The dynamics of a self-gravitating shell of matter is derived from the Hilbert variational principle and then described as an (infinite-dimensional, constrained) Hamiltonian system. The method used here enables us to define a singular Riemann tensor of a noncontinuous connection via standard formulas of differential geometry, with derivatives understood in the sense of distributions. Bianchi identities for the singular curvature are proved. They match the conservation laws for the singular energy-momentum tensor of matter. The Rosenfed-Belinfante and Noether theorems are proved to be valid still in the case of these singular objects. The assumption about the continuity of the four-dimensional space-time metric is widely discussed.

We study the gravitational collapse in five-dimensional de Sitter (dS) spacetime and discuss the existence of the conformal boundaries at future timelike infinity (${\mathcal{I}}^{+}$) from the perspective of the dS/conformal field theories correspondence. We investigate the motion of a spherical dust shell and the black-hole area bounds. The latter includes the analysis of the trapping horizon and the initial data with spindle-shaped matter distribution. In all the above analyses we find the evidences that guarantee the existence of the conformal boundaries at future timelike infinity which may be essential to apply the dS/conformal field theories correspondence.

We investigate the accuracy of slow-roll inflation in light of current observational constraints, which do not allow for a large deviation from scale invariance. We investigate the applicability of the first and second order slow-roll approximations for inflationary models, including those with large running of the scalar spectral index. We compare the full numerical solutions with those given by the first and second order slow-roll formulas. We find that even first order slow roll is generally accurate; the largest deviations arise in models with large running where the error in the power spectrum can be at the level of 1%–2%. Most of this error comes from inaccuracy in the calculation of the slope and not of the running or higher order terms. Second order slow roll does not improve the accuracy over first order. We also argue that in the basis ${ϵ}_0=1/H$, ${ϵ}_{n+1}=d\ln |{ϵ}_n|/dN$, introduced by Schwarz et al. (2001), slow roll does not require all of the parameters to be small. For example, even a divergent ${ϵ}_3$ leads to finite solutions which are accurately described by a slow-roll approximation. Finally, we argue that power spectrum parametrization recently introduced by Abazaijan, Kadota and Stewart does not work for models where spectral index changes from red to blue, while the usual Taylor expansion remains a good approximation.

We use analytic techniques to study the gravitational force that would be produced by different Kuiper-Belt mass distributions. In particular, we study the 3-dimensional rings (and wedge) whose densities vary as the inverse of the distance, as a constant, as the inverse-squared of the distance, as well as that which varies according to the Boss-Peale model. These analytic calculations yield physical insight into the physics of the problem. They also verify that physically viable models of this type can produce neither the magnitude nor the constancy of the Pioneer anomaly.

In this paper we present an analytical treatment of gravitational lensing by Kerr black holes in the limit of very large deflection angles, restricting to observers in the equatorial plane. We accomplish our objective starting from the Schwarzschild black hole and adding corrections up to second order in the black hole spin. This is sufficient to provide a full description of all caustics and the inversion of lens mapping for sources near them. On the basis of these formulae we argue that relativistic images of low mass x-ray binaries around Sgr ${\mathrm{A}}^{*}$ are very likely to be seen by future x-ray interferometry missions.

An upper limit on the masses of scalar superpartners in split supersymmetry is found by considering cosmological constraints on long-lived gluinos. Over most of parameter space, the most stringent constraint comes from big bang nucleosynthesis. A TeV-mass gluino must have a lifetime of less than 100 seconds to avoid altering the abundances of D and ${}^6\mathrm{L}\mathrm{i}$. This sets an upper limit on the supersymmetry breaking scale $m_S$ of ${10}^9$ GeV.

In the framework based on the quasipotential method and relativistic quark model a new covariant expression for the heavy quark fragmentation amplitude to fragment into the pseudoscalar and vector $S$-wave heavy mesons is obtained. It contains all possible relativistic corrections including the terms connected with the transformation law of the bound state wave function to the reference frame of the moving meson. Relativistic corrections of order ${\mathbf{p}}^2/m^2$ to the heavy quark fragmentation distributions into $(\overline{c}c)$, $(\overline{b}c)$, $(\overline{b}b)$ states are calculated as functions of the longitudinal momentum fraction $z$ and the transverse momentum $p_T$ relative to the jet axis.

High energy scattering in the QCD parton model was recently shown to be a reaction-diffusion process and, thus, to lie in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. We recall that the latter appears naturally in the context of the parton model. We provide a thorough numerical analysis of the mean-field approximation, given in QCD by the Balitsky-Kovchegov equation. In the framework of a simple stochastic toy model that captures the relevant features of QCD, we discuss and illustrate the universal properties of such stochastic models. We investigate, in particular, the validity of the mean-field approximation and how it is broken by fluctuations. We find that the mean-field approximation is a good approximation in the initial stages of the evolution in rapidity.

Liquid Xenon (LXe) is expected to be an excellent target and detection medium to search for dark matter in the form of Weakly Interacting Massive Particles (WIMPs). We have measured the scintillation efficiency of nuclear recoils with kinetic energy between 10.4 and 56.5 keV relative to that of 122 keV gamma rays from ${}^{57}\mathrm{C}\mathrm{o}$. The scintillation yield of 56.5 keV recoils was also measured as a function of applied electric field, and compared to that of gamma rays and alpha particles. The $\mathrm{Xe}$ recoils were produced by elastic scattering of 2.4 MeV neutrons in liquid xenon at a variety of scattering angles. The relative scintillation efficiency is $0.130\pm 0.024$ and $0.227\pm 0.016$ for the lowest and highest energy recoils, respectively. This is about $15\%$ less than the value predicted by Lindhard, based on nuclear quenching. Our results are in good agreement with more recent theoretical predictions that consider the additional reduction of scintillation yield due to biexcitonic collisions in LXe.

Using 58 million $J/\psi$ events accumulated with the BES II detector, branching fractions for the ${\eta }_c\to VV$ decays, ${\eta }_c\to \rho \rho$, ${\eta }_c\to K^{*}{\overline{K}}^{*}$, ${\eta }_c\to \omega \omega$, and ${\eta }_c\to \varphi \varphi$, are measured. The branching fractions are $Br({\eta }_c\to \rho \rho )=(1.23\pm 0.37\pm 0.50)\times {10}^{-2}$, $Br({\eta }_c\to K^{*}{\overline{K}}^{*})=(10.3\pm 2.6\pm 4.3)\times {10}^{-3}$, $Br({\eta }_c\to \omega \omega )<6.3\times {10}^{-3}$ (90% C.L.), and $Br({\eta }_c\to \varphi \varphi )=(2.5\pm 0.5\pm 0.9)\times {10}^{-3}$. The process ${\eta }_c\to \omega \varphi$ is also searched for, and the 90% C.L. upper limit $Br({\eta }_c\to \omega \varphi )<1.7\times {10}^{-3}$ is obtained for this process.

Using a sample of $232\times {10}^6{\rm Y}(4S)\to B\overline{B}$ events collected with the BABAR detector at the PEP-II $B$ factory we study the decay $B^{-}\to [K^{+}{\pi }^{-}{]}_D{K}^{*-}$ where the $K^{+}{\pi }^{-}$ is either from a Cabibbo-favored ${\overline{D}}^0$ decay or doubly-suppressed $D^0$ decay. We measure two observables that are sensitive to the Cabibbo-Kobayashi-Maskawa angle $\gamma$; the ratio $R$ of the charge-averaged branching fractions for the suppressed and favored decays; and the charge asymmetry $A$ of the suppressed decays: $R=0.046\pm 0.031(\mathrm{stat})\pm 0.008(\mathrm{syst})$, $A=-0.22\pm 0.61(\mathrm{stat})\pm 0.17(\mathrm{syst})$.

Using a sample of $232\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ events collected with the BABAR detector at the PEP-II $B$ Factory in 1999–2004, we study $B^{-}\to D^0{K}^{*}(892{)}^{-}$ decays where $K^{*-}\to K_S^0{\pi }^{-}$ and $D^0\to K^{-}{\pi }^{+}$, $K^{-}{\pi }^{+}{\pi }^0$, $K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ (non-$CP$ final states); $K^{+}{K}^{-}$, ${\pi }^{+}{\pi }^{-}$ ($CP+$ eigenstates); $K_S^0{\pi }^0$, $K_S^0\varphi$, and $K_S^0\omega$ ($CP-$ eigenstates). We measure four observables that are sensitive to the angle $\gamma$ of the CKM unitarity triangle; the partial-rate charge asymmetries ${\mathcal{A}}_{CP\pm }$ and the ratios of the $B$-decay branching fraction in $CP\pm$ and non-$CP$ decays ${\mathcal{R}}_{CP\pm }$: ${\mathcal{A}}_{CP+}=-0.08\pm 0.19(\mathrm{stat})\pm 0.08(\mathrm{syst})$, ${\mathcal{A}}_{CP-}=-0.26\pm 0.40(\mathrm{stat})\pm 0.12(\mathrm{syst})$, ${\mathcal{R}}_{CP+}=1.96\pm 0.40(\mathrm{stat})\pm 0.11(\mathrm{syst})$, and ${\mathcal{R}}_{CP-}=0.65\pm 0.26(\mathrm{stat})\pm 0.08(\mathrm{syst})$.

The 511 keV photons from the galactic center can be explained by positrons produced through $Q$-ball decay. In the scheme of gauge-mediated supersymmetry breaking, large $Q$ balls with lepton charge are necessarily long-lived. In particular, the lifetime can be as long as (or even longer than) the age of the Universe. If kinematically allowed, such large $Q$ balls decay into positrons, which eventually annihilate with electrons into 511 keV photons. Our scenario is realized within the minimal supersymmetric standard model in the inflationary universe, which is very plausible.

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local symmetries of $Ad{S}_{d+1}$ space due to the embedding of an $Ad{S}_d$ brane. The resulting action is an $SO(2,d)$ invariant $AdS$ form of the Einstein-Hilbert action, which in addition to the $Ad{S}_d$ gravitational vielbein, also includes a massive vector field localized on the brane. Its long wavelength dynamics is the same as a massive Abelian vector field coupled to gravity in $Ad{S}_d$ space.

The deep imaging of the field of an observed lensing event by a cosmic string reveals many additional lensing events. We study the statistics of such string lensing. We derive explicit expressions for the distributions of image separations of lensing by a cosmic string and point out that they are quite sensitive to parameters which characterize the cosmic string, such as the redshift and tension of the cosmic string. Thus the statistics of string lensing events add new important information on the cosmic string which cannot be obtained from the detailed investigation of one lensing event.

In theories with chiral couplings, one of the important consistency requirements is that of the cancellation of a gauge anomaly. In particular, this is one of the conditions imposed on the hypercharges in the standard model. However, anomaly cancellation condition of the standard model looks unnatural from the perspective of a theory with extra dimensions. Indeed, if our world were embedded into an odd-dimensional space, then the full theory would be automatically anomaly-free. In this paper we discuss the physical consequences of anomaly noncancellation for effective 4-dimensional field theory. We demonstrate that in such a theory parallel electric and magnetic fields get modified. In particular, this happens for any particle possessing both electric charge and magnetic moment. This effect, if observed, can serve as a low energy signature of extra dimensions. On the other hand, if such an effect is absent or is very small, then from the point of view of any theory with extra dimensions it is just another fine-tuning and should acquire theoretical explanation.

The question of whether information is lost in black holes is investigated using Euclidean path integrals. The formation and evaporation of black holes is regarded as a scattering problem with all measurements being made at infinity. This seems to be well formulated only in asymptotically AdS spacetimes. The path integral over metrics with trivial topology is unitary and information preserving. On the other hand, the path integral over metrics with nontrivial topologies leads to correlation functions that decay to zero. Thus at late times only the unitary information preserving path integrals over trivial topologies will contribute. Elementary quantum gravity interactions do not lose information or quantum coherence.

The dynamics of Bianchi IX models with two scale factors $A(t)$ and $B(t)$ is reexamined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. We make a complete numerical construction of topological structures present in the phase space of the model, as the center manifold of periodic orbits and the stable and unstable cylinders of orbits that emerge from the center manifold, associated to a saddle-center critical point. We exhibit the homoclinic intersections of the unstable and stable cylinders that produce homoclinic chaos in the models. $A=0$ is not a singularity of the Hamiltonian dynamics and any truncation of the dynamics at $A=0$ is bound to a loss of information. We make an explicit construction of a set with a horseshoe structure in the $A>0$ region, of initial conditions corresponding to initially expanding universes. We show that the dynamics of this set is chaotic even if restricted to the region $A>0$ and has the Einstein universe configuration as a chaotic scatterer. The result however demands the information of the Hamiltonian dynamics in whole phase space, including the region $A<0$. This refutes recent claims that no homoclinic chaos is present in the dynamics of the model.

The curvaton reheating in a tachyonic braneworld inflationary universe model with an exponential potential is studied. We have found that the energy density in the kinetic epoch, has a complicated dependencies of the scale factor. For different scenarios the temperature of reheating is computed, finding an upper limit that lies in the range ${10}^{14}$–${10}^{16}$ GeV.