We study analytically the relaxation phase of perturbed, rapidly rotating black holes. In particular, we derive a simple formula for the fundamental quasinormal resonances of near-extremal Kerr black holes. The formula is expressed in terms of the black hole physical parameters: $\omega =m\Omega -i2\pi T_{\mathrm{BH}}(n+\frac{1}{2})$, where $T_{\mathrm{BH}}$ and $\Omega$ are the temperature and angular velocity of the black hole, and $m$ is the azimuthal harmonic index of a corotating equatorial mode. This formula implies that the relaxation period $\tau \sim 1/\Im \omega$ of the black hole becomes extremely long as the extremal limit $T_{\mathrm{BH}}\to 0$ is approached. The analytically derived formula is shown to agree with direct numerical computations of the black hole resonances. We use our results to demonstrate analytically the fact that near-extremal Kerr black holes saturate the recently proposed universal relaxation bound.

In this paper, new exact solutions in eight-dimensional Lovelock theory will be presented. These solutions are the vacuum static wormhole, the black hole, and generalized Bertotti-Robinson space-times with nontrivial torsion. All of the solutions have a cross product structure of the type $M_5\times {\Sigma }_3$, where $M_5$ is a five-dimensional manifold and ${\Sigma }_3$ a compact constant curvature manifold. The wormhole is the first example of a smooth vacuum static Lovelock wormhole which is neither Chern-Simons nor Born-Infeld. It will be also discussed how the presence of torsion affects the “navigableness” of the wormhole for scalar and spinning particles. It will be shown that the wormhole with torsion may act as “geometrical filter”: A very large torsion may “increase the traversability” for scalars while acting as a “polarizator” on spinning particles. This may have interesting phenomenological consequences.

We address the problem of studying the decay of the inflaton field $\varphi$ to another scalar field $\chi$ through parametric resonance in the case of a coupling that involves several decay modes. This amounts to the presence of extra harmonic terms in the perturbation of the $\chi$ field dynamics. For the case of two frequencies we compute the geometry of the resonance regions, which is significantly altered due to the presence of noncuspidal resonance regions associated to higher harmonics and to the emergence of instability “pockets.” We discuss the effect of this change in the efficiency of the energy transfer process for the simplest case of a coupling given by a combination of the two interaction terms of homogeneous degree usually considered in the literature. We find that the presence of higher harmonics has limited cosmological implications.

We study the evolution of linear density perturbations in the context of interacting scalar field-dark matter cosmologies, where the presence of the coupling acts as a stabilization mechanism for the runaway behavior of the scalar self-interaction potential as in the case of the chameleon model. We show that, in the “adiabatic” background regime of the system, the rise of unstable growing modes of the perturbations is suppressed by the slow-roll dynamics of the field. Furthermore, the coupled system behaves as an inhomogeneous adiabatic fluid. In contrast, instabilities may develop for large values of the coupling constant, or along nonadiabatic solutions, characterized by a period of high-frequency dumped oscillations of the scalar field. In the latter case, the dynamical instabilities of the field fluctuations, which are typical of oscillatory scalar field regimes, are amplified and transmitted by the coupling to dark matter perturbations.

A period of slow contraction with equation of state $w>1$, known as an ekpyrotic phase, has been shown to flatten and smooth the universe if it begins the phase with small perturbations. In this paper, we explore how robust and powerful the ekpyrotic smoothing mechanism is by beginning with highly inhomogeneous and anisotropic initial conditions and numerically solving for the subsequent evolution of the universe. Our studies, based on a universe with gravity plus a scalar field with a negative exponential potential, show that some regions become homogeneous and isotropic while others exhibit inhomogeneous and anisotropic behavior in which the scalar field behaves like a fluid with $w=1$. We find that the ekpyrotic smoothing mechanism is robust in the sense that the ratio of the proper volume of the smooth to nonsmooth region grows exponentially fast along time slices of constant mean curvature.

We show that nonpertubative lattice studies of four-dimensional $\mathcal{N}=4$ super-Yang-Mills are within reach. We use Ginsparg-Wilson fermions to avoid gluino masses and an exact implementation of the (chiral) $R$-symmetry, which greatly limits the number of counterterms that must be fine-tuned. Only bosonic operators require fine-tuning, so all tunings can be done “offline” by a Ferrenberg-Swendsen type reweighting. We show what measurables can be used to perform the tuning.

In this paper we describe gauge invariant multiquark states generalizing the path integral framework developed by Parrinello, Jona-Lasinio, and Zwanziger to amend the Faddeev-Popov approach. This allows us to produce states such that, in a limit which we call the ice limit, fermions are dressed with glue exclusively from the fundamental modular region associated with Coulomb gauge. The limit can be taken analytically without difficulties, avoiding the Gribov problem. This is illustrated by an unambiguous construction of gauge invariant mesonic states for which we simulate the static quark-antiquark potential.

There is a group-theoretical connection between fermion mixing matrices and minimal horizontal symmetry groups. Applying this connection to the tribimaximal neutrino mixing matrix, we show that the minimal horizontal symmetry group for leptons is uniquely $S_4$, the permutation group of four objects.

We consider QCD at temperatures $T$ near $T_c$, where the theory deconfines. We distinguish between a “complete” quark-gluon plasma (QGP), where the vacuum expectation value of the renormalized Polyakov loop is near unity, essentially constant with $T$, and the “semi”-QGP, where the loop changes strongly with $T$. Lattice simulations indicate that in QCD, there is a semi-QGP from below $T_c$ to a few times that. Using a semiclassical model, we compute the shear viscosity, $\eta$, to leading order in perturbation theory. We find that near $T_c$, where the expectation value of the Polyakov loop is small, that $\eta /T^3$ is suppressed by two powers of the loop. For heavy ions, this suggests that during the initial stages of the collision, hydrodynamic behavior at the LHC will be characterized by a shear viscosity which is significantly larger than that at RHIC.

Dark energy models with a single scalar field cannot cross the equation of state divide set by a cosmological constant. More general models that allow crossing require additional degrees of freedom to ensure gravitational stability. We show that a parameterized post-Friedmann description of cosmic accelerzation provides a simple but accurate description of multiple scalar field crossing models. Moreover the prescription provides a well-controlled approximation for a wide range of “smooth” dark energy models. It conserves energy and momentum and is exact in the metric evolution on scales well above and below the transition scale to relative smoothness. Standard linear perturbation tools have been altered to include this description and made publicly available for studies of the dark energy involving cosmological structure out to the horizon scale.

We study the string dual to $N=1$ supersymmetric QCD deformed by a quartic superpotential in the quark superfields. We present a unified view of the previous results in the literature and find new exact solutions and new asymptotic solutions. Then we study the physics encoded in these backgrounds, giving, among other things, a resolution to an old puzzle related to the beta function and a sufficient criteria for screening. We also extend our results to the $SO(N_c)$ case where we present a candidate for the Wilson loop in the spinorial representation. Various aspects of this line of research are critically analyzed.

There is a unique Lorentz-violating modification of the Maxwell theory of photons, which maintains gauge invariance, , and renormalizability. Restricting the modified-Maxwell theory to the isotropic sector and adding a standard spin- Dirac particle with minimal coupling to the nonstandard photon , the resulting modified-quantum-electrodynamics model involves a single dimensionless “deformation parameter,” . The exact tree-level decay rates for two processes have been calculated: vacuum Cherenkov radiation for the case of positive and photon decay for the case of negative . From the inferred absence of these decays for a particular high-quality ultrahigh-energy-cosmic-ray event detected at the Pierre Auger Observatory and a well-established excess of TeV gamma-ray events observed by the High Energy Stereoscopic System telescopes, a two-sided bound on is obtained, which improves by 8 orders of magnitude upon the best direct laboratory bound. The implications of this result are briefly discussed.

We use the leading singularity technique to determine the planar three-loop five-particle amplitude in $\mathcal{N}=4$ super Yang-Mills in terms of a simple basis of integrals. We analytically compute the integral coefficients for both the parity-even and the parity-odd parts of the amplitude. The parity-even part involves only dual conformally invariant integrals. Using the method of obstructions we numerically evaluate two previously unfixed coefficients that appear in the three-loop Bern Dixon Smirnov ansatz.

We present a new leptogenesis scenario, where the lepton asymmetry is generated by $CP$-violating decays of heavy electroweak singlet neutrinos via electromagnetic dipole moment couplings to the ordinary light neutrinos. Akin to the usual scenario where the decays are mediated through Yukawa interactions, we have shown, by explicit calculations, that the desired asymmetry can be produced through the interference of the corresponding tree-level and one-loop decay amplitudes involving the effective dipole moment operators. We also find that the relationship of the leptogenesis scale to the light neutrino masses is similar to that for the standard Yukawa-mediated mechanism.

We analyze the role of Lorentz symmetry in the perturbative nongravitational anomalies for a single family of fermions. The theory is assumed to be translational-invariant, power-counting renormalizable and based on a local action, but is allowed to have general Lorentz violating operators. We study the conservation of global and gauge currents associated with general internal symmetry groups and find, by using a perturbative approach, that Lorentz symmetry does not participate in the clash of symmetries that leads to the anomalies. We first analyze the triangle graphs and prove that there are regulators for which the anomalous part of the Ward identities exactly reproduces the Lorentz-invariant case. Then we show, by means of a regulator independent argument, that the anomaly cancellation conditions derived in Lorentz-invariant theories remain necessary ingredients for anomaly freedom.

We pursue the possibility of using subcritical string theory in 4 spacetime dimensions to establish a string dual for large $N$ QCD. In particular we study the even G-parity sector of the 4 dimensional Neveu-Schwarz dual resonance model as the natural candidate for this string theory. Our point of view is that the open string dynamics given by this model will determine the appropriate subcritical closed string theory, a tree level background of which should describe the sum of planar multiloop open string diagrams. We examine the one-loop open string diagram, which contains information about the closed string spectrum at weak coupling. Higher loop open string diagrams will be needed to determine closed string interactions. We also analyze the field theory limit of the one-loop open string diagram and recover the correct running coupling behavior of the limiting gauge theory.

Binary neutron-star systems represent primary sources for the gravitational-wave detectors that are presently operating or are close to being operating at the target sensitivities. We present a systematic investigation in full general relativity of the dynamics and gravitational-wave emission from binary neutron stars which inspiral and merge, producing a black hole surrounded by a torus. Our results represent the state of the art from several points of view: (i) We use high-resolution shock-capturing methods for the solution of the hydrodynamics equations and high-order finite-differencing techniques for the solution of the Einstein equations; (ii) We employ adaptive mesh-refinement techniques with “moving boxes” that provide high-resolution around the orbiting stars; (iii) We use as initial data accurate solutions of the Einstein equations for a system of binary neutron stars in irrotational quasicircular orbits; (iv) We exploit the isolated-horizon formalism to measure the properties of the black holes produced in the merger; (v) Finally, we use two approaches, based either on gauge-invariant perturbations or on Weyl scalars, to calculate the gravitational waves emitted by the system. Within our idealized treatment of the matter, these techniques allow us to perform accurate evolutions on time scales never reported before (i.e. $\sim 30\mathrm{ms}$) and to provide the first complete description of the inspiral and merger of a neutron-star binary leading to the prompt or delayed formation of a black hole and to its ringdown. We consider either a polytropic equation of state or that of an ideal fluid and show that already with this idealized treatment a very interesting phenomenology can be described. In particular, we show that while higher-mass polytropic binaries lead to the prompt formation of a rapidly rotating black hole surrounded by a dense torus, lower-mass binaries give rise to a differentially rotating star, which undergoes large oscillations and emits large amounts of gravitational radiation. Eventually, also the hyper-massive neutron star collapses to a rotating black hole surrounded by a torus. Finally, we also show that the use of a nonisentropic equation of state leads to significantly different evolutions, giving rise to a delayed collapse also with high-mass binaries, as well as to a more intense emission of gravitational waves and to a geometrically thicker torus.

The strong equivalence principle is extended in application to averaged dynamical fields in cosmology to include the role of the average density in the determination of inertial frames. The resulting cosmological equivalence principle is applied to the problem of synchronization of clocks in the observed universe. Once density perturbations grow to give density contrasts of order 1 on scales of tens of megaparsecs, the integrated deceleration of the local background regions of voids relative to galaxies must be accounted for in the relative synchronization of clocks of ideal observers who measure an isotropic cosmic microwave background. The relative deceleration of the background can be expected to represent a scale in which weak-field Newtonian dynamics should be modified to account for dynamical gradients in the Ricci scalar curvature of space. This acceleration scale is estimated using the best-fit nonlinear bubble model of the universe with backreaction. At redshifts $z\lesssim 0.25$ the scale is found to coincide with the empirical acceleration scale of modified Newtonian dynamics. At larger redshifts the scale varies in a manner which is likely to be important for understanding dynamics of galaxy clusters, and structure formation. Although the relative deceleration, typically of order ${10}^{-10}{\mathrm{ms}}^{-2}$, is small, when integrated over the lifetime of the universe it amounts to an accumulated relative difference of 38% in the rate of average clocks in galaxies as compared to volume-average clocks in the emptiness of voids. A number of foundational aspects of the cosmological equivalence principle are also discussed, including its relation to Mach’s principle, the Weyl curvature hypothesis, and the initial conditions of the universe.

We demonstrate in examples that the covariant retarded Green’s functions in electromagnetism and linearized gravity work as expected in de Sitter spacetime. We first clarify how retarded Green’s functions should be used in spacetimes with spacelike past infinity such as de Sitter spacetime. In particular, we remind the reader of a general formula which gives the field for given initial data on a Cauchy surface and a given source (a charge or stress-energy tensor distribution) in its future. We then apply this formula to three examples: (i) electromagnetism in the future of a Cauchy surface in Minkowski spacetime, (ii) electromagnetism in de Sitter spacetime, and (iii) linearized gravity in de Sitter spacetime. In each example the field is reproduced correctly as predicted by the general argument. In the third example we construct a linearized gravitational field from two equal point masses located at the “North and South Poles” which is nonsingular on the cosmological horizon and satisfies a covariant gauge condition and show that this field is reproduced by the retarded Green’s function with corresponding gauge parameters.

We generalize the Bekenstein-Sandvik-Barrow-Magueijo model for the variation of the fine-structure “constant,” $\alpha$, to include an exponential or inverse power-law self-potential for the scalar field $\phi$ which drives the time variation of $\alpha$, and consider the dynamics of $\phi$ in such models. We find solutions for the evolution of $\phi$ or $\alpha$ in matter-, radiation-, and dark-energy-dominated cosmic eras. In general, the evolution of $\phi$ is well determined solely by either the self-potential or the coupling to matter, depending on the model parameters. The results are general and applicable to other models where the evolution of a scalar field is governed by a matter coupling and a self-potential. We find that the existing astronomical data stringently constrains the possible evolution of $\alpha$ between redshifts $z\simeq 1–3.5$ and the present, and this leads to a very strong limit on the allowed deviation of the potential from that of a pure cosmological constant.