Recently, new arguments [E. Barausse, S. Matarrese, and A. Riotto, Phys. Rev. D 71, 063537 (2005).][E. W. Kolb, S. Matarrese, A. Notari, and A. Riotto, hep-th/0503117 [Phys. Rev. Lett. (to be published)].] for how corrections from super-Hubble modes can explain the present-day acceleration of the universe have appeared in the literature. However, in this paper, we argue that, to second order in spatial gradients, these corrections only amount to a renormalization of local spatial curvature, and thus cannot account for the negative deceleration. Moreover, cosmological observations already put severe bounds on such corrections, at the level of a few percent, while in the context of inflationary models, these corrections are typically limited to $\sim {10}^{-5}$. Currently there is no general constraint on the possible correction from higher order gradient terms, but we argue that such corrections are even more constrained in the context of inflationary models.

This work analyzes Doppler-effect experiments in terms of a general framework for violations of Lorentz symmetry: the Standard-Model Extension. These experiments are found to be sensitive to heretofore unprobed combinations of Lorentz-violation coefficients associated with protons and electrons. New bounds at the level of ${10}^{-11}$ and ${10}^{-8}$ for proton coefficients and ${10}^{-2}$ for electron coefficients emerge from a recent experiment.

We carry out a feasibility study for the lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the $\theta$ term. We develop the strategy to obtain the nucleon EDM from the $CP$-odd electromagnetic form factor $F_3$ at small $\theta$, in which NEDM is given by $\underset{q^2\to 0}{lim}\theta F_3(q^2)/(2m_N)$, where $q$ is the momentum transfer and $m_N$ is the nucleon mass. We first derive a formula which relates $F_3$, a matrix element of the electromagnetic current between nucleon states, with vacuum expectation values of nucleons and/or the current. In the expansion of $\theta$, the parity-odd part of the nucleon-current-nucleon three-point function contains contributions not only from the parity-odd form factors but also from the parity-even form factors multiplied by the parity-odd part of the nucleon two-point function, and, therefore, the latter contribution must be subtracted to extract $F_3$. We then perform an explicit lattice calculation employing the domain-wall quark action with the renormalization group improved gauge action in quenched QCD at $a^{-1}\simeq 2\mathrm{GeV}$ on a ${16}^3\times 32\times 16$ lattice. At the quark mass $m_{f}a=0.03$, corresponding to $m_{\pi }/m_{\rho }\simeq 0.63$, we accumulate 730 configurations, which allow us to extract the parity-odd part in both two- and three-point functions. Employing two different Dirac $\gamma$ matrix projections, we show that a consistent value for $F_3$ cannot be obtained without the subtraction described above. We obtain $F_3(q^2\simeq 0.58{\mathrm{GeV}}^2)/(2m_N)=-0.024(5)e·\mathrm{fm}$ for the neutron and $F_3(q^2\simeq 0.58{\mathrm{GeV}}^2)/(2m_N)=0.021(6)e·\mathrm{fm}$ for the proton.

When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as $1/4$ BPS states in five-dimensional supersymmetric $U(N_{\mathrm{C}})$ gauge theory with $N_{\mathrm{F}}(\ge N_{\mathrm{C}})$ fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all $1/4$ BPS solutions are generated by an $N_{\mathrm{C}}\times N_{\mathrm{F}}$ matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed.

Analytical $r$-mode solutions are investigated within the linearized theory in the case of a slowly rotating, Newtonian, barotropic, nonmagnetized, perfect-fluid star in which the gravitational radiation (GR) reaction force is present. For the GR reaction term we use the 3.5 post-Newtonian order expansion of the GR force, in order to include the contribution of the current quadrupole moment. We find the explicit expression for the $r$-mode velocity perturbations and we conclude that they are sinusoidal with the same frequency as the well-known GR force-free linear $r$-mode solution, and that the GR force drives the $r$-modes unstable with a growth time scale that agrees with the expression first found by Lindblom, Owen, and Morsink. We also show that the amplitude of these velocity perturbations is corrected, relatively to the GR force-free case, by a term of order ${\Omega }^6$, where $\Omega$ is the angular velocity of the star.

We present a comprehensive full-sky 3-dimensional analysis of the weak lensing fields and their corresponding power spectra. Using the formalism of spin-weight spherical harmonics and spherical Bessel functions, we relate the two-point statistics of the harmonic expansion coefficients of the weak lensing shear and convergence to the power spectrum of the matter density perturbations, and derive small-angle limits. Such a study is relevant in view of the next generation of large-scale weak lensing surveys which will provide distance information about the sources through photometric redshifts. This opens up the possibility of accurate cosmological parameter estimation via weak lensing, with an emphasis on the equation of state of dark energy.

The origin of a family-independent “extra $U(1)$”, discovered by Barr, Bednarz, and Benesh and independently by Ma, and whose phenomenology has recently been studied by Ma and Roy, is discussed. Even though it satisfies anomaly constraints in a highly economical way, with just a single extra triplet of leptons per family, this extra $U(1)$ cannot come from four-dimensional grand unification. However, it is shown here that it can come from a Pati-Salam scheme with an extra $U(1)$, which explains the otherwise surprising cancellation of anomalies.

We perform a global analysis of the tree-level open-string amplitudes in the limit $s\ll M_S^2$. Based on the present data from the Tevatron, HERA, and LEP 2, we set a lower limit on the string scale $M_S\ge 0.69–1.96\mathrm{TeV}$ at 95% confidence level for the Chan-Paton factors $|T|=0-4$. We also estimate the expected sensitivities at the CERN LHC, which can be as high as 19 TeV for $|T|=4$.

The local composite operator $A_{\mu }^2$ is added to the Zwanziger action, which implements the restriction to the Gribov region $\Omega$ in Euclidean Yang-Mills theories in the Landau gauge. We prove that Zwanziger’s action with the inclusion of the operator $A_{\mu }^2$ is renormalizable to all orders of perturbation theory, obeying the renormalization group equations. This allows us to study the dimension two gluon condensate $⟨A_{\mu }^2⟩$ by the local composite operator formalism when the restriction to the Gribov region $\Omega$ is taken into account. The resulting effective action is evaluated at one-loop order in the $\overline{\mathrm{MS}}$ scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to $⟨A_{\mu }^2⟩$, but the expansion parameter turns out to be rather large. Furthermore, an optimization of the perturbative expansion in order to reduce the dependence on the renormalization scheme is performed. The properties of the vacuum energy, with or without the inclusion of the condensate $⟨A_{\mu }^2⟩$, are investigated. In particular, it is shown that in the original Gribov-Zwanziger formulation, i.e. without the inclusion of the operator $A_{\mu }^2$, the resulting vacuum energy is always positive at one-loop order, independently from the choice of the renormalization scheme and scale. In the presence of $⟨A_{\mu }^2⟩$, we are unable to come to a definite conclusion at the order considered. In the $\overline{\mathrm{MS}}$ scheme, we still find a positive vacuum energy, again with a relatively large expansion parameter, but there are renormalization schemes in which the vacuum energy is negative, albeit the dependence on the scheme itself appears to be strong. Concerning the behavior of the gluon and ghost propagators, we recover the well-known consequences of the restriction to the Gribov region, and this in the presence of $⟨A_{\mu }^2⟩$, i.e. an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. Such a behavior is in qualitative agreement with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations.

Based on results of a search for the lepton-family-number-violating decay $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$ with data collected by experiment E865 at the Alternating Gradient Synchrotron of Brookhaven National Laboratory, we place an upper limit on the branching ratio at $2.1\times {10}^{-11}$ (90% C.L.). Combining the results with earlier E865 data and those of a previous experiment, E777, an upper limit on the branching ratio of $1.3\times {10}^{-11}$ (90% C.L.) is obtained.

We report the observation of ${\overline{B}}^0\to D^0{\eta }^{\prime }$ and the first observation of ${\overline{B}}^0\to D^{*0}{\eta }^{\prime }$, using $140{\mathrm{fb}}^{-1}$ of data collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider. We find the branching fractions to be $\mathcal{B}({\overline{B}}^0\to D^0{\eta }^{\prime })=[1.14\pm 0.20(\mathrm{stat})+0.10-0.13(\mathrm{syst})]\times {10}^{-4}$ and $\mathcal{B}({\overline{B}}^0\to D^{*0}{\eta }^{\prime })=[1.21\pm 0.34(\mathrm{stat})\pm 0.22(\mathrm{syst})]\times {10}^{-4}$ with significances including systematic uncertainties of 8.9 and 5.3 standard deviations, respectively.

We study noncommutative geometry at the quantum mechanics level by means of a model where noncommutativity of both configuration and momentum spaces is considered. We analyze how this model affects the problem of the two-dimensional gravitational quantum well and use the latest experimental results for the two lowest energy states of neutrons in the Earth’s gravitational field to establish an upper bound on the fundamental momentum scale introduced by noncommutativity, namely, $\sqrt{\eta }\lesssim 1\mathrm{meV}/c$, a value that can be improved in the future by up to $3$ orders of magnitude. We show that the configuration space noncommutativity has, in leading order, no effect on the problem. We also analyze some features introduced by the model, especially a correction to the presently accepted value of Planck’s constant to $1$ part in ${10}^{24}$.

Highly accurate numerical solutions to the problem of black holes surrounded by uniformly rotating rings in axially symmetric, stationary spacetimes are presented. The numerical methods developed to handle the problem are discussed in some detail. Related Newtonian problems are described and numerical results provided, which show that configurations can reach an inner mass-shedding limit as the mass of the central object increases. Exemplary results for the full relativistic problem for rings of constant density are given and the deformation of the event horizon due to the presence of the ring is demonstrated. Finally, we provide an example of a system for which the angular momentum of the central black hole divided by the square of its mass exceeds one ($J_{\mathrm{c}}/M_{\mathrm{c}}^2>1$).

In this paper a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface of these spheres, boundary conditions need to be imposed. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes with specific boundary conditions at their apparent horizons. We give representative examples corresponding to initial data that fulfill the requirements of the quasistationary framework, which combines the thin-sandwich formulation of the constraint equations with the isolated horizon conditions for black holes in quasiequilibrium. For all examples considered, numerical solutions with extremely high accuracy were obtained with moderate computational effort. Moreover, the method proves to be applicable even when tending toward limiting cases such as large radius ratios for the black holes.

We present arguments for the existence of both globally regular and black hole solutions of the Einstein equations with a conformally coupled scalar field, in the presence of a negative cosmological constant, for space-time dimensions greater than or equal to four. These configurations approach asymptotically anti-de Sitter space-time and are indexed by the central value of the scalar field. We also study the stability of these solutions, and show that, at least for all the solutions studied numerically, they are linearly stable.

I examine the standard formalism of calculating curvature perturbations in inflation at horizon crossing, and derive a general relation which must be satisfied for the horizon-crossing formalism to be valid. This relation is satisfied for the usual cases of power-law and slow-roll inflation. I then consider a model for which the relation is strongly violated, and the curvature perturbation evolves rapidly on superhorizon scales. This model has Hubble slow-roll parameter $\eta =3$, but predicts a scale-invariant spectrum of density perturbations. I consider the case of hybrid inflation with large $\eta$, and show that such solutions do not solve the “$\eta$ problem” in supergravity. These solutions correspond to field evolution which has not yet relaxed to the inflationary attractor solution, and may make possible new, more natural models on the string landscape.

We prove the existence of one quarter supersymmetric type IIB configurations that arise as nontrivial scaling solutions of the standard five-dimensional Kerr–anti-de Sitter black holes by the explicit construction of its Killing spinors. This neutral, spinning solution is asymptotic to the static anti-de Sitter space-time with cosmological constant $-\frac{1}{{\ell }^2}$, it has two finite equal angular momenta $J_1=\pm J_2$, mass $M=\frac{1}{\ell }(|J_1|+|J_2|)$ and a naked singularity. We also address the scaling limit associated with one-half supersymmetric solution with only one angular momentum.

Recently BABAR and Belle have measured anomalous large transverse polarizations in some pure penguin $B\to VV$ decays, which might be inconsistent with the standard model expectations. We try to explore its implications for $R$-parity violating (RPV) supersymmetry. The QCD factorization approach is employed for the hadronic dynamics of $B$ decays. We find that it is possible to have parameter spaces solving the anomaly. Furthermore, we have derived stringent bounds on relevant $R$-parity violating couplings from the experimental data, which is useful for further studies of RPV phenomena.