Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first three, the line of sight is tangent to a smooth caustic surface. The curvature of the surface at the tangent point is positive, negative or zero. In the fourth case the line of sight passes near a cusp. For each we derive the map between the image and source planes. In some cases, a point source has multiple images and experiences infinite magnification when the images merge. Unfortunately, for the dark matter caustics expected in realistic galactic halo models, the angular resolution required to resolve the multiple images is not presently achievable. A more promising approach aims to observe the distortions caused by dark matter caustics in the images of extended sources, such as radio jets.

We discuss the onset of symmetry breaking from the false vacuum in generic scenarios in which the mass squared of the symmetry breaking (Higgs) field depends linearly with time, as it occurs, via the evolution of the inflaton, in models of hybrid inflation. We show that the Higgs fluctuations evolve from quantum to classical during the initial stages. This justifies the subsequent use of real-time lattice simulations to describe the fully nonperturbative and nonlinear process of symmetry breaking. The early distribution of the Higgs field is that of a smooth classical Gaussian random field, and consists of lumps whose shape and distribution is well understood analytically. The lumps grow with time and develop into “bubbles” which eventually collide among themselves, thus populating the high momentum modes, in their way towards thermalization at the true vacuum. With the help of some approximations we are able to provide a quasianalytic understanding of this process.

The Laser Interferometer Space Antenna will operate as an AM-FM receiver for gravitational waves. For binary systems, the source location, orientation and orbital phase are encoded in the amplitude and frequency modulation. The same modulations spread a monochromatic signal over a range of frequencies, making it difficult to identify individual sources. We present a method for detecting and subtracting individual binary signals from a data stream with many overlapping signals.

We extend previous analyses of the interplay between nonuniversalities in the gaugino mass sector and the thermal relic densities of LSP neutralinos, in particular to the case of moderate to large $\tan \beta .$ We introduce a set of parameters that generalizes the standard unified scenario to cover the complete allowed parameter space in the gaugino mass sector. We discuss the physical significance of the cosmologically preferred degree of degeneracy between charginos and the LSP and study the effect this degree of degeneracy has on the prospects for direct detection of relic neutralinos in the next round of dark matter detection experiments. Last, we compare the fine-tuning required to achieve a satisfactory relic density with the case of universal gaugino masses, as in minimal supergravity, and find it to be of a similar magnitude. The sensitivity of quantifiable measures of fine-tuning on such factors as the gluino mass and top and bottom masses is also examined.

We study the process of electron-positron annihilation into back-to-back jets, where in each jet a pair of hadrons is detected. The orientation of these two pairs with respect to each other can be used to extract the interference fragmentation functions in a clean way: for instance, from BELLE or BABAR experiment data. This is of relevance for studies of the transversity distribution function. In particular, we focus on two azimuthal asymmetries. The first one has already been studied by Artru and Collins, but is now expressed in terms of interference fragmentation functions. The second asymmetry is new and involves a function that is related to longitudinal jet handedness. This asymmetry offers a different way of studying handedness correlations.

In a previous paper, a binary black hole four-metric was presented in a post-Newtonian corotating coordinate system valid only up to the holes’ apparent horizons. In this paper, I define an ingoing coordinate transformation that extends this corotating coordinate system through the holes’ horizons and into their interiors. The motivation for using ingoing coordinates is that numerical simulations of black holes require the computational grid to extend inside the horizons. The coordinate transformation presented here makes the binary black hole four-metric suitable as a source of initial data for numerical simulations.

Recent results show that atmospheric ${\nu }_{\mu }$ oscillate with $\delta m^2\simeq 3\times {10}^{-3}{\mathrm{eV}}^2$ and ${\sin }^{2}2{\theta }_{\mathrm{atm}}\simeq 1,$ and that conversion into ${\nu }_e$ is strongly disfavored. The Super-Kamiokande (SK) Collaboration, using a combination of three techniques, reports that their data favor ${\nu }_{\mu }\to {\nu }_{\tau }$ over ${\nu }_{\mu }\to {\nu }_{\mathrm{sterile}}.$ This distinction is extremely important for both four-neutrino models and cosmology. We propose that neutrino-proton elastic scattering $(\nu +\overrightarrow{p}\nu +p)$ in water Čerenkov detectors can also distinguish between active and sterile oscillations. This was not previously recognized as a useful channel since only about 2% of struck protons are above the Čerenkov threshold. Nevertheless, in the present SK data there should be about 40 identifiable events. We show that these events have unique particle identification characteristics, point in the direction of the incoming neutrinos, and correspond to a narrow range of neutrino energies (1–3 GeV, oscillating near the horizon). This channel will be particularly important in Hyper-Kamiokande, with $\sim 40$ times higher rate. Our results have other important applications. First, for a similarly small fraction of atmospheric neutrino quasielastic events, the proton is relativistic. This uniquely selects ${\nu }_{\mu }$ (not ${\overline{\nu }}_{\mu })$ events, useful for understanding matter effects, and allows determination of the neutrino energy and direction, useful for the $L/E$ dependence of oscillations. Second, using accelerator neutrinos, both elastic and quasielastic events with relativistic protons can be seen in the K2K 1-kton near detector and MiniBooNE.

We present explicitly another example of a temperature inversion symmetry in the Casimir effect for a nonsymmetric boundary condition. We also give an interpretation for our result.

A general-covariant extension of Einstein’s field equations is considered with a view to numerical relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_{\mu }.$ Einstein’s solutions are recovered when the additional four-vector vanishes, so that the energy and momentum constraints amount to the covariant algebraic condition $Z_{\mu }=0.\mathrm{}$ The extended field equations can be supplemented by suitable coordinate conditions in order to provide symmetric hyperbolic evolution systems: this is actually the case for either harmonic coordinates or normal coordinates with harmonic slicing.

We investigate the class of quadratic detectors (i.e., the statistic is a bilinear function of the data) for the detection of poorly modeled gravitational transients of short duration. We point out that all such detection methods are equivalent to passing the signal through a filter bank and linearly combining the output energy. Existing methods for the choice of the filter bank and of the weight parameters (to be multiplied by the output energy of each filter before summation) rely essentially on the two following ideas: (i) the use of the likelihood function based on a (possibly noninformative) statistical model of the signal and the noise; (ii) the use of Monte Carlo simulations for the tuning of parametric filters to get the best detection probability while keeping the false alarm rate fixed. We propose a third approach according to which the filter bank is “learned” from a set of training data. By-products of this viewpoint are that, contrarily to previous methods, (i) there is no requirement of an explicit description of the probability density function of the data when the signal is present and (ii) the filters we use are nonparametric. The learning procedure may be described as a two step process: first, estimate the mean and covariance of the signal with the training data; second, find the filters which maximize a contrast criterion referred to as the deflection between the “noise only” and “signal + noise” hypotheses. The deflection is homogeneous to the signal-to-noise ratio and it uses the quantities estimated at the first step. We apply this original method to the problem of the detection of supernovae core collapses. We use the catalog of waveforms provided recently by Dimmelmeier et al. to train our algorithm. We expect such a detector to have better performances in this particular problem provided that the reference signals are reliable.

Although recent data on the muon anomalous magnetic moment strongly disfavor the constrained minimal supersymmetric standard model with $\mu <0,$ they cannot exclude it because of theoretical ambiguities. We consider this model supplemented by a Yukawa quasi-unification condition which allows an acceptable b-quark mass. We find that the cosmological upper bound on the lightest sparticle relic abundance is incompatible with the data on the branching ratio of $\overrightarrow{b}s\gamma ,$ which is evaluated by including all the next-to-leading order corrections. Thus, this scheme is not viable.

We consider a σ-model formulation of open string theory in the presence of D-branes. We perform two-loop computations and discuss gravitational corrections to the Born-Infeld action when branes are nontrivially embedded in a curved ambient space. In particular, for the case of a stack of N coincident D-branes we analyze couplings of the form $R_{\mathrm{ijkl}}\left[{\Phi }^i{\Phi }^j\right]\left[{\Phi }^k{\Phi }^l\right].$

A novel scenario of leptogenesis is investigated in the supersymmetric neutrino seesaw model. The right-handed sneutrino $Ñ$ and the $\phi$ field in the $\tilde{L}{H}_u$ direction of the slepton and Higgs doublets together start coherent evolution after inflation with a right-handed neutrino mass $M_N$ smaller than the Hubble parameter of inflation. Then, after some period the motion of $Ñ$ and $\phi$ is drastically changed by the cross coupling $M_N{h}_{\nu }{N}^{*}\phi \phi$ from the $M_N\mathrm{NN}$ and $h_{\nu }{\mathrm{NLH}}_u$ terms, and the significant asymmetries of $Ñ$ and $\tilde{L}$ are generated. The $\tilde{L}$ asymmetry is fixed later by the thermal effect as the lepton number asymmetry for baryogenesis, while the $Ñ$ asymmetry disappears through the decays $\overrightarrow{Ñ}\overline{L}{\overline{\tilde{H}}}_u,\tilde{L}{H}_u$ with almost the same rate but opposite final lepton numbers.

We reconsider the option of extracting the transversity distribution by using interference fragmentation functions into two leading hadrons inside the same current jet. To this end, we perform a new study of two-hadron fragmentation functions. We derive new positivity bounds on them. We expand the hadron pair system in relative partial waves, so that we can naturally incorporate in a unified formalism specific cases already studied in the literature, such as the fragmentation functions arising from the interference between the s- and p-wave production of two mesons, as well as the production of a spin-one hadron. In particular, our analysis clearly distinguishes two different ways to access the transversity distribution in two-hadron semi-inclusive leptoproduction.

Stellar structure in braneworlds is markedly different from that in ordinary general relativity. As an indispensable first step towards a more general analysis, we completely solve the “on brane” 4-dimensional Gauss and Codazzi equations for an arbitrary static spherically symmetric star in a Randall-Sundrum type II braneworld. We then indicate how these on-brane boundary data should be propagated into the bulk in order to determine the full 5-dimensional spacetime geometry. Finally, we demonstrate how this procedure can be generalized to solid objects such as planets.

We study nonconformal quantum scalar fields and averages of their local observables (such as $〈{\phi }^2{〉}^{\mathrm{ren}}$ and $〈T_{\mu \nu }{〉}^{\mathrm{ren}})$ in the spacetime of a two-dimensional black hole. In order to get an analytical approximation for these expressions the WKB approximation is often used. We demonstrate that at the horizon the WKB approximation is violated for a nonconformal field, that is, when the field mass or/and the parameter of nonminimal coupling does not vanish. We propose a new “uniform approximation” which solves this problem. We use this approximation to obtain an improved analytical approximation for $〈{\phi }^2{〉}^{\mathrm{ren}}$ in the two-dimensional black hole geometry. We compare the results obtained with numerical calculations.

We continue our investigation of the properties of the noise kernel in curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D 63, 104001 (2001)] by working out explicit examples by means of the modified point-separation scheme and the Gaussian approximation for the Green functions in the manner of Bekenstein, Parker, and Page [J. D. Bekenstein and L. Parker, Phys. Rev. D 23, 2850 (1981); D. N. Page, ibid. 25, 1499 (1982)]. In the first part we consider the class of optical spacetimes. As a first example we derive the regularized noise kernel for a thermal field in flat space. It is useful for black hole nucleation considerations. In the second example of an optical-Schwarzschild spacetime we obtain after this procedure a finite expression for the noise kernel at the horizon. In the second part we consider the noise kernel for a scalar field in the Schwarzschild black hole. Knowledge of the noise kernel is essential for studying issues related to black hole horizon fluctuations and Hawking radiation back reaction. Much of the work in this part is to determine how the divergent piece conformally transforms under the point-separation scheme. For the Schwarzschild metric we find that the fluctuations of the stress tensor of the Hawking flux in the far field region checks with the analytic results given by Campos and Hu earlier [A. Campos and B. L. Hu, Phys. Rev. D 58, 125021 (1998); Int. J. Theor. Phys. 38, 1253 (1999)]. We also verify Page’s result for the stress tensor, which, though used often, still lacks a rigorous proof, since in his original work the direct use of the conformal transformation was circumvented. We find that the noise kernel at the Schwarzschild horizon is finite. This dispels speculations in some recent papers that the black hole fluctuations diverge at the horizon. However, as already manifest in the optical case, the Gaussian approximated Green function which works surprisingly well for the stress tensor at the Schwarzschild horizon produces significant error in the noise kernel evaluated there. We check this using the trace anomaly expression and identify the failure as occurring at the fourth covariant derivative order.

We call into question a recently proposed idea on how the short-distance behavior of QCD correlation functions constrains hadronic states to become degenerate parity eigenstates as one goes up in the spectrum. In particular, we point out that the sum rules which have been proposed in this context are in general regulator dependent and thus ill defined.

We study the low-energy phenomenology of the little Higgs model. We first discuss the linearized effective theory of the “littlest Higgs model” and study the low-energy constraints on the model parameters. We identify sources of the corrections to low-energy observables, discuss model-dependent arbitrariness, and outline some possible directions of extensions of the model in order to evade the precision electroweak constraints. We then explore the characteristic signatures to test the model in the current and future collider experiments. We find that the CERN LHC has great potential to discover the new $\mathrm{SU}\left(2\right)\mathrm{}$ gauge bosons and the possible new $U\left(1\right)\mathrm{}$ gauge boson to the multi-TeV mass scale. Other states such as the colored vectorlike quark T and doubly charged Higgs boson ${\Phi }^{++}$ may also provide interesting signals. At a linear collider, precision measurements on the triple gauge boson couplings could be sensitive to the new physics scale of a few TeV. We provide a comprehensive list of the linearized interactions and vertices for the littlest Higgs model in the appendices.