A class of dynamical shift conditions is shown to lead to a pseudohyperbolic evolution system, both in the Z4 and in the BSSN numerical relativity formalisms. This is done by using a plane-wave analysis which can be viewed as an extension of the standard Fourier analysis for this kind of systems. The proposed class generalizes the harmonic shift condition, where light speed is the only nontrivial characteristic speed, and it is contained into the multiparameter family of minimal distortion shift conditions recently proposed by Lindblom and Scheel. The relationship with the analogous “dynamical freezing” shift conditions used in black hole simulations is discussed.

We show that the naked singularities arising in dust collapse from smooth initial data (which include those discovered by Eardley and Smarr, Christodoulou, and Newman) are removed when we make a transition to higher dimensional spacetimes. Cosmic censorship is then restored for dust collapse, which will always produce a black hole as the collapse end state for dimensions $D>~6,$ under conditions to be motivated physically such as the smoothness of initial data from which the collapse develops.

We study the physics of a single discrete gravitational extra dimension using the effective field theory for massive gravitons. We first consider a minimal discretization with 4D gravitons on the sites and nearest neighbor hopping terms. At the linear level, 5D continuum physics is recovered correctly, but at the nonlinear level the theory becomes highly nonlocal in the discrete dimension. There is a peculiar UV/IR connection, where the scale of strong interactions at high energies is related to the radius of the dimension. These new effects formally vanish in the limit of zero lattice spacing, but do not do so quickly enough to reproduce the continuum physics consistently in an effective field theory up to the 5D Planck scale. Nevertheless, this model does make sense as an effective theory up to energies parametrically higher than the compactification scale. In order to have a discrete theory that appears local in the continuum limit, the lattice action must have interactions between distant sites. We speculate on the relevance of these observations to the construction of finite discrete theories of gravity in four dimensions.

The arrival times of gravitational waves and optical light from orbiting binaries provide a mechanism to understand the propagation speed of gravity when compared to that of light or electromagnetic radiation. This is achieved with a measurement of any offset between the optically derived orbital phase and that derived from gravitational wave data, at a specified location of one binary component with respect to the other. Using a sample of close white dwarf binaries (CWDBs) detectable with the Laser Interferometer Space Antenna and optical light curve data related to binary eclipses from meter-class telescopes for the same sample, we determine the accuracy to which orbital phase differences can be extracted. We consider an application of these measurements involving a variation of the speed of gravity, when compared to the speed of light, due to a massive graviton. For a subsample of $\sim 400$ CWDBs with high signal-to-noise ratio gravitational wave and optical data with magnitudes brighter than 25, the combined upper limit on the graviton mass is at the level of $\sim 6\times {10}^{-24}\mathrm{eV}.$ This limit is two orders of magnitude better than the present limit derived by Yukawa-correction arguments related to the Newtonian potential and applied to the Solar System.

We report on a search for gravitational wave bursts using data from the first science run of the Laser Interferometer Gravitational Wave Observatory (LIGO) detectors. Our search focuses on bursts with durations ranging from 4 to 100 ms, and with significant power in the LIGO sensitivity band of 150 to 3000 Hz. We bound the rate for such detected bursts at less than 1.6 events per day at a 90% confidence level. This result is interpreted in terms of the detection efficiency for ad hoc waveforms (Gaussians and sine Gaussians) as a function of their root-sum-square strain $h_{\mathrm{rss}};$ typical sensitivities lie in the range $h_{\mathrm{rss}}\sim {10}^{-19}–{10}^{-17}\mathrm{strain}/\sqrt{\mathrm{Hz}},$ depending on the waveform. We discuss improvements in the search method that will be applied to future science data from LIGO and other gravitational wave detectors.

Geometric inequalities of classical differential geometry are used to extend to higher dimensional spacetimes the Penrose-Gibbons isoperimetric inequality and the hoop conjecture of general relativity.

We study neutrino masses and mixing in R-parity violating supersymmetric models with generic soft supersymmetry breaking terms. Neutrinos acquire masses from various sources: tree level neutrino–neutralino mixing and loop effects proportional to bilinear and/or trilinear R-parity violating parameters. Each of these contributions is controlled by different parameters and has different suppression or enhancement factors that we identify. Within an Abelian horizontal symmetry framework these factors are related and specific predictions can be made. We find that the main contributions to the neutrino masses are from the tree level and the bilinear loops and that the observed neutrino data can be accommodated once mild fine-tuning is allowed.

In the framework of the 5D low-energy effective field theory of the heterotic string with no vector fields excited, we combine two nonlinear methods in order to construct a solitonic field configuration. We first apply the inverse scattering method on a trivial vacuum solution and obtain a stationary axisymmetric two-soliton configuration consisting of a massless gravitational field coupled to a nontrivial chargeless dilaton and to an axion field endowed with charge. The implementation of this method was done following a scheme previously proposed by Yurova. We also show that within this scheme it is not possible to get massive gravitational solitons at all. We then apply a nonlinear Lie-Bäcklund matrix transformation of Ehlers type on this massless solution and get a massive rotating axisymmetric gravitational soliton coupled to axion and dilaton fields endowed with charges. We study as well some physical properties of the constructed massless and massive solitons and discuss the effect of the generalized solution generating technique on the seed solution and its further generalizations.

We find asymptotically anti–de Sitter solutions in $\mathcal{N}=8\mathrm{}$ supergravity which have a negative total energy. This is possible since the boundary conditions required for the positive energy theorem are stronger than those required for a finite mass (and allowed by string theory). But the stability of the anti–de Sitter vacuum is still ensured by the positivity of a modified energy, which includes an extra surface term. Some of the negative energy solutions describe the classical evolution of nonsingular initial data to naked singularities. Since there is an open set of such solutions, cosmic censorship is violated generically in supergravity. Using the dual field theory description, we argue that these naked singularities will be resolved in the full string theory.

We measure cosmological parameters using the three-dimensional power spectrum $P\left(k\right)\mathrm{}$ from over 200 000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with Wilkinson Microwave Anisotropy Probe (WMAP) and other data. Our results are consistent with a “vanilla” flat adiabatic cold dark matter model with a cosmological constant without tilt ${(n}_s=1),$ running tilt, tensor modes, or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening $1\sigma$ constraints on the Hubble parameter from $h\approx {0.74}_{-0.07}^{+0.18\mathrm{}}$ to $h\approx {0.70}_{-0.03}^{+0.04\mathrm{}},$ on the matter density from ${\Omega }_m\approx 0.25\pm 0.10$ to ${\Omega }_m\approx 0.30\pm 0.04$ $\left(1\mathrm{}\sigma \right)$ and on neutrino masses from $<11\mathrm{}$ to $<0.6\mathrm{}\mathrm{eV}$ (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the Two Degree Field Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from $t_0\approx {16.3}_{-1.8}^{+2.3\mathrm{}}\mathrm{Gyr}$ to $t_0\approx {14.1}_{-0.9}^{+1.0\mathrm{}}\mathrm{Gyr}$ by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.

Predictive Higgs-boson–fermion couplings can be obtained when a specific texture for the fermion mass matrices is included in the general two-Higgs doublet model. We derive the form of these couplings in the charged lepton sector using a Hermitian mass matrix ansatz with four-texture zeros. The presence of unconstrained phases in the vertices ${\phi }_i{l}_i{l}_j$ modifies the pattern of flavor-violating Higgs boson interactions. Bounds on the model parameters are obtained from present limits on rare lepton flavor-violating processes, which could be extended further by the search for the decay $\overrightarrow{\tau }\mu \mu \mu$ and $\mu -e$ conversion at future experiments. The signal from Higgs boson decays ${\phi }_i\to \tau \mu$ could be searched for at the CERN Large Hadron Collider, while $e-\mu$ transitions could produce a detectable signal at a future $e\mu$ collider, through the reaction $e^{+}{\mu }^{-}\to h^0\to {\tau }^{+}{\tau }^{-}.$

Based on tree-level open-string scattering amplitudes in the low string-scale scenario, we derive the massless fermion scattering amplitudes. The amplitudes are required to reproduce those of the standard model at the tree level in the low energy limit. We then obtain four-fermion contact interactions by expanding in inverse powers of the string scale and explore the constraints on the string scale from low energy data. The Chan-Paton factors and the string scale are treated as free parameters. We find that data from the neutral and charged current processes at DESY HERA, Drell-Yan process at the Fermilab Tevatron, and from CERN LEP-II put lower bounds on the string scale $M_S,$ for typical values of the Chan-Paton factors, in the range $M_S>~0.9-1.3\mathrm{TeV},$ comparable to Tevatron bounds on $Z^{\prime }$ and $W^{\prime }$ masses.

Quantum chromodynamics (QCD) at finite temperature $\mathrm{}\left(T\right),$ baryon chemical potential $\left({\mu }_{\mathrm{B}}\right),$ and isospin chemical potential $\left({\mu }_{\mathrm{I}}\right)$ is studied in the strong coupling limit on a lattice with staggered fermions. With the use of large dimensional expansion and the mean field approximation, we derive an effective action written in terms of the chiral condensate and pion condensate as a function of T, ${\mu }_{\mathrm{B}},$ and ${\mu }_{\mathrm{I}}.$ The phase structure in the space of T and ${\mu }_{\mathrm{B}}$ is elucidated, and simple analytical formulas for the critical line of the chiral phase transition and the tricritical point are derived. The effects of a finite quark mass (m) and finite ${\mu }_{\mathrm{I}}$ on the phase diagram are discussed. We also investigate the phase structure in the space of T, ${\mu }_{\mathrm{I}},$ and m, and clarify the correspondence between color SU(3) QCD with finite isospin density and color SU(2) QCD with finite baryon density. Comparisons of our results with those from recent Monte Carlo lattice simulations on finite density QCD are given.

Against the conventional picture that the mass matrix forms in the quark sectors will take somewhat different structures from those in the lepton sectors, on the basis of the idea that all the mass matrices of quarks and leptons have the same texture, a universal texture of quark and lepton mass matrices is proposed by assuming a discrete symmetry $Z_3$ and an extended flavor $2\leftrightarrow 3$ symmetry. The texture is described by three parameters (including the phase parameter). The neutrino masses and mixings are investigated according to this ansatz.

Captures of stellar-mass compact objects (COs) by massive $\left(\sim {10}^6{M}_{\odot }\right)$ black holes (MBHs) are potentially an important source for LISA, the proposed space-based gravitational-wave (GW) detector. The orbits of the inspiraling COs are highly complicated; they can remain rather eccentric up until the final plunge, and display extreme versions of relativistic perihelion precession and Lense-Thirring precession of the orbital plane. The amplitudes of the strongest GW signals are expected to be roughly an order of magnitude smaller than LISA’s instrumental noise, but in principle (i.e., with sufficient computing power) the GW signals can be disentangled from the noise by matched filtering. The associated template waveforms are not yet in hand, but theorists will very likely be able to provide them before LISA launches. Here we introduce a family of approximate (post-Newtonian) capture waveforms, given in (nearly) analytic form, for use in advancing LISA studies until more accurate versions are available. Our model waveforms include most of the key qualitative features of true waveforms, and cover the full space of capture-event parameters (including orbital eccentricity and the MBH’s spin). Here we use our approximate waveforms to (i) estimate the relative contributions of different harmonics (of the orbital frequency) to the total signal-to-noise ratio, and (ii) estimate the accuracy with which LISA will be able to extract the physical parameters of the capture event from the measured waveform. For a typical source (a ${10M}_{\odot }$ CO captured by a ${10}^6{M}_{\odot }$ MBH at a signal-to-noise ratio of 30), we find that LISA can determine the MBH and CO masses to within a fractional error of $\sim {10}^{-4},$ measure ${S/M}^2$ (where S and M are the MBH’s mass and spin) to within $\sim {10}^{-4},$ and determine the location to the source on the sky to within $\sim {10}^{-3}$ stradians.

Data collected by the GEO 600 and LIGO interferometric gravitational wave detectors during their first observational science run were searched for continuous gravitational waves from the pulsar $\mathrm{J}1939+2134$ at twice its rotation frequency. Two independent analysis methods were used and are demonstrated in this paper: a frequency domain method and a time domain method. Both achieve consistent null results, placing new upper limits on the strength of the pulsar’s gravitational wave emission. A model emission mechanism is used to interpret the limits as a constraint on the pulsar’s equatorial ellipticity.

A supersymmetric version of the ${\mathrm{SU}\left(3\right)\mathrm{}}_L\otimes {U\left(1\right)\mathrm{}}_X$ gauge model is presented. The model is embedded in a ${\mathrm{SU}\left(6\right)\mathrm{}}_L\otimes {U\left(1\right)\mathrm{}}_X$ gauge group and it has been built up completely chiral anomaly free and without any exotic charges in the fermionic content. The minimal supersymmetric standard model can be seen as an effective theory of this larger symmetry. We analyze how the spectrum of the new model can shift the upper bound on the CP-even Higgs boson and we find that it can be moved up to 143 GeV.

We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose an explicitly symmetry-breaking source term $h\overline{\psi }i{\gamma }_5{\tau }^3\psi$ was added to the fermion action. The order parameter $〈\overline{\psi }i{\gamma }_5{\tau }^3\psi 〉$ was computed with the hybrid Monte Carlo algorithm at several values of $(\beta ,\kappa ,h)$ on lattices of sizes $4^4$ to ${12}^4$ and extrapolated to $h=0.\mathrm{}$ The existence of a parity-flavor breaking phase can be confirmed at $\beta =4.0\mathrm{}$ and 4.3, while we do not find parity-flavor breaking at $\beta =4.6\mathrm{}$ and 5.0.

We study the topological susceptibility $\chi$ in QCD with two quark flavors using lattice field configurations that have been produced with an $O\left(a\right)\mathrm{}$-improved clover quark action. We find clear evidence for the expected suppression at a small quark mass $m_q$ and examine the variation of $\chi$ with this mass and the lattice spacing a. A joint continuum and chiral extrapolation yields good agreement with theoretical expectations as ${a,m}_q\to 0.$ A moderate increase in autocorrelation is observed on the more chiral ensembles, but within large statistical errors. Finite volume effects are negligible for the Leutwyler-Smilga parameter $x_{\mathrm{LS}}\gtrsim 10,$ and no evidence for a nearby phase transition is observed.

The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is examined to extract the Hamiltonian limit, using standard path integral Monte Carlo (PIMC) methods. We examine the mean plaquette and string tension and compare them to results obtained within the Hamiltonian framework of Kogut and Susskind. The results are a significant improvement upon previous Hamiltonian estimates, despite the extrapolation procedure necessary to extract observables. We conclude that the PIMC method is a reliable method of obtaining results for the Hamiltonian version of the theory. Our results also clearly demonstrate the universality between the Hamiltonian and Euclidean formulations of lattice gauge theory. It is particularly important to take into account the renormalization of both the anisotropy, and the Euclidean coupling ${\beta }_E,$ in obtaining these results.