We discuss the algebraic construction of topological models (of both Schwarz- and Witten-type) within the Batalin-Vilkovisky formalism and we elaborate on a simple description of vector supersymmetry within this framework.

Motivated by recent evidence indicating that quantum Einstein gravity (QEG) might be nonperturbatively renormalizable, the exact renormalization group equation of QEG is evaluated in a truncation of theory space which generalizes the Einstein-Hilbert truncation by the inclusion of a higher-derivative term ${(R}^2).\mathrm{}$ The beta functions describing the renormalization group flow of the cosmological constant, Newton’s constant, and the $R^2$ coupling are computed explicitly. The fixed point properties of the 3-dimensional flow are investigated, and they are confronted with those of the 2-dimensional Einstein-Hilbert flow. The non-Gaussian fixed point predicted by the latter is found to generalize to a fixed point on the enlarged theory space. In order to test the reliability of the $R^2$ truncation near this fixed point we analyze the residual scheme dependence of various universal quantities; it turns out to be very weak. The two truncations are compared in detail, and their numerical predictions are found to agree with a surprisingly high precision. Because of the consistency of the results it appears increasingly unlikely that the non-Gaussian fixed point is an artifact of the truncation. If it is present in the exact theory QEG is probably nonperturbatively renormalizable and “asymptotically safe.” We discuss how the conformal factor problem of Euclidean gravity manifests itself in the exact renormalization group approach and show that, in the $R^2$ truncation, the investigation of the fixed point is not afflicted with this problem. Also the Gaussian fixed point of the Einstein-Hilbert truncation is analyzed; it turns out that it does not generalize to a corresponding fixed point on the enlarged theory space.

Using the Hopf fibration and starting from a four-dimensional noncommutative Moyal plane $R_{\theta }^2\times R_{\theta }^2$ we obtain a star product for the noncommutative (fuzzy) $R_{\lambda }^3$ defined by $\left[x^i{,x}^j\right]=i\lambda {\epsilon }_{\mathrm{ijk}}{x}^k.$ Furthermore, we show that there is a projection function which allows us to reduce the functions on $R_{\lambda }^3$ to that of the fuzzy sphere, and hence we introduce a new star product on the fuzzy sphere. We will then briefly discuss how using our method one can extract information about the field theory on the fuzzy sphere and $R_{\lambda }^3$ from the corresponding field theories on $R_{\theta }^2\times R_{\theta }^2$ space.

We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two Kerr-Schild black holes to fix the freely specifiable data. We find that these initial-data sets differ significantly, with the ADM energy varying by as much as 5% of the total mass. We find that all initial-data sets currently used for evolutions might contain unphysical gravitational radiation of the order of several percent of the total mass. This is comparable to the amount of gravitational-wave energy observed during the evolved collision. More astrophysically realistic initial data will require more careful choices of the freely specifiable data and boundary conditions for both the metric and extrinsic curvature. However, we find that the choice of extrinsic curvature affects the resulting data sets more strongly than the choice of conformal metric.

We study numerically the evolution of spacetime, and in particular of a spacetime singularity, inside a black hole under a class of perturbations of noncompact support. We use a very simplified toy model of a spherical charged black hole which is perturbed nonlinearly by a self-gravitating, spherical scalar field. The latter grows logarithmically with advanced time along an outgoing characteristic hypersurface. We find that for that class of perturbations a portion of the Cauchy horizon survives as a noncentral, null singularity.

Within the weak-field, post-Newtonian approximation of the metric theories of gravity, we determine the one-way time transfer up to the order ${1/c}^4,$ the unperturbed term being of order $1/c,$ and the frequency shift up to the order ${1/c}^4.$ We adapt the method of the world function developed by Synge to the Nordvedt-Will parametrized post-Newtonian (PPN) formalism. We get an integral expression for the world function up to the order ${1/c}^3$ and we apply this result to the field of an isolated, axisymmetric rotating body. We give a new procedure enabling us to calculate the influence of the mass and spin multipole moments of the body on the time transfer and the frequency shift up to the order ${1/c}^4.$ We obtain explicit formulas for the contributions of the mass, of the quadrupole moment and of the intrinsic angular momentum. In the case where the only PPN parameters different from zero are $\beta$ and γ, we deduce from these results the complete expression of the frequency shift up to the order ${1/c}^4.$ We briefly discuss the influence of the quadrupole moment and of the rotation of the Earth on the frequency shifts in the ESA’s Atomic Clock Ensemble in Space mission.

We study anti–de Sitter black holes in the Einstein-Gauss-Bonnet and the generic $R^2$ gravity theories, evaluate different thermodynamic quantities, and also examine the possibilities of Hawking-Page–type thermal phase transitions in these theories. In the Einstein theory, with a possible cosmological term, one observes a Hawking-Page phase transition only if the event horizon is a hypersurface of positive constant curvature $\mathrm{}(k=1\mathrm{}).$ But, with the Gauss-Bonnet and/or the $(\mathrm{Riemann}{)}^2$ interaction terms, there may occur a similar phase transition for a horizon of negative constant curvature $(k=-1).$ We examine the finite coupling effects, and find that $N>\mathrm{}5\mathrm{}$ could trigger a Hawking-Page phase transition in the latter theory. For the Gauss-Bonnet black holes, one relates the entropy of the black hole to a variation of the geometric property of the horizon based on the first law and Noether charge. With a $(\mathrm{Riemann}{)}^2$ term, however, we can do this only approximately, and the two results agree when $r_H\gg L,$ the size of the horizon is much bigger than the AdS curvature scale. We establish some relations between bulk data associated with the AdS black hole and boundary data defined on the horizon of the AdS geometry. Following a heuristic approach, we estimate the difference between Hubble entropy $\left({\mathcal{S}}_H\right)$ and Bekenstein-Hawking entropy $\left({\mathcal{S}}_{\mathrm{BH}}\right)$ with a $(\mathrm{Riemann}{)}^2$ term, which, for $k=0\mathrm{}$ and $k=-1,$ implies ${\mathcal{S}}_{\mathrm{BH}}<~{\mathcal{S}}_H.$

In this paper time-dependent solutions of supergravities with a dilaton and an arbitrary rank antisymmetric tensor field are found. Although the solutions are nonsupersymmetric the equations of motion can be integrated in a simple form. Such supergravity solutions are related to Euclidean or spacelike branes $(S$-branes).

We study wave propagation in local nonlinear electrodynamical models. Particular attention is paid to the derivation and the analysis of the Fresnel equation for the wave covectors. For the class of local nonlinear Lagrangian nondispersive models, we demonstrate how the originally quartic Fresnel equation factorizes, yielding the generic birefringence effect. We show that the closure of the effective constitutive (or jump) tensor is necessary and sufficient for the absence of birefringence, i.e., for the existence of a unique light cone structure. As another application of the Fresnel approach, we analyze the light propagation in a moving isotropic nonlinear medium. The corresponding effective constitutive tensor contains nontrivial skewon and axion pieces. For nonmagnetic matter, we find that birefringence is induced by the nonlinearity, and derive the corresponding optical metrics.

We consider the process of black hole formation in particle collisions in the exactly solvable framework of (2+1)-dimensional anti–de Sitter gravity. An effective Hamiltonian describing the near horizon dynamics of a head-on collision is given. The Hamiltonian exhibits a universal structure, with the formation of a horizon at a critical distance. Based on this, we evaluate the action for the process and discuss the semiclassical amplitude for black hole formation. The derived amplitude is seen to contain no exponential suppression or enhancement. Comments on the conformal field theory description of the process are made.

We discuss the propagation of dark matter perturbations with nonzero velocity dispersion in cosmological models. In particular a nonzero massive neutrino component may well have a significant effect on the matter power spectrum and cosmic microwave background anisotropy. We present a covariant analysis of the evolution of a dark matter distribution via a two-dimensional momentum-integrated hierarchy of multipole equations. This can be expanded in the velocity weight to provide accurate approximate equations if the matter is nonrelativistic, and we also perform an expansion in the mass to study the propagation of relativistic matter perturbations. We suggest an approximation to the exact hierarchy that can be used to calculate efficiently the effect of the massive neutrinos on the CMB power spectra. We implement the corresponding scalar mode equations numerically achieving a considerable reduction in computation time compared with previous approaches.

We investigate the possibility of using the proposed SNAP satellite in combination with low-$z$ supernova searches to distinguish between different inverse power-law quintessence models. If the true model is that of a cosmological constant, we determine the prospects of ruling out the inverse power-law potential. We show that SNAP combined with e.g., the SNfactory and an independent measurement of the mass energy density to 17% accuracy can distinguish between an inverse power-law potential and a cosmological constant and put severe constraints on the power-law exponent.

By the effort of several researchers, it has been recently established that the dynamical behavior of the cosmological perturbation on superhorizon scales is well approximated by that of the long wavelength limit, and that the latter can be constructed from the evolution of corresponding exactly homogeneous universe. Using these facts, we investigate the evolution of the cosmological perturbation on superhorizon scales in the universe dominated by oscillating multiple scalar fields which are generally interacting with each other, and the ratio of whose masses is incommensurable. Since the scalar fields oscillate rapidly around the local minimum of the potential, we use the action angle variables. We find that this problem can be formulated as the canonical perturbation theory in which the perturbed part appearing as the result of the expansion of the universe and the interaction of the scalar fields is bounded by the negative power of time. We show that by constructing the canonical transformations properly, the transformed Hamiltonian becomes simple enough to be solved. As a result of the investigation using the long wavelength limit and the canonical perturbation theory, under sufficiently general conditions we prove that for the adiabatic growing mode the Bardeen parameter stays constant and that for all the other modes the Bardeen parameter decays. From the viewpoint of the ergodic theory, it is discussed that, for the Bardeen parameter, the singularities appear probabilistically. This analysis serves the understanding of the evolution of the cosmological perturbations on superhorizon scales during reheating.

The most general homogeneous and isotropic statistical ensemble of linear scalar perturbations regular at early times in a universe with only photons, baryons, neutrinos, and a cold dark matter (CDM) component is described by a $5\times 5$ symmetric matrix-valued generalization of the power spectrum. This description is complete if the perturbations are Gaussian, and even in the non-Gaussian case determines the expectation values of all observables quadratic in the small perturbations. The matrix valued power spectrum describes the auto and cross correlations of the adiabatic, baryon isocurvature, CDM isocurvature, neutrino density isocurvature, and neutrino velocity isocurvature modes. In this paper we examine the prospects for constraining or discovering isocurvature modes using forthcoming MAP and Planck measurements of the cosmic microwave background (CMB) anisotropy. We also consider the degradation in estimates of the cosmological parameters resulting from the inclusion of these modes. In the case of the MAP measurement of the temperature alone, the degradation is catastrophic. When isocurvature modes are admitted, uncertainties in the amplitudes of the mode auto- and cross correlations, and in the cosmological parameters, become of order one. With the inclusion of polarization (at an optimistic sensitivity) the situation improves for the cosmological parameters, but the isocurvature modes are still only weakly constrained. Measurements with Planck’s estimated errors are far more constraining once polarization is included. If Planck operates as planned, the amplitudes of isocurvature modes will be constrained to less than 10% of the adiabatic mode, and simultaneously key cosmological parameters will be estimated to within a few percent or better.

We propose a model for cosmic inflation which is based on an effective description of strongly interacting, nonsupersymmetric matter within the framework of dynamical Abelian projection and centerization. The underlying gauge symmetry is assumed to be $\mathrm{SU}(N+1\mathrm{})\mathrm{}$ with $N\gg 1.$ Appealing to a thermodynamical treatment, the ground-state structure of the model is classically determined by a potential for the inflaton field (dynamical monopole condensate) which allows for nontrivially BPS saturated and thereby stable solutions. For $T<\mathrm{}{M}_P$ this leads to decoupling of gravity from the inflaton dynamics. The ground state dynamics implies a heat capacity for the vacuum leading to inflation for temperatures comparable to the mass scale M of the potential. The dynamics has an attractor property. In contrast with the usual slow-roll paradigm we have $m\gg H$ during inflation. As a consequence, density perturbations generated from the inflaton are irrelevant for the formation of large-scale structure, and the model has to be supplemented with an inflaton independent mechanism for the generation of spatial curvature perturbations. Within a small fraction of the Hubble time inflation is terminated by a transition of the theory to its center symmetric phase. The spontaneously broken $Z_{N+1\mathrm{}}$ symmetry stabilizes relic vector bosons in the epochs following inflation. These heavy relics contribute to the cold dark matter of the universe and potentially originate the UHECRs beyond the GZK bound.

We point out that the relic densities of singlet (sterile) neutrinos of interest in viable warm and cold dark matter scenarios depend on the characteristics of the QCD transition in the early universe. In the most promising of these dark matter scenarios, the production of the singlets occurs at or near the QCD transition. Since production of the singlets, their dilution, and the disappearance of weak scatterers occur simultaneously, we calculate these processes contemporaneously to obtain accurate predictions of relic sterile neutrino mass density. Therefore, a determination of the mass and superweak mixing of the singlet neutrino through, for example, its radiative decay, along with a determination of its contribution to the critical density, can provide insight into the finite-temperature QCD transition.

The framework for considering the astronomical and cosmological observations in the context of scalar-tensor quintessence in which the quintessence field also accounts for a time dependence of the gravitational constant is developed. The constraints arising from nucleosynthesis, the variation of the constant, and the post-Newtonian measurements are taken into account. A simple model of supernovae is presented in order to extract the dependence of their light curves with the gravitational constant; this implies a correction when fitting the luminosity distance. The properties of perturbations as well as CMB anisotropies are also investigated.

In most supersymmetric theories, charginos ${\tilde{\chi }}_{1,2}^{\pm }$ belong to the class of the lightest supersymmetric particles and the couplings of Higgs bosons to charginos are in general complex so that the $\mathrm{CP}$-violating chargino contributions to the loop-induced coupling of the lightest Higgs boson to two photons can be sizable even in the decoupling limit of large pseudoscalar mass $m_A$ with only the lightest Higgs boson kinematically accessible at future high energy colliders. We introduce a specific benchmark scenario of $\mathrm{CP}$ violation consistent with the electric dipole moment constraints and with a commonly accepted baryogenesis mechanism in the minimal supersymmetric standard model. Based on the benchmark scenario of $\mathrm{CP}$ violation, we demonstrate that the fusion of the lightest Higgs boson in linearly polarized photon-photon collisions can allow us to confirm the existence of the $\mathrm{CP}$-violating chargino contributions even in the decoupling regime of the Higgs sector for nearly degenerate SU(2) gaugino and Higgsino mass parameters of about the electroweak scale.

We confront the new physics models with extra isosinglet down quarks in the new $\mathrm{CP}$ violation experimental era with $\sin \left(2\mathrm{}\beta \right)$ and ${\epsilon }^{\prime }/\epsilon$ measurements, $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ events, and $x_s$ limits. The closeness of the new experimental results to the standard model theory requires us to include full standard model (SM) amplitudes in the analysis. In models allowing mixing to a new isosinglet down quark, as in ${\mathrm{E}}_6,$ flavor changing neutral currents are induced that allow a $Z^0$ mediated contribution to $B-\overline{B}$ mixing and which bring in new phases. In $(\rho ,\eta ),$ $(x_s,\sin (\gamma \left)\right),$ and $(x_s,\sin (2\mathrm{}{\phi }_s\left)\right)$ plots we still find much larger regions in the four down quark model than in the SM, reaching down to $\eta \approx 0,$ $0<~\sin \left(\gamma \right)<~1,$ $-0.75<~\sin \left(2\mathrm{}\alpha \right)<~0.15,$ and $\sin \left(2\mathrm{}{\phi }_s\right)$ down to zero, all at $1\sigma .$ We elucidate the nature of the cancellation in an order ${\lambda }^5$ four down quark mixing matrix element which satisfies the experiments and reduces the number of independent angles and phases. We also evaluate tests of unitarity for the $3\times 3$ Cabibbo-Kobayashi-Maskawa submatrix.

We analyze the fate of the unbroken $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}$ color gauge interactions for two-light-flavor color superconductivity at nonzero temperature. Using a simple glueball Lagrangian model, we compute the deconfining or confining critical temperature and show that it is smaller than the critical temperature for the onset of the superconductive state itself. The breaking of Lorentz invariance, induced already at zero temperature by the quark chemical potential, is shown to heavily affect the value of the critical temperature and all of the relevant features related to the deconfining transition. Modifying the Polyakov loop model to describe the $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}$ immersed in the diquark medium, we argue that the deconfinement transition is second order. Having constructed part of the equation of state for the two-color superconducting phase at low temperatures, our results may be relevant for the physics of compact objects featuring a two-flavor color superconductive state.