A primordial cosmological magnetic field induces Faraday rotation of the cosmic microwave background polarization. This rotation produces a curl-type polarization component even when the unrotated polarization possesses only gradient-type polarization, as expected from scalar density perturbations. We compute the angular power spectrum of curl-type polarization arising from small Faraday rotation due to a weak stochastic primordial magnetic field with a power-law power spectrum. The induced polarization power spectrum peaks at arc minute angular scales. Faraday rotation is one of the few cosmological sources of curl-type polarization, along with primordial tensor perturbations, gravitational lensing, and the vector and tensor perturbations induced by magnetic fields; the Faraday rotation signal peaks on significantly smaller angular scales than any of these, with a power spectrum amplitude which can be comparable to that from gravitational lensing. Prospects for detection are briefly discussed.

Little Higgs models offer an interesting approach to weakly coupled electroweak symmetry breaking without fine-tuning. The original little Higgs models were plagued by strong constraints from electroweak precision data which required a fine-tuning to be reintroduced. An economical solution to this problem is to introduce a discrete symmetry (analogous to $R$-parity of SUSY) called $T$-parity. $T$-parity not only eliminates most constraints from electroweak precision data, but it also leads to a promising dark matter candidate. In this paper we investigate the dark matter candidate in the littlest Higgs model with $T$-parity. An upper bound on the symmetry breaking scale $f\lesssim 1.8\mathrm{T}\mathrm{e}\mathrm{V}$ naturally arises from calculating the relic density. We begin the study of the LHC phenomenology of the littlest Higgs model with $T$-parity. We find that the model offers an interesting collider signature that has a generic missing energy signal which could “fake” SUSY at the LHC. We also investigate the properties of the heavy partner of the top quark which is common to all littlest Higgs models, and how its properties are modified with the introduction of $T$-parity. We include an appendix with a list of Feynman rules specific to the littlest Higgs with $T$-parity to facilitate further study.

We study global topological defects in the Jacobson-Corley model which breaks Lorentz symmetry and involves up to fourth order derivatives. There is a window in the parameter space in which no solution exists. Otherwise, different profiles are allowed for the same values of the parameters. For a scale of Lorentz violation much higher than the scale of gauge symmetry breaking, the energy densities are higher, of the same order or smaller than in the usual case for domain walls, cosmic strings, and hedgehogs, respectively. Possible cosmological implications are suggested.

We outline a full nonperturbative proof of planar (large-$N$) equivalence between bosonic correlators in a theory with Majorana fermions in the adjoint representation and one with Dirac fermions in the two-index (anti) symmetric representation. In a particular case (one-flavor), this reduces to our previous result—planar equivalence between super-Yang-Mills theory and a nonsupersymmetric “orientifold field theory.” The latter theory becomes one-flavor massless QCD at $N=3$.

In a recently proposed model of “ghost condensation,” spatially homogeneous states may mix, via tunneling, with inhomogeneous states which are somewhat similar to bubbles in the theory of false vacuum decay, the corresponding bubble nucleation rate being exponentially sensitive to the ultraviolet completion of the model. The conservation of energy and charge requires that the energy density is negative and the field is strongly unstable in a part of the nucleated bubble. Unlike in the theory of false vacuum decay, this region does not expand during subsequent real-time evolution. In the outer part, positive energy outgoing waves develop, which eventually form shocks. Behind the outgoing waves and away from the bubble center, the background settles down to its original value. The outcome of the entire process is thus a microscopic region of negative energy and strong field—“hole in the ghost condensate”—plus a collection of outgoing waves (particles of the ghost condensate field) carrying away finite energy.

We introduce horizon pretracking as a method for analyzing numerically generated spacetimes of merging black holes. Pretracking consists of following certain modified constant expansion surfaces during a simulation before a common apparent horizon has formed. The tracked surfaces exist at all times, and are defined so as to include the common apparent horizon if it exists. The method provides a way for finding this common apparent horizon in an efficient and reliable manner at the earliest possible time. We can distinguish inner and outer horizons by examining the distortion of the surface. Properties of the pretracking surface such as its expansion, location, shape, area, and angular momentum can also be used to predict when a common apparent horizon will appear, and its characteristics. The latter could also be used to feed back into the simulation by adapting, e.g., boundary or gauge conditions even before the common apparent horizon has formed.

Deriving the gravitational field of the high-energy objects is an important theme because the black holes might be produced in particle collisions in the brane world scenario. In this paper, we develop a method for boosting the metric of the stationary objects and taking the lightlike limit in higher-dimensional spacetimes, using the Kerr black hole as one example. We analytically construct the metric of lightlike Kerr black holes and find that this method contains no ambiguity in contrast to the four-dimensional case. We discuss the possible implications of our results in the brane world context.

To support the validity of a factorizable metric ansatz used in string cosmology, we investigate a toy problem in the Randall-Sundrum I model. For this purpose, we revise the gradient expansion method to conform to the factorizable metric ansatz. By solving the five-dimensional equations of motion and substituting the results into the action, we obtain the four-dimensional effective action. It turns out that the resultant action is equivalent to that obtained by assuming the factorizable metric ansatz. Our analysis gives the support of the validity of the factorizable metric ansatz.

We focus on the dynamical aspects on Newton-Hooke space-time ${\mathcal{NH}}_{+}$ mainly from the viewpoint of geometric contraction of the de Sitter spacetime with Beltrami metric. (The term spacetime is used to denote a space with non-degenerate metric, while the term space-time is used to denote a space with degenerate metric.) We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newton’s gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schrödinger equation from the geometric contraction, where we can relate the conservative probability in some sense to the mass density in the Newton-Hooke continuous medium mechanics. Similar consideration may apply to the Newton-Hooke space-time ${\mathcal{NH}}_{-}$ contracted from anti-de Sitter spacetime.

The standard adiabatic approximation to phasing of gravitational waves from inspiralling compact binaries uses the post-Newtonian expansions of the binding energy and gravitational wave flux both truncated at the same relative post-Newtonian order. Motivated by the eventual need to go beyond the adiabatic approximation we must view the problem as the dynamics of the binary under conservative post-Newtonian forces and gravitational radiation damping. From the viewpoint of the dynamics of the binary, the standard approximation at leading order is equivalent to retaining the 0PN and 2.5PN terms in the acceleration and neglecting the intervening 1PN and 2PN terms. A complete mathematically consistent treatment of the acceleration at leading order should include all PN terms up to 2.5PN without any gaps. These define the standard and complete non-adiabatic approximants, respectively. We propose a new and simple complete adiabatic approximant constructed from the energy and flux functions. At the leading order it uses the 2PN energy function rather than the 0PN one in the standard approximation so that in spirit it corresponds to the dynamics where there are no missing post-Newtonian terms in the acceleration. We compare the overlaps of the standard and complete adiabatic approximant templates with the exact waveform (in the adiabatic approximation) for a test particle orbiting a Schwarzschild black hole. Overlaps are computed using both the white-noise spectrum and the initial laser interferometer gravitational wave observatory (LIGO) noise spectrum. The complete adiabatic approximants lead to a remarkable improvement in the effectualness (i.e., larger overlaps with the exact signal) at lower PN ($<3\mathrm{P}\mathrm{N}$) orders. However, standard adiabatic approximants of order $\ge 3\mathrm{P}\mathrm{N}$ are nearly as good as the complete adiabatic approximants for the construction of effectual templates. In general, faithfulness (i.e., smaller biases in the estimation of parameters) of complete approximants is also better than that of standard approximants. Standard and complete approximants beyond the adiabatic approximation are next studied using the Lagrangian models of Buonanno, Chen, and Vallisneri in the test mass limit. A limited extension of the results to the case of comparable mass binaries is provided. In this case, standard adiabatic approximants achieve an effectualness of 0.965 at order 3PN. If the comparable mass case is qualitatively similar to the test mass case then neither the improvement of the accuracy of energy function from 3PN to 4PN nor the improvement of the accuracy of flux function from 3.5PN to 4PN will result in a significant improvement in effectualness in the comparable mass case for terrestrial laser interferometric gravitational wave detectors.

Inflationary cosmology provides a natural mechanism for the generation of primordial perturbations which seed the formation of observed cosmic structure and lead to specific signals of anisotropy in the cosmic microwave background radiation. In order to test the broad inflationary paradigm as well as particular models against precision observations, it is crucial to be able to make accurate predictions for the power spectrum of both scalar and tensor fluctuations. We present detailed calculations of these quantities utilizing direct numerical approaches as well as error-controlled uniform approximations, comparing with the (uncontrolled) traditional slow-roll approach. A simple extension of the leading-order uniform approximation yields results for the power spectra amplitudes, the spectral indices, and the running of spectral indices, with accuracy of the order of $0.1\%$—approximately the same level at which the transfer functions are known. Several representative examples are used to demonstrate these results.

We have developed a theoretical model and a numerical code for stationary rotating superfluid neutron stars in full general relativity. The underlying two-fluid model is based on Carter’s covariant multifluid hydrodynamic formalism. The two fluids, representing the superfluid neutrons on one hand, and the protons and electrons on the other, are restricted to uniform rotation around a common axis, but are allowed to have different rotation rates. We have performed extensive tests of the numerical code, including quantitative comparisons to previous approximative results for these models. The results presented here are the first “exact” calculations of such models in the sense that no approximations (other than that inherent in a discretized numerical treatment) are used. Using this code we reconfirm the existence of prolate-oblate shaped configurations. We studied the dependency of the Kepler rotation limit and of the mass-density relation on the relative rotation rate. We further demonstrate how one can simulate a (albeit fluid) neutron-star crust by letting one fluid extend further outwards than the other, which results in interesting cases where the Kepler limit is actually determined by the outermost but slower fluid.

We constructed a model of neutrino masses using Froggatt-Nielsen mechanism with $U(1)\times Z_3\times Z_2$ flavor symmetry. The model predicts that $(2/3)m_2/m_3\sim \sqrt{2}\sin {\theta }_{13}$ at lepton number violating scale $M_1$. It is shown that the small values for $m_2/m_3$ and $\sin {\theta }_{13}$ are consequences of breaking discrete symmetries.

We consider various constraints on Higgsless models of electroweak symmetry breaking based on a bulk $\mathrm{S}\mathrm{U}(2{)}_L\times \mathrm{S}\mathrm{U}(2{)}_R\times \mathrm{U}(1{)}_{B-L}$ gauge group in warped space. First we show that the $S$ parameter which is positive if fermions are localized on the Planck brane can be lowered (or made vanishing) by changing the localization of the light fermions. If the wave function of the light fermions is almost flat their coupling to the gauge boson Kaluza-Klein (KK) modes will be close to vanishing, and therefore contributions to the $S$ parameter will be suppressed. At the same time the experimental bounds on such $Z^{\prime }$ and $W^{\prime }$ gauge bosons become very weak, and their masses can be lowered to make sure that perturbative unitarity is not violated in this theory before reaching energies of several TeV. The biggest difficulty of these models is to incorporate a heavy top quark mass without violating any of the experimental bounds on bottom quark gauge couplings. In the simplest models of fermion masses a sufficiently heavy top quark also implies an unacceptably large correction to the $Zb\overline{b}$ vertex and a large splitting between the KK modes of the top and bottom quarks, yielding large loop corrections to the $T$ parameter. We present possible directions for model building where perhaps these constraints could be obeyed as well.

We study how the exotic particles and supersymmetric partners would affect the discovery limit at the Tevatron and LHC for neutral gauge bosons in generic $E_6$ models. We examine the $Z^{\prime }$ decay in the extreme case that all of the particles are massless, then consider how the masses of nonstandard model particles will affect the discovery limit. We also calculate the discovery limit for a supersymmetric $E_6$ model with a secluded sector as a concrete example of a model with a definite set of exotic particles. Its discovery limit is small compared with other $E_6$ models due to the $U^{\prime }(1)$ charge assignment.

It is pointed out that dipion invariant mass spectrum in $X(3872)\to J/\psi \pi \pi$ is a useful probe for the $J^{PC}$ quantum number of the $X(3872)$, complementary to the angular distributions. If $X(3872)$ is a ${}^{1}P_1$ state, the dipion has a peak at a low $m_{\pi \pi }$ region, which is not in accordance with the preliminary Belle data. If $X(3872)$ is a ${}^{3}D_2$ or ${}^{3}D_3$ state, the dipion spectrum shows a peak at a high $m_{\pi \pi }$ region, which is broader than the $\rho$ resonance that might come from the decay of a molecular state: $(D\overline{D^{*}})(I=1)\to J/\psi \rho \to J/\psi {\pi }^{+}{\pi }^{-}$. Better measurement of the $m_{\pi \pi }$ spectrum will shed light on the nature of $X(3872)$.

The triply heavy baryons in the standard model formed in direct $c$ and $b$ quark fragmentation are the ${\Omega }_{ccc}$, ${\Omega }_{ccb}$, ${\Omega }_{cbb}$ and ${\Omega }_{bbb}$ baryons. We calculate their fragmentation functions in leading order of perturbative QCD. The universal fragmentation probabilities fall within the range of ${10}^{-5}-{10}^{-7}$.We also evaluate their cross section at the LHC ($\sqrt{s}=14$ TeV) using next-to-leading order matrix elements for heavy quark-antiquark pair production. We present the differential cross sections as functions of the transverse momentum as well as the total cross sections. They range from a few nb to a few pb.

We propose and discuss a numerical use for our previous precision results for the radiative corrections to unpolarized spin one-half baryon semileptonic decays, which is not compromised to fixing the form factors at prescribed values. We present various cross-checks and comparisons with other results available in the literature of such analytical radiative corrections. Our analysis, however, is general and applies to all charge assignments to the baryons allowed by heavy quarks. The procedure is exemplified with the processes ${\Xi }^0\to {\Sigma }^{+}e\overline{\nu }$ and ${\Lambda }_c^{+}\to \Lambda e^{+}\nu$.

We derive maps relating currents and their divergences in non-Abelian $\mathrm{U}(N)$ noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. For the U(1) theory, in the slowly-varying-field approximation, these maps are also seen to connect the star-gauge-covariant anomaly in the noncommutative theory with the standard Adler-Bell-Jackiw anomaly in the commutative version. For arbitrary fields, derivative corrections to the maps are explicitly computed up to $O({\theta }^2)$.