If dark matter in the galactic halo is composed of bosons that form a Bose-Einstein condensate, then it is likely that the rotation of the halo will lead to the nucleation of vortices. After a review of the Gross-Pitaevskii equation, the Thomas-Fermi approximation and vortices in general, we consider vortices in detail. We find strong bounds for the boson mass, interaction strength, the shape and quantity of vortices in the halo, the critical rotational velocity for the nucleation of vortices and, in the Thomas-Fermi regime, an exact solution for the mass density of a single, axisymmetric vortex.

A generalized true anomaly-type parametrization, convenient to describe both bound and open orbits of a two-body system in general relativity is introduced. A complete description of the time evolution of both the radial and angular equations of a binary system taking into account the first order post-Newtonian (1PN) corrections is given. The gravitational radiation field emitted by the system is computed in the 1PN approximation including higher multipole moments beyond the standard quadrupole term. The gravitational waveforms in the time domain are explicitly given up to the 1PN order for unbound orbits, but the results are also illustrated on binaries on elliptic orbits with special attention given to the effects of eccentricity.

In this paper, we derive rotating black string solutions in the presence of two kinds of nonlinear electromagnetic fields, so-called Born-Infeld and power Maxwell invariant. Investigation of the solutions show that for the Born-Infeld black string the singularity is timelike and the asymptotic behavior of the solutions is anti–de Sitter, but for power Maxwell invariant solutions, depending on the values of nonlinearity parameter, the singularity may be timelike as well as spacelike and the solutions are not asymptotically anti–de Sitter for all values of the nonlinearity parameter. Next, we calculate the conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the nonlinearity parameter. We also compute the entropy, temperature, the angular velocity, the electric charge, and the electric potential of the solutions, in which the conserved and thermodynamics quantities satisfy the first law of thermodynamics.

This article presents detailed discussions and calculations of the recent paper “Quantum Regge calculus of Einstein-Cartan theory” in [9]. The Euclidean space-time is discretized by a four-dimensional simplicial complex. We adopt basic tetrad and spin-connection fields to describe the simplicial complex. By introducing diffeomorphism and local Lorentz invariant holonomy fields, we construct a regularized Einstein-Cartan theory for studying the quantum dynamics of the simplicial complex and fermion fields. This regularized Einstein-Cartan action is shown to properly approach to its continuum counterpart in the continuum limit. Based on the local Lorentz invariance, we derive the dynamical equations satisfied by invariant holonomy fields. In the mean-field approximation, we show that the averaged size of 4-simplex, the element of the simplicial complex, is larger than the Planck length. This formulation provides a theoretical framework for analytical calculations and numerical simulations to study the quantum Einstein-Cartan theory.

A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding to simplicial geometries. On the one hand, this could serve as a starting point for a derivation of spin foam models by canonical quantization. On the other, it elucidates the interpretation of the boundary Hilbert space that arises in spin foam models. More precisely, we discuss different versions of the simplicity constraints, namely, gauge-variant and gauge-invariant versions. In the gauge-variant version, the primary and secondary simplicity constraints take a similar form to the reality conditions known already in the context of (complex) Ashtekar variables. Subsequently, we describe the effect of these primary and secondary simplicity constraints on gauge-invariant variables. This allows us to illustrate their equivalence to the so-called diagonal, cross and edge simplicity constraints, which are the gauge-invariant versions of the simplicity constraints. In particular, we clarify how the so-called gluing conditions arise from the secondary simplicity constraints. Finally, we discuss the significance of degenerate configurations, and the ramifications of our work in a broader setting.

We consider a cosmological setup, based on renormalizable superpotential terms, in which a superheavy scale $F$-term hybrid inflation is followed by a Peccei-Quinn phase transition, resolving the strong $CP$ and $\mu$ problems of the minimal supersymmetric standard model. We show that the field which triggers the Peccei-Quinn phase transition can remain after inflation well above the Peccei-Quinn scale thanks to (i) its participation in the supergravity and logarithmic corrections during the inflationary stage and (ii) the high reheat temperature after the same period. As a consequence, its presence influences drastically the inflationary dynamics and the universe suffers a second period of reheating after the Peccei-Quinn phase transition. Confronting our inflationary predictions with the current observational data, we find that, for about the central value of the spectral index, the grand unification scale can be identified with its supersymmetric value for the relevant coupling constant $\kappa \simeq 0.002$ and, more or less, natural values, $\pm (0.01–0.1)$, for the remaining parameters. On the other hand, the final reheat temperature after the Peccei-Quinn phase transition turns out to be low enough so as the gravitino problem is avoided.

In this work we investigate the duality linking standard and tachyon scalar field homogeneous and isotropic cosmologies in $N+1$ dimensions. We determine the transformation between standard and tachyon scalar fields and between their associated potentials, corresponding to the same background evolution. We show that, in general, the duality is broken at a perturbative level, when deviations from a homogeneous and isotropic background are taken into account. However, we find that for slow-rolling fields the duality is still preserved at a linear level. We illustrate our results with specific examples of cosmological relevance, where the correspondence between scalar and tachyon scalar field models can be calculated explicitly.

Several anomalies appear to be present in the large-angle cosmic microwave background anisotropy maps of the Wilkinson Microwave Anisotropy Probe, including the alignment of large-scale multipoles. Models in which isotropy is spontaneously broken (e.g., by a scalar field) have been proposed as explanations for these anomalies, as have models in which a preferred direction is imposed during inflation. We examine models inspired by these, in which isotropy is broken by a multiplicative factor with dipole and/or quadrupole terms. We evaluate the evidence provided by the multipole alignment using a Bayesian framework, finding that the evidence in favor of the model is generally weak. We also compute approximate changes in estimated cosmological parameters in the broken-isotropy models. Only the overall normalization of the power spectrum is modified significantly.

The generation of lepton asymmetry below the electroweak scale has a considerable impact on production of dark matter sterile neutrinos. Oscillations or decays of the heavier sterile neutrinos in the neutrino minimal standard model can give rise to the requisite lepton asymmetry, provided the masses of the heavier neutrinos are sufficiently degenerate. We study the renormalization group evolution of the mass difference of these singlet fermions to understand the degree of necessary fine-tuning. We construct an example of the model that can lead to a technically natural realization of this low-energy degeneracy.

We construct an explicit, TeV-scale model of decaying dark matter in which the approximate stability of the dark matter candidate is a consequence of a global symmetry that is broken only by instanton-induced operators generated by a non-Abelian dark gauge group. The dominant dark matter decay channels are to standard model leptons. Annihilation of the dark matter to standard model states occurs primarily through the Higgs portal. We show that the mass and lifetime of the dark matter candidate in this model can be chosen to be consistent with the values favored by fits to data from the PAMELA and Fermi-LAT experiments.

We consider the embedding of the supersymmetric standard model with broken R-parity in the minimal supergravity (mSUGRA) model. We restrict ourselves to the case of broken lepton number, the ${\mathrm{B}}_3$ mSUGRA model. We first study in detail how the tree-level neutrino mass depends on the mSUGRA parameters. We find, in particular, a strong dependence on the trilinear supersymmetry breaking $A$-parameter, even in the vicinity of the mSUGRA SPS1a point. We then reinvestigate the bounds on the trilinear R-parity violating couplings at the unification scale from the low-energy neutrino masses including dominant one-loop contributions. These bounds were previously shown to be very strict, as low as $\mathcal{O}({10}^{-6})$ for SPS1a. We show that these bounds are significantly weakened when considering the full mSUGRA parameter space. In particular the ratio between the tree-level and one-loop neutrino masses is reduced such that it may agree with the observed neutrino mass hierarchy. We discuss in detail how and in which parameter regions this effect arises.

An exact expression is derived for the $(\omega ,\mathit{p})=0$ thermal correlator of shear stress in SU($N_c$) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator of the energy density. The operator product expansion shows that the same linear combination has a finite limit when $\omega \to \infty$. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as ${\alpha }_s^2(\omega )$ and obeys a sum rule. The trace anomaly makes a potential contribution to the spectral sum rule which remains to be fully calculated, but which I estimate to be numerically small for $T\gtrsim 3T_c$. By contrast with the bulk channel, the shear channel spectral density is then overall enhanced as compared to the spectral density in vacuo.

We present a QCD-based model where rescattering between final state partons in deep inelastic scattering leads to events with large rapidity gaps and a leading proton. In the framework of this model the amplitude for multiple gluon exchanges is calculated in the eikonal approximation to all orders in perturbation theory. Both large and small invariant mass $M_X$ limits are considered. The model successfully describes the precise HERA data on the diffractive deep inelastic cross section in the whole available kinematical range and gives new insight into the density of gluons at very small momentum fractions in the proton.

We present an analysis of semileptonic decays of orbitally, $P$-wave excited $B_s$ meson states $B_s^{**}$, including the newly found narrow $B_{s1}(5830)$ and $B_{s2}^{*}(5840)$ states, into low-lying $D_s$ mesons ($D_s(1968)$, $D_s^{*}(2112)$, $D_{sJ}(2317)$, $D_{sJ}(2460)$) within the framework of the heavy quark effective theory. The relevant universal form factors are estimated using QCD sum rules at the leading order of the heavy quark expansion. The decay widths are predicted and the branching ratios are estimated.

In this paper we discuss a supersymmetric $D_4\times Z_5$ model which leads to vanishing reactor mixing angle ${\theta }_{13}=0$ and maximal atmospheric mixing ${\theta }_{23}=\pi /4$ in the lepton sector at leading order, due to the preservation of nontrivial distinct $D_4$ subgroups in the charged lepton and neutrino sectors, respectively. The solar mixing angle ${\theta }_{12}$ remains undetermined and is expected to be of order one. Since right-handed charged leptons transform as singlets under $D_4$, the charged lepton mass hierarchy can be naturally accounted for. The model predicts inverted mass hierarchy for neutrinos. Additionally, we show that, unlike in most of the other models of this type, all vacuum expectation values of gauge singlets (flavons) can be determined through mass parameters of the superpotential. Next-to-leading order corrections to lepton masses and mixings are calculated and shown to be under control; in particular, the corrections to ${\theta }_{23}=\pi /4$ and ${\theta }_{13}=0$ are of the order of the generic expansion parameter $ϵ\approx 0.04$ and arise dominantly from the charged lepton sector.

We consider a D2-brane in the pp-wave backgrounds obtained from ${\mathrm{AdS}}_4\times C{P}^3$ when electric and magnetic fields have been turned on. Upon fixing the light-cone gauge, light-cone Hamiltonian and Bogomolni-Prasad-Sommerfield configurations are obtained. In particular we study Bogomolni-Prasad-Sommerfield configurations with an electric dipole on the two-sphere giant and a giant graviton rotating in transverse directions. Moreover we show that the gauge field living on the D2-brane is replaced by a scalar field in the light-cone Hamiltonian. We also present a matrix model by regularizing (quantizing) 2-brane theory.

Recently, the asymptotic behavior of three-dimensional anti-de Sitter (AdS) gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two dimensional conformal group and that included a falloff of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely, the chirality that has the milder behavior at infinity. The other chirality blows up faster than AdS and does not define an asymptotically AdS spacetime. By contrast, both chiralities are subdominant with respect to the asymptotic behavior of AdS spacetime below the chiral point. Nevertheless, the boundary conditions given in the earlier treatment only included one of the two chiralities (which could be either one) at a time. We investigate in this paper whether one can generalize these boundary conditions in order to consider simultaneously both chiralities below the chiral point. We show that this is not possible if one wants to keep the two-dimensional conformal group as asymptotic symmetry group. Hence, the boundary conditions given in the earlier treatment appear to be the best possible ones compatible with conformal symmetry. In the course of our investigations, we provide general formulas controlling the asymptotic charges for all values of the topological mass (not just below the chiral point).

Fefferman and Graham showed some time ago that four-dimensional conformal geometries could be analyzed in terms of six-dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently, it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein’s equations are then equivalent to the existence of a parallel scale tractor (a six-component vector subject to a certain first order covariant constancy condition at every point in four-dimensional spacetime). These results suggest a six-dimensional description of four-dimensional physics, a viewpoint promulgated by the 2 times physics program of Bars. The Fefferman-Graham construction relies on a triplet of operators corresponding, respectively, to a curved six-dimensional light cone, the dilation generator and the Laplacian. These form an $\mathfrak{s}\mathfrak{p}(2)$ algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four-dimensional gravity is recast in terms of six-dimensional quantum mechanics by melding the 2 times and tractor approaches. This parent formulation of gravity is built from an infinite set of six-dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four-dimensional one built from a scalar doublet, a tractor-vector multiplet and a conformal class of metrics.

A perturbative expansion of loop quantum cosmological transitions amplitudes of Bianchi I models is performed. Following the procedure outlined in [1,2] for isotropic models, it is shown that the resulting expansion can be written in the form of a series of amplitudes each with a fixed number of transitions mimicking a spin foam expansion. This analogy is more complete than in the isotropic case, since there are now the additional anisotropic degrees of freedom which play the role of “coloring” of the spin foams. Furthermore, the isotropic expansion is recovered by integrating out the anisotropies.