We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularization scheme, parametrized by a general cutoff function and infinitely many higher point vertices, is left unspecified. Calculations proceed iteratively, by integrating by parts with respect to the effective cutoff, thus introducing effective propagators, and differentials of vertices that can be expanded using the flow equations; many cancellations occur on using the fact that the effective propagator is the inverse of the classical Wilsonian two-point vertex. We demonstrate the power of these methods by computing the beta function up to two loops in massless four dimensional scalar field theory, obtaining the expected universal coefficients, independent of the details of the regularization scheme.

Lensing in a spherically symmetric and static spacetime is considered, based on the lightlike geodesic equation without approximations. After fixing two radius values $r_O$ and $r_S,$ lensing for an observation event somewhere at $r_O$ and static light sources distributed at $r_S$ is coded in a lens equation that is explicitly given in terms of integrals over the metric coefficients. The lens equation relates two angle variables and can be easily plotted if the metric coefficients have been specified; this allows us to visualize in a convenient way all relevant lensing properties, giving image positions, apparent brightnesses, image distortions, etc. Two examples are treated: lensing by a Barriola-Vilenkin monopole and lensing by an Ellis wormhole.

In this paper we consider spacetimes in vacuum general relativity—possibly coupled to a scalar field—with a positive cosmological constant $\Lambda .$ We employ the isolated horizons (IH) formalism where the boundary conditions imposed are that of two horizons, one of black hole type and the other, serving as outer boundary, a cosmological horizon. As particular cases, we consider the Schwarzschild–de Sitter spacetime, in both $2+1$ and $3+1$ dimensions. Within the IH formalism, it is useful to define two different notions of energy for the cosmological horizon, namely, the “mass” and the “energy.” Empty de Sitter space provides a striking example of such a distinction: its horizon energy is zero but the horizon mass takes a finite value given by $\pi /\left(2\mathrm{}\sqrt{\Lambda }\right).\mathrm{}$ For both horizons we study their thermodynamic properties, compare our results with those of Euclidean Hamiltonian methods and construct some generalized Bekenstein entropy bounds. We discuss these new entropy bounds and compare them with some recently proposed entropy bounds in the cosmological setting.

Stationary rotationally symmetric perfect fluid spacetimes are studied. We formulate the Einstein equations with a cosmological constant in a corotating Lorentz triad, and all stationary symmetric perfect fluid solutions to 2+1 Einstein gravity are derived. Stationary spacetimes containing perfect fluids with a constant energy density and a linear or a polytropic barotropic equation of state are explicitly shown. All known static circularly symmetric perfect fluid spacetimes can be obtained from the here derived stationary cosmological perfect fluid solutions.

We continue our studies of spherically symmetric self-similar solutions in the $\mathrm{SU}\left(2\right)\mathrm{}$ sigma model coupled to gravity. Using mixed numerical and analytical methods we show the existence of an unstable periodic solution lying at the boundary between the basins of two generic attractors.

Tracing over the degrees of freedom inside (or outside) a subvolume V of Minkowski space in a given quantum state $|\psi 〉$ results in a statistical ensemble described by a density matrix $\rho .$ This enables one to relate quantum fluctuations in V when in the state $|\psi 〉$ to statistical fluctuations in the ensemble described by $\rho .$ These fluctuations scale linearly with the surface area of V. If V is half of space, then $\rho$ is the density matrix of a canonical ensemble in Rindler space. This enables us to “derive” the area scaling of thermodynamic quantities in Rindler space from the area scaling of quantum fluctuations in half of Minkowski space. When considering shapes other than half of Minkowski space, even though area scaling persists, $\rho$ does not have an interpretation as a density matrix of a canonical ensemble in a curved, or geometrically nontrivial, background.

Explicit expressions are found for the axisymmetric metric perturbations of the closed, flat and open Friedmann-Robertson-Walker universes caused by toroidal motions of the cosmic fluid. The perturbations are decomposed in vector spherical harmonics on 2-spheres, but the radial dependence is left general. Solutions for general odd-parity l-pole perturbations are given for either angular velocities or angular momenta prescribed. In particular, in the case of closed universes the solutions require a special treatment of the Legendre equation.

If perturbations beyond the horizon have the velocities prescribed everywhere then the dragging of inertial frames near the origin is suppressed by an exponential factor. However if perturbations are prescribed in terms of their angular momenta there is no such suppression. We resolve this paradox and in doing so give new explicit results for the dragging of inertial frames in closed, flat, and open universes with and without a cosmological constant.

A broad class of dark energy models, which have been proposed in attempts at solving the cosmological constant problems, predict a late time variation of the equation of state with redshift. The variation occurs as a scalar field picks up speed on its way to negative values of the potential. The negative potential energy eventually turns the expansion into contraction and the local universe undergoes a big crunch. In this paper we show that cross-correlations of the cosmic microwave background anisotropy and matter distribution, in combination with other cosmological data, can be used to forecast the imminence of such cosmic doomsday.

We demonstrate the existence of two-field Q-ball solutions of the scalar field equations of supersymmetric D- and F-term hybrid inflation. The solutions consist of a complex inflaton field together with a real symmetry breaking field. Such inflatonic Q-balls may play a fundamental role in reheating and the post-inflation era of supersymmetric hybrid inflation models.

We reexamine the problem of boiling and surface evaporation of quark nuggets in the cosmological quark-hadron transition with the explicit consideration of pairing between quarks in a color-flavor locked state. Assuming that primordial quark nuggets are actually formed, we analyze the consequences of pairing on the rates of boiling and surface evaporation in order to determine whether they could have survived with substantial mass. We find a substantial quenching of the $\mathrm{evaporation}+\mathrm{boiling}$ processes, which suggests the survival of primordial nuggets for the currently considered range of the pairing gap $\Delta .$ Boiling is shown to depend on the competition of an increased stability window and the suppression of the rate, and is not likely to dominate the destruction of the nuggets. If surface evaporation dominates, the fate of the nuggets depends on the features of the initial mass spectrum of the nuggets, their evaporation rate, and the value of the pairing gap, as shown and discussed in the text.

We use the method of QCD sum rules to investigate a possible hybrid baryon with the quantum numbers of the $\Lambda .$ Using a current composed of uds quarks in a color octet and a gluon, a strange hybrid, the ${\Lambda }_H,$ is found about 500 MeV above the $\Lambda ,$ and we identify it as the $\Lambda \mathrm{}\left(1600\right).$ Using our sigma or glueball model we predict a large branching fraction for the ${\Lambda }_H\to \Lambda +\sigma (\pi \pi$ resonance), and the experimental search for this decay mode could provide a test of the hybrid nature of the $\Lambda \mathrm{}\left(1600\right).$

We study lepton-flavor violating slepton production and decay at a future $e^{+}{e}^{-}$ linear collider in the context of the seesaw mechanism in minimal supergravity post CERN LEP benchmark scenarios. The present knowledge of the neutrino sector as well as improved future measurements are taken into account. We calculate the signal cross sections $\sigma {(e}^{\pm }{e}^{-}\to l_{\beta }^{\pm }{l}_{\alpha }^{-}{\tilde{\chi }}_b^0{\tilde{\chi }}_a^0),$ $l_{\delta }=e,\mu ,\tau ,$ $\alpha \ne \beta ,$ and estimate the main background processes. Furthermore, we investigate the correlations of these signals with the corresponding lepton-flavor violating rare decays $l_{\alpha }\to l_{\beta }\gamma .$ It is shown that these correlations are relatively weakly affected by the uncertainties in the neutrino data but are very sensitive to the model parameters. Hence, they are particularly well suited for probing the origin of lepton-flavor violation.

We construct a consistent action for a massive spinning quark on the end of a QCD string that leads to a pure Thomas precession of the quark’s spin. The string action is modified by the addition of Grassmann degrees of freedom to the string such that the equations of motion for the quark spin follow from boundary conditions, just as do those for the quark’s position.

The presently most accurate prediction for the W-boson mass in the standard model is obtained by combining the complete two-loop result with the known higher-order QCD and electroweak corrections. The numerical impact of the different contributions is analyzed in detail. A simple parametrization of the full result is presented, which approximates the full result for $M_W$ to better than 0.5 MeV for $10\mathrm{GeV}<~M_H<~1\mathrm{TeV}$ if the other parameters are varied within their combined 2σ region around their experimental central values. The different sources of remaining theoretical uncertainties are investigated. Their effect on the prediction of $M_W$ is estimated to be about 4 MeV for $M_H\lesssim 300\mathrm{GeV}.$

We study the departures from classical synchrotron radiation due to the noncommutativity of the coordinates. We find that these departures are significant but do not give tight bounds on the magnitude of the noncommutative parameter. On the other hand, these results could be used in future investigations in this direction. We also find an acausal behavior for the electromagnetic field due to the presence in the theory of two different speeds of light. This effect naturally arises even if only ${\theta }^{12}$ is different from zero.

We present an alternative approach to setting initial data in general relativity. We do not use a conformal decomposition, but instead express the 3-metric in terms of a given unit vector field and one unknown scalar field. In the case of axisymmetry, we have written a program to solve the resulting nonlinear elliptic equation. We have obtained solutions, both numerically and from a linearized analytic method, for a perturbation of a Schwarzschild black hole.

In the curvaton model of inflation, where a second scalar field, the “curvaton,” is responsible for the observed inhomogeneity, a nonzero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino, cold dark matter and baryon components. We find that the current data can only place upper limits on the level of isocurvature perturbations. These can be translated into upper limits on the neutrino degeneracy parameter. In the case that lepton number is created before curvaton decay, we find that the limit on the neutrino degeneracy parameter is comparable with that obtained from big-bang nucleosynthesis. For the case that lepton number is created by curvaton decay we find that the absolute value of the non-Gaussianity parameter, $|f_{\mathrm{nl}}|,$ must be less than 10 (95% confidence interval).

We study the distribution of gluons in transverse space in the nucleon at moderately small x $\left(\sim {10}^{-2}\right).\mathrm{}$ At large transverse distances (impact parameters) the gluon density is generated by the “pion cloud” of the nucleon, and can be calculated in terms of the gluon density in the pion. We investigate the large-distance behavior in two different approaches to chiral dynamics: (i) phenomenological soft-pion exchange; (ii) the large-$N_c$ picture of the nucleon as a classical soliton of the pion field, which corresponds to degenerate N and $\Delta$ states. The large-distance contributions from the “pion cloud” cause a $\sim 20\%$ increase in the overall transverse size of the nucleon if x drops significantly below $M_{\pi }{/M}_N.$ This is in qualitative agreement with the observed increase of the slope of the t dependence of the $J/\psi$ photoproduction cross section at DESY HERA compared to fixed-target energies. We argue that the glue in the pion cloud could be probed directly in hard electroproduction processes accompanied by “pion knockout,” ${\gamma }^{*}+\overrightarrow{N}\gamma (or\rho ,J/\psi )+\pi {+N}^{\prime },$ where the transverse momentum of the emitted pion is large while that of the outgoing nucleon is restricted to values of order $M_{\pi }.$