The classification of a certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in $d\ge 5$ dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for $d>5$. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximally symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum.

The interaction between gravitational and electromagnetic waves in the presence of a static magnetic field is studied. The field strength of the static field is allowed to surpass the Schwinger critical field, such that the QED effects of vacuum polarization and magnetization are significant. Equations governing the interaction are derived and analyzed. It turns out that the energy conversion from gravitational to electromagnetic waves can be significantly altered due to the QED effects. The consequences of our results are discussed.

Multistate dark matter (DM) models with small mass splittings and couplings to light hidden sector bosons have been proposed as an explanation for the PAMELA/Fermi/H.E.S.S. high-energy lepton excesses. We investigate this proposal over a wide range of DM density profiles, in the framework of concrete models with doublet or triplet dark matter and a hidden SU(2) gauge sector that mixes with standard model hypercharge. The gauge coupling is bounded from below by the DM relic density, and the Sommerfeld enhancement factor is explicitly computable for given values of the DM and gauge boson masses $M$, $\mu$ and the (largest) dark matter mass splitting $\delta M_{12}$. Sommerfeld enhancement is stronger at the galactic center than near the Sun because of the radial dependence of the DM velocity profile, which strengthens the inverse Compton (IC) gamma ray constraints relative to usual assumptions. We find that the PAMELA/Fermi/H.E.S.S. lepton excesses are marginally compatible with the model predictions, and with CMB and Fermi gamma ray constraints, for $M\cong 800\mathrm{GeV}$, $\mu \lesssim 200\mathrm{MeV}$, and a dark matter profile with noncuspy Einasto parameters $\alpha \gtrsim 0.20$, $r_s\sim 30\mathrm{kpc}$. We also find that the annihilating DM must provide only a subdominant ($\lesssim 0.4$) component of the total DM mass density, since otherwise the boost factor due to Sommerfeld enhancement is too large.

We present a detailed implementation of two parallel bispectrum estimation methods which can be applied to general nonseparable primordial and cosmic microwave background (CMB) bispectra. The method exploits bispectrum mode decompositions on the tetrahedral domain of allowed wave number or multipole values, using both separable basis functions and related orthonormal modes. We provide concrete examples of such modes constructed from symmetrized tetrahedral polynomials, demonstrating the rapid convergence of expansions describing nonseparable bispectra. We use these modes to create rapid and robust pipelines for generating simulated CMB maps of high resolution ($l>2000$) given an arbitrary primordial power spectrum and bispectrum or an arbitrary late-time CMB angular power spectrum and bispectrum. By extracting coefficients for the same separable basis functions from an observational map, we are able to present an efficient $f_{\mathrm{NL}}$ estimator for a given theoretical model with a nonseparable bispectrum. The estimator has two manifestations, comparing the theoretical and observed coefficients at either primordial or late times, thus encompassing a wider range of models, including secondary anisotropies and lensing as well as active models, such as cosmic strings. We provide examples and validation of both $f_{\mathrm{NL}}$ estimation methods by direct comparison with simulations in a WMAP-realistic context. In addition, we demonstrate how the full primordial and CMB bispectrum can be extracted from observational maps using these mode expansions, irrespective of the theoretical model under study. We also propose a universal definition of the bispectrum parameter $F_{\mathrm{NL}}$, so that the integrated bispectrum on the observational domain can be more consistently compared between theoretical models. We obtain WMAP5 estimates of $f_{\mathrm{NL}}$ for the equilateral model from both our primordial and late-time estimators which are consistent with each other, as well as results already published in the literature. These general bispectrum estimation methods should prove useful for non-Gaussianity analysis with the Planck satellite data, as well as in other contexts.

A smooth inflaton potential is generally assumed when calculating the primordial power spectrum, implicitly assuming that a very small oscillation in the inflaton potential creates a negligible change in the predicted halo mass function. We show that this is not true. We find that a small oscillating perturbation in the inflaton potential in the slow-roll regime can alter significantly the predicted number of small halos. A class of models derived from supergravity theories gives rise to inflaton potentials with a large number of steps and many trans-Planckian effects may generate oscillations in the primordial power spectrum. The potentials we study are the simple quadratic (chaotic inflation) potential with superimposed small oscillations for small field values. Without leaving the slow-roll regime, we find that for a wide choice of parameters, the predicted number of halos change appreciably. For the oscillations beginning in the ${10}^7–{10}^8{M}_{\odot }$ range, for example, we find that only a 5% change in the amplitude of the chaotic potential causes a 50% suppression of the number of halos for masses between ${10}^7–{10}^8{M}_{\odot }$ and an increase in the number of halos for masses $<{10}^6{M}_{\odot }$ by factors $\sim 15–50$. We suggest that this might be a solution to the problem of the lack of observed dwarf galaxies in the range ${10}^7–{10}^8{M}_{\odot }$. This might also be a solution to the reionization problem where a very large number of Population III stars in low mass halos are required.

Detection of magnetic-type ($B$-type) polarization in CMB radiation plays a crucial role in probing the relic gravitational wave background. In this paper, we propose a new method to deconstruct a polarization map on an incomplete sky in real space into purely electric and magnetic polarization-type maps, $\mathcal{E}(\widehat{\gamma })$ and $\mathcal{B}(\widehat{\gamma })$, respectively. The main properties of our approach are as follows: First, the fields $\mathcal{E}(\widehat{\gamma })$ and $\mathcal{B}(\widehat{\gamma })$ are constructed in real space with minimal loss of information. This loss of information arises due to the removal of a narrow edge of the constructed map in order to remove various numerical errors, including those arising from finite pixel size. Second, this method is fast and can be efficiently applied to high resolution maps due to the use of the fast spherical harmonics transformation. Third, the constructed fields, $\mathcal{E}(\widehat{\gamma })$ and $\mathcal{B}(\widehat{\gamma })$, are scalar fields. For this reason various techniques developed to deal with temperature anisotropy maps can be directly applied to analyze these fields. As a concrete example, we construct and analyze an unbiased estimator for the power spectrum of the $B$ mode of polarization $C_{\ell }^{BB}$. Basing our results on the performance of this estimator, we discuss the relic gravitational wave detection ability of two future ground-based CMB experiments, the Q/U Imaging Experiment and Polarization of Background Microwave Radiation.

A new determination of the Newtonian gravitational constant $G$ is presented by using a torsion pendulum with the time-of-swing method. Compared with our previous measurement with the same method, several improvements greatly reduced the uncertainties as follows: (i) two stainless steel spheres with more homogeneous density are used as the source masses instead of the cylinders used in the previous experiment, and the offset of the mass center from the geometric center is measured and found to be much smaller than that of the cylinders; (ii) a rectangular glass block is used as the main body of the pendulum, which has fewer vibration modes and hence improves the stability of the period and reduces the uncertainty of the moment of inertia; (iii) both the pendulum and source masses are placed in the same vacuum chamber to reduce the error of measuring the relative positions; (iv) changing the configurations between the “near” and “far” positions is remotely operated by using a stepper motor to lower the environmental disturbances; and (v) the anelastic effect of the torsion fiber is first measured directly by using two disk pendulums with the help of a high-$Q$ quartz fiber. We have performed two independent $G$ measurements, and the two $G$ values differ by only 9 ppm. The combined value of $G$ is $(6.67349\pm 0.00018)\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$ with a relative uncertainty of 26 ppm.

In this paper we calculate the technicolor correction to the production of a charged top pion in association with a $W$ boson via $b\overline{b}$ annihilation at the CERN Large Hadron Collider in the context of the topcolor assisted technicolor model. We find that the cross section of $pp\to b\overline{b}\to W^{\pm }{\pi }_t^{\mp }$ at the tree level can reach a few hundred femtobarns for reasonable ranges of the parameters, roughly corresponding to the result of the process $pp\to b\overline{b}\to W^{\pm }{H}^{\mp }$ in the minimal supersymmetric standard model; the relative corrections arising from the one-loop diagrams are about a few percent to two dozen percent, and they will increase the cross section at the tree level. As a comparison, we also discuss the size of the hadron cross section via the other subprocess $gg\to W^{\pm }{\pi }_t^{\mp }$.

Fermions with magnetic charges can contribute to anomalies. We derive the axial anomaly and gauge anomalies for monopoles and dyons, and find eight new gauge anomaly cancellation conditions in a general theory with both electric and magnetic charges. As a by-product, we also extend the Zwanziger two-potential formalism to include the $\theta$ parameter, and elaborate on the condition for $CP$ invariance in theories with fermionic dyons.

We study relativistic stars in the context of scalar-tensor theories of gravity that try to account for the observed cosmic acceleration and satisfy the local gravity constraints via the chameleon mechanism. More specifically, we consider two types of models: scalar-tensor theories with an inverse power law potential and $f(R)$ theories. Using a relaxation algorithm, we construct numerically static relativistic stars, both for constant energy density configurations and for a polytropic equation of state. We can reach a gravitational potential up to $\Phi \sim 0.3$ at the surface of the star, even in $f(R)$ theories with an “unprotected” curvature singularity. However, we find static configurations only if the pressure does not exceed one third of the energy density, except possibly in a limited region of the star (otherwise, one expects tachyonic instabilities to develop). This constraint is satisfied by realistic equations of state for neutron stars.

In the brane world scenario, possessing the self-tuning property of the cosmological constant, we study the probability amplitude for an initial state of the Universe to transform to final states with some curvatures. In the Kim, Kyae, and Lee model, there exists a finite range of parameters such that the transition amplitude to a near flat universe is exponentially dominated by the smallness of curvature, $\gtrsim e^{\mathrm{positive}\mathrm{number}/{\overline{\Lambda }}^2}$, i.e., it is dominated by an almost flat universe of $|\overline{\Lambda }|<ϵ$.

We perform a detailed study of the renormalization group equations in the inverse seesaw model. Especially, we derive compact analytical formulas for the running of the neutrino parameters in the standard model and the minimal supersymmetric standard model, and illustrate that, due to large Yukawa coupling corrections, significant running effects on the leptonic mixing angles can be naturally obtained in the proximity of the electroweak scale, perhaps even within the reach of the LHC. In general, if the mass spectrum of the light neutrinos is nearly degenerate, the running effects are enhanced to experimentally accessible levels, well suitable for the investigation of the underlying dynamics behind the neutrino mass generation and the lepton flavor structure. In addition, the effects of the seesaw thresholds are discussed, and a brief comparison to other seesaw models is carried out.

In models with dynamical electroweak symmetry breaking, this breaking is normally communicated to quarks and leptons by a set of vector bosons with masses generated via sequential breaking of a larger gauge symmetry. In reasonably ultraviolet-complete theories of this type, the number of stages of breaking of the larger gauge symmetry is usually equal to the observed number of quark and lepton generations, $N_{\mathrm{gen}}=3$. Here we investigate the general question of how the construction and properties of these models depend on $N_{\mathrm{gen}}$, regarded as a variable. We build and analyze models with illustrative values of $N_{\mathrm{gen}}$ different from 3 (namely $N_{\mathrm{gen}}=1,2,4$) that exhibit the necessary sequential symmetry breaking down to a strongly coupled sector that dynamically breaks electroweak symmetry. Our results for variable $N_{\mathrm{gen}}$ show that one can robustly obtain, for this latter sector, a theory with a gauge coupling that is large but slowly running, controlled by an approximate infrared fixed point of the renormalization group. Owing to this, we find that for all of the values of $N_{\mathrm{gen}}$ considered, standard-model fermions of the highest generation have masses that can be comparable to the electroweak-symmetry-breaking scale. We also study the interplay of multiple strongly coupled gauge symmetries in these models.

QCD with two flavors of massless color-sextet quarks is considered as a model for conformal/walking technicolor. If this theory possesses an infrared fixed point, as indicated by 2-loop perturbation theory, it is a conformal (unparticle) field theory. If, on the other hand, a chiral condensate forms on the weak-coupling side of this would-be fixed point, the theory remains confining. The only difference between such a theory and regular QCD is that there is a range of momentum scales over which the coupling constant runs very slowly (walks). In this first analysis, we simulate the lattice version of QCD with two flavors of staggered quarks at finite temperatures on lattices of temporal extent $N_t=4$ and 6. The deconfinement and chiral-symmetry restoration couplings give us a measure of the scales associated with confinement and chiral-symmetry breaking. We find that, in contrast to what is seen with fundamental quarks, these transition couplings are very different. $\beta =6/g^2$ for each of these transitions increases significantly from $N_t=4$ and $N_t=6$ as expected for the finite-temperature transitions of an asymptotically free theory. This suggests a walking rather than a conformal behavior, in contrast to what is observed with Wilson quarks. In contrast to what is found for fundamental quarks, the deconfined phase exhibits states in which the Polyakov loop is oriented in the directions of all three cube roots of unity. At very weak coupling the states with complex Polyakov loops undergo a transition to a state with a real, negative Polyakov loop.

We propose a new method to evaluate the Lellouch-Lüscher factor which relates the $\Delta I=3/2$ $K\to \pi \pi$ matrix elements computed on a finite lattice to the physical (infinite-volume) decay amplitudes. The method relies on the use of partially twisted boundary conditions, which allow the s-wave $\pi \pi$ phase shift to be computed as an almost continuous function of the center-of-mass relative momentum and hence for its derivative to be evaluated. We successfully demonstrate the feasibility of the technique in an exploratory computation.

We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic dissipative fluid dynamics are always stable. We then perform a linear stability analysis in a Lorentz-boosted frame. Provided that the ratio of the relaxation time for the shear stress tensor ${\tau }_{\pi }$ to the sound attenuation length ${\Gamma }_s=4\eta /3(\epsilon +P)$ fulfills a certain asymptotic causality condition, the equations of motion give rise to stable solutions. Although the group velocity associated with perturbations may exceed the velocity of light in a certain finite range of wave numbers, we demonstrate that this does not violate causality, as long as the asymptotic causality condition is fulfilled. Finally, we compute the characteristic velocities and show that they remain below the velocity of light if the ratio ${\tau }_{\pi }/{\Gamma }_s$ fulfills the asymptotic causality condition.

The electromagnetic form factors of the $\Delta$ baryon are evaluated within the framework of a covariant spectator quark model, where S- and D-states are included in the $\Delta$ wave function. We predict all the four $\Delta$ multipole form factors: the electric charge $G_{E0}$, the magnetic dipole $G_{M1}$, the electric quadrupole $G_{E2}$ and the magnetic octupole $G_{M3}$. We compare our predictions with other theoretical calculations. Our results are compatible with the available experimental data and recent lattice QCD data.

An extension of the minimal supersymmetric standard model called the $\mu \nu \mathrm{SSM}$ does not allow a conventional thermal leptogenesis scenario because of the low scale seesaw that it utilizes. Hence, we investigate the possibility of electroweak baryogenesis. Specifically, we identify a parameter region for which the electroweak phase transition is sufficiently strongly first order to realize electroweak baryogenesis. In addition to transitions that are similar to those in the next-to-minimal supersymmetric standard model, we find a novel class of phase transitions in which there is a rotation in the singlet vector space.

It is shown that the end point of the first-order transition line, which merges into a crossover regime in the phase diagram of the Nambu–Jona-Lasinio model, extended to include the six-quark ’t Hooft and eight-quark interaction Lagrangians, is pushed toward vanishing chemical potential and higher temperatures with increasing strength of the Okubo-Zweig-Iizuka–violating eight-quark interactions. We clarify the connection between the location of the end point in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. We show how the $8q$ interactions affect the number of effective quark degrees of freedom. We are able to obtain the correct asymptotics for this number at large temperatures by using the Pauli-Villars regularization.