrum in ${\tau }^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}{\nu }_{\tau }$ decay.

We investigate the stability and fluctuations of a soft-wall model that has an asymptotically anti-de Sitter metric and a scalar field that has an asymptotically power-law dependence in the conformal coordinate. By imposing UV boundary conditions, the soft-wall mass scale can be fixed to be near the TeV scale and causes the radion to no longer be massless. A hierarchy between the weak scale and the Planck scale can be generated for various particle spectrum behavior, although natural values only occur for a gravitational sector containing scalar fields that act like unparticles. In addition, if bulk standard model fields have nonstandard couplings to the gravitational sector, then a discrete particle spectrum can be realized in the nongravitational sector. This allows for the possibility of an unparticle solution to the hierarchy problem.

We provide a nonlinear realization of supergravity with an arbitrary number of supersymmetries by means of coset construction. The number of gravitino degrees of freedom counts the number of supersymmetries, which will possibly be probed in future experiments. We also consider Goldstino embedding in the construction to discuss the relation to nonlinear realizations with rigid supersymmetries.

A covariant spectator constituent quark model is applied to study the $\gamma N\to \Delta (1600)$ transition. Two processes are important in the transition: a photon couples to the individual quarks of the $\Delta (1600)$ core (quark core), and a photon couples to the intermediate pion-baryon states (pion cloud). While the quark core contributions are estimated assuming $\Delta (1600)$ as the first radial excitation of $\Delta (1232)$, the pion cloud contributions are estimated based on an analogy with the $\gamma N\to \Delta (1232)$ transition. To estimate the pion cloud contributions in the $\gamma N\to \Delta (1600)$ transition, we include the relevant intermediate states, $\pi N$, $\pi \Delta$, $\pi N(1440)$ and $\pi \Delta (1600)$. Dependence on the four-momentum transfer squared, $Q^2$, is predicted for the magnetic dipole transition form factor, $G_M^{*}(Q^2)$, as well as the helicity amplitudes, $A_{1/2}(Q^2)$ and $A_{3/2}(Q^2)$. The results at $Q^2=0$ are compared with the existing data.

The existence of Abelian gauge symmetries in four-dimensional $F$-theory compactifications depends on the global geometry of the internal Calabi-Yau four-fold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such $U(1)$ symmetries along the Coulomb and the Higgs branch. As one application we examine Abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In $SU(5)$ grand unified theory (GUT) models this mechanism enforces a global $U(1{)}_X$ symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau four-folds and their mirror duals starting from an underlying $E_8$ and $E_7\times U(1)$ enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze $F$-theory GUT models.

In the literature, the asymptotic freedom property of the ($-{\varphi }^4$) theory is always concluded from real-line calculations while the theory is known to be a non-real-line one. In this article, we test the existence of the asymptotic freedom in the $(-{\varphi }^4{)}_{3+1}$ theory using the mean field approach. In this approach and contrary to the original Hamiltonian, the obtained effective Hamiltonian is rather a real-line one. Accordingly, this work resembles the first reasonable analysis for the existence of the asymptotic freedom property in the $\mathcal{P}\mathcal{T}$-symmetric ($-{\varphi }^4$) theory. In this respect, we calculated three different amplitudes of different positive dimensions (in mass units) and find that all of them go to very small values at high energy scales (small coupling) in agreement with the spirit of the asymptotic freedom property of the theory. To test the validity of our calculations, we obtained the asymptotic behavior of the vacuum condensate in terms of the coupling, analytically, and found that the controlling factor $\Lambda$ has the value $\frac{(4\pi {)}^2}{6}=26.319$ compared to the result $\Lambda =26.3209$ from the literature, which was obtained via numerical predictions. We assert that the nonblowup of the massive quantities at high energy scales predicted in this work strongly suggests the possibility of the solution of the famous hierarchy puzzle in a standard model with the $\mathcal{P}\mathcal{T}$-symmetric Higgs mechanism.

We propose a general framework to describe Planckian deviations from special relativity compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to special relativity going beyond the energy power expansion of effective field theories. We discuss the conditions in which these Planckian effects might be experimentally observable in the near future, together with the nontrivial limits of applicability of this asymptotic approach that such a situation would produce, both at the very high (ultraviolet) and the very low (infrared) energy regimes.

We show that in a sufficiently strong magnetic field the QCD vacuum may undergo a transition to a new phase where charged ${\rho }^{\pm }$ mesons are condensed. In this phase the vacuum behaves as an anisotropic inhomogeneous superconductor which supports superconductivity along the axis of the magnetic field. In the directions transverse to the magnetic field the superconductivity is absent. The magnetic-field-induced anisotropic superconductivity—which is realized in the cold vacuum, i.e. at zero temperature and density—is a consequence of a nonminimal coupling of the $\rho$ mesons to the electromagnetic field. The onset of the superconductivity of the charged ${\rho }^{\pm }$ mesons should also induce an inhomogeneous superfluidity of the neutral ${\rho }^0$ mesons. We also argue that due to simple kinematical reasons a strong enough magnetic field makes the lifetime of the $\rho$ mesons longer by closing the main channels of the strong decays of the $\rho$ mesons into charged pions.

In rotating neutron stars the existence of the Coriolis force allows the presence of the so-called Rossby oscillations (r-modes) which are known to be unstable to emission of gravitational waves. Here, for the first time, we introduce the magnetic damping rate in the evolution equations of r-modes. We show that r-modes can generate very strong toroidal fields in the core of accreting millisecond pulsars by inducing differential rotation. We shortly discuss the instabilities of the generated magnetic field and its long time-scale evolution in order to clarify how the generated magnetic field can stabilize the star.

We study electromagnetic perturbations around a Kerr black hole surrounded by a thin disk on the equatorial plane. Our main purpose is to reveal the black hole superradiance of electromagnetic waves emitted from the disk surface. The outgoing Kerr-Schild field is used to describe the disk emission, and the superradiant scattering is represented by a vacuum wave field which is added to satisfy the ingoing condition on the horizon. The formula to calculate the energy flux on the disk surface is presented, and the energy transport in the disk-black hole system is investigated. Within the low-frequency approximation we find that the energy extracted from the rotating black hole is mainly transported back to the disk, and the energy spectrum of electromagnetic waves observed at infinity is also discussed.

We study the noninertial effects of rotating frames on the Landau quantization for neutral particles with a permanent magnetic dipole moment in the presence of a linear topological defect. We build a rotating frame where the field configuration acts on the dipole moment of the neutral particle without any torque, which agrees with the Landau quantization established previously. We will show that the noninertial effects modify the cyclotron frequency obtained in the absence of rotation, but they do not break the infinity degeneracy of the Landau levels. However, the presence of the topological defect modifies the cyclotron frequency and breaks the degeneracy of the Landau levels.

We study rotating boson stars in five spacetime dimensions. The boson fields consist of a complex doublet scalar field. Considering boson stars rotating in two orthogonal planes with both angular momenta of equal magnitude, a special ansatz for the boson field and the metric allows for solutions with nontrivial dependence on the radial coordinate only. The charge of the scalar field equals the sum of the angular momenta. The rotating boson stars are globally regular and asymptotically flat. For our choice of a sextic potential, the rotating boson star solutions possess a flat spacetime limit. We study the solutions in flat and curved spacetime.

We investigate the implications of energy dependence of the speed of photons, one of the candidate effects of quantum-gravity theories that has been most studied recently, from the perspective of observations in different reference frames. We examine how a simultaneous burst of photons would be measured by two observers with a relative velocity, establishing some associated conditions for the consistency of theories. For scenarios where the Lorentz transformations remain valid, these consistency conditions allow us to characterize the violations of Lorentz symmetry through an explicit description of the modification of the quantum-gravity scale in boosted frames with respect to its definition in a preferred frame. When applied to relativistic scenarios with a deformation of Lorentz invariance that preserves the equivalence of inertial observers, we find an insightful characterization of the necessity to adopt in such frameworks nonclassical features of spacetime geometry, e.g. events that are at the same spacetime point for one observer cannot be considered at the same spacetime point for other observers. Our findings also suggest that, at least in principle (and perhaps one day even in practice), measurements of the dispersion of photons in relatively boosted frames can be particularly valuable for the purpose of testing these scenarios.

Model gravitational waveforms must be accurate enough to be useful for detection of signals and measurement of their parameters, so appropriate accuracy standards are needed. Yet these standards should not be unnecessarily restrictive, making them impractical for the numerical and analytical modelers to meet. The work of Lindblom, Owen, and Brown [Phys. Rev. D 78, 124020 (2008)] is extended by deriving new waveform accuracy standards which are significantly less restrictive while still ensuring the quality needed for gravitational-wave data analysis. These new standards are formulated as bounds on certain norms of the time-domain waveform errors, which makes it possible to enforce them in situations where frequency-domain errors may be difficult or impossible to estimate reliably. These standards are less restrictive by about a factor of 20 than the previously published time-domain standards for detection, and up to a factor of 60 for measurement. These new standards should therefore be much easier to use effectively.

We consider a quantum field on a lukewarm black hole spacetime. We introduce a new uniform approximation to the radial equation, constructed using an extension of Green-Liouville asymptotics. We then use this new approximation to construct the renormalized vacuum polarization in the Hartle-Hawking vacuum. Previous calculations of the vacuum polarization rely on the WKB approximation to the solutions of the radial equation; however, the nonuniformity of the WKB approximations obscures the results of these calculations near both horizons. The use of our new approximation eliminates these obscurities, enabling us to obtain explicitly finite and easily calculable values of the vacuum polarization on the two horizons.

We examine the wave functionals describing the collapse of a self-gravitating dustball in an exact quantization of the gravity-dust system. We show that ingoing (collapsing) dust shell modes outside the apparent horizon must necessarily be accompanied by outgoing modes inside the apparent horizon, whose amplitude is suppressed by the square root of the Boltzmann factor at the Hawking temperature. Likewise, ingoing modes in the interior must be accompanied by outgoing modes in the exterior, again with an amplitude suppressed by the same factor. A suitable superposition of the two solutions is necessary to conserve the dust probability flux across the apparent horizon; thus, each region contains both ingoing and outgoing dust modes. If one restricts oneself to considering only the modes outside the apparent horizon then one should think of the apparent horizon as a partial reflector, the probability for a shell to reflect being given by the Boltzmann factor at the Hawking temperature determined by the mass contained within it. However, if one considers the entire wave function, the outgoing wave in the exterior is seen to be the transmission through the horizon of the interior outgoing wave that accompanies the collapsing shells. This transmission could allow information from the interior to be transferred to the exterior.

The Einstein’s gravity theory can be formulated as an $SL(2,C)$ gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an $SL(2,C)$ formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.