The fundamental concepts of Riemannian geometry, such as differential forms, the vielbein, metric, connection, torsion, and curvature, are generalized in the context of noncommutative geometry. This allows us to construct the Einstein-Hilbert-Cartan terms, in addition to the bosonic and fermionic ones in the Lagrangian of an action functional on noncommutative spaces. As an example, and also as a prelude to the standard model that includes gravitational interactions, we present a model of chiral spinor fields on a curved two-sheeted space-time with two distinct Abelian gauge fields. In this model, the full spectrum of the generalized metric consists of pairs of tensors, vectors, and scalar fields. They are coupled to the chiral fermions and the gauge fields leading to possible parity violation effects triggered by gravity.

We show that a particular set of global modes for the massive de Sitter scalar field (the de Sitter waves) allows us to manage the group representations and the Fourier transform in the flat (Minkowskian) limit. This is in opposition to the usual acceptance based on a previous result, suggesting the appearance of negative energy in the limit process. This method also confirms that the Euclidean vacuum, in de Sitter spacetime, is preferred as far as one wishes to recover ordinary quantum field theory in the flat limit.

We compute the cosmological perturbations generated in the brane world inflation driven by the bulk inflaton. Different from the model in which inflation is a brane effect, we exhibit the modification of the power spectrum of scalar perturbations due to the existence of a fifth dimension. With the change of the initial vacuum, we investigate the dependence of the correction of the power spectrum on the choice of the vacuum.

A Fermi ball is a kind of nontopological soliton with fermions trapped in its domain wall, and has been suggested to arise from the spontaneous symmetry breaking of the approximate $Z_2$ symmetry in the early universe. We find that the neutral thin-wall Fermi ball is stable in the limited region of the scalar self-coupling constant $\lambda$ and the Yukawa coupling constant G. We find that the Fermi ball is stabilized due to the curvature effect of the domain wall caused by the fermion sector. We also discuss whether such a stable Fermi ball may contribute to cold dark matter.

We propose a sensitive way to test the anomalous HVV couplings ${(V=W}^{\pm },Z^0)$ of the Higgs boson $\mathrm{}\left(H\right),$ which can arise from either the dimension-3 effective operator in a nonlinearly realized Higgs sector or the dimension-6 effective operators in a linearly realized Higgs sector, via studying the VV scattering processes at the CERN LHC. The gold-plated pure leptonic decay modes of the final state weak bosons in the processes $p\overrightarrow{p}\mathrm{VVjj}$ are studied. For comparison, we also analyze the constraints from the precision electroweak data, the expected precision of the measurements of the Higgs boson production rate, decay width and branching ratios at the Fermilab Tevatron run-2 and the CERN LHC, and the requirement of unitarity of the S matrix. We show that, with an integrated luminosity of $300{\mathrm{fb}}^{-1}$ and sufficient kinematical cuts for suppressing the backgrounds, studying the process $p\overrightarrow{p}{W}^{+}{W}^{+}j\overrightarrow{j}{l}^{+}\nu l^{+}\nu \mathrm{jj}$ can probe the anomalous HWW couplings at a few tens of percent level for the nonlinearly realized Higgs sector, and at the level of $0.01–0.08{\mathrm{TeV}}^{-1}$ for the linearly realized effective Lagrangian.

The first results from the KamLAND experiment in conjunction with the global solar neutrino data have demonstrated the striking ability to constrain the $\Delta m_{\odot }^2\left(\Delta m_{21}^2\right)$ very precisely. However the allowed range of ${\theta }_{\odot }\left({\theta }_{12}\right)$ did not change much with the inclusion of the KamLAND results. In this paper we probe if future data from KamLAND can increase the accuracy of the allowed range in ${\theta }_{\odot }$ and conclude that even after 3 kton yr of statistics and with the most optimistic error estimates, KamLAND may find it hard to significantly improve the bounds on the mixing angle obtained from the solar neutrino data. We discuss the ${\theta }_{12}$ sensitivity of the survival probabilities in matter (vacuum) as relevant for the solar (KamLAND) experiments. We find that the presence of matter effects in the survival probabilities for ${}^8\mathrm{B}$ neutrinos gives the solar neutrino experiments SK and SNO an edge over KamLAND, as far as ${\theta }_{12}$ sensitivity is concerned, particularly near the maximal mixing. Among solar neutrino experiments we identify SNO as a most promising candidate for constraining ${\theta }_{12}$ and make a projected sensitivity test for the mixing angle by reducing the error in the neutral current measurement at SNO. Finally, we argue that the most accurate bounds on ${\theta }_{12}$ can be achieved in a reactor experiment, if the corresponding baseline and energy can be tuned to a minimum in the survival probability. We propose a new reactor experiment that can give the value of ${\tan }^2{\theta }_{12}$ to within 14%. We also discuss the future Borexino and LowNu experiments.

We study supersymmetry breaking in the lattice $N=1\mathrm{}$ Wess-Zumino model by the world-line path integral algorithm. The ground state energy and supersymmetric Ward identities are exploited to support the expected symmetry breaking in finite volume. Non-Gaussian fluctuations of the topological charge are discussed and related to the infinite volume transition.

The addition of a topological Chern-Simons term to three-dimensional higher-derivative gravity is not a good therapy to cure the nonunitarity of the aforementioned theory. Moreover, ${R+R}^2$ gravity in (2+1)D, which is unitary at the tree level, becomes tree-level nonunitary when it is augmented by the abovementioned topological term. Therefore, unlike what is claimed in the literature, topological higher-derivative gravity in (2+1)D is not tree-level unitary and neither is topological three-dimensional ${R+R}^2$ gravity.

We present new classes of supersymmetric standardlike models from a type IIA ${\mathbf{T}}^6/({\mathbf{Z}}_2\times {\mathbf{Z}}_2)$ orientifold with intersecting D6-branes. D6-branes can wrap general supersymmetric three-cycles of ${\mathbf{T}}^6={\mathbf{T}}^2\times {\mathbf{T}}^2\times {\mathbf{T}}^2,$ and any ${\mathbf{T}}^2$ is allowed to be tilted. The models still suffer from additional exotics; however, we obtain solutions with fewer Higgs doublets, as well as models with all three families of left-handed quarks and leptons arising from the same intersecting sector, and examples of a genuine left-right symmetric model with three copies of left-handed and right-handed families of quarks and leptons.

We provide a unified formula for the quantum decay rate of heavy objects (particles) whatever they may be: topological and nontopological solitons, X particles, cosmic defects, microscopic black holes, fundamental strings, as well as the particle decays in the standard model. Extreme energy cosmic ray (EECR) top-down scenarios are based on relics from the early Universe. The key point in the top-down scenarios is the necessity to adjust the lifetime of the heavy object to the age of the Universe. This ad hoc requirement needs a very high dimensional operator to govern its decay and/or an extremely small coupling constant. The arguments produced to fine-tune the relic lifetime to the age of the Universe are critically analyzed. The natural lifetimes of such heavy objects are, however, microscopic times associated with the grand unified theory energy scale $(\sim {10}^{-28}\sec$ or shorter). It is at this energy scale (by the end of inflation) that they could have been abundantly formed in the early Universe, and it seems natural that they decayed shortly after being formed. The annihilation scenario for EECRs (“wimpzillas”) is also considered and its inconsistencies analyzed.

Gravity coupled to an arbitrary number of antisymmetric tensors and scalar fields in arbitrary space-time dimensions is studied in the context of general, static, spherically symmetric solutions with many orthogonally intersecting branes. Neither supersymmetry nor a harmonic gauge is assumed. It is shown that the system reduces to a Toda-like system after an adequate redefinition of the transverse radial coordinate r. The duality $\overrightarrow{r}1/r$ in the set of solutions is observed.

We consider the thermodynamics of a minimally coupled massive scalar field in a $\mathrm{}(3+1)\mathrm{}$-dimensional Taub-NUT background. The brick wall model of ’t Hooft is used. When Schwarzschild-like coordinates are used it is found that the usual radial brick wall cutoff parameter is required to regularize the solution. Free energy of the scalar field is obtained through explicit counting of states. It is found that the free energy and the entropy are quadratically divergent in the cutoff parameter.

We discuss D-braneworld cosmology; that is, the brane is described by the Born-Infeld action. Compared with the usual Randall-Sundrum braneworld cosmology where the brane action is the Nambu-Goto one, we can see some drastic changes in the very early universe: (i) the universe may experience a rapidly accelerating phase; (ii) the closed universe may avoid the initial singularity. We also briefly address the dynamics of the cosmology in the open string metric, which might be more favored than the induced metric from the viewpoint of the D-brane.

The starburst galaxies M82 and NGC253 have been proposed as the primary sources of cosmic rays with energies above ${10}^{18.7}\mathrm{eV}.$ For energies $\gtrsim {10}^{20.3}\mathrm{eV}$ the model predicts strong anisotropies. We calculate the probabilities that the latter can be due to chance occurrence. For the highest energy cosmic ray events in this energy region, we find that the observed directionality has less than 1% probability of occurring due to random fluctuations. Moreover, during the first 5 years of operation at Auger, the observation of even half the predicted anisotropy has a probability of less than ${10}^{-5}$ to occur by chance fluctuation. Thus, this model can be subject to test at very small cost to the Auger priors budget and, whatever the outcome of that test, valuable information on the galactic magnetic field will be obtained.

We discuss the possibility of generating adiabatic density perturbations from spatial fluctuations in the inflaton decay rate which are due to quantum fluctuations of light moduli fields coupling to the inflaton. We point out that nonrenormalizable operators, which lift the flatness of the moduli potential, play an important role for the density perturbations. In particular, the nonrenormalizable terms give rise to a considerable damping of the fluctuations and thereby pose an obstruction to the construction of possible models.

The Hartree ensemble approximation is studied in the “symmetric phase” of $1+1$ dimensional $\lambda {\phi }^4$ theory. In comparison with the “broken phase” studied previously, it is shown that the dynamical evolution of observables such as the particle distribution, energy exchange and auto-correlation functions is substantially slower. Approximate thermalization is found only for relatively large energy densities and couplings.

Very light pseudoscalars can arise from the symmetry-breaking sector in many extensions of the standard model. If their mass is below 200 MeV, they can be long-lived and have interesting phenomenology. We discuss the experimental constraints on several models with light pseudoscalars, including one in which the pseudoscalar is naturally fermiophobic. Taking into account the stringent bounds from rare K and B decays, we find allowed parameter space in each model that may be accessible in direct production experiments. In particular, we study the photoproduction of light pseudoscalars at Jefferson Lab and conclude that a beam dump experiment could explore some of the allowed parameter space of these models.

Lepton-flavor-violating decays of the type $\overrightarrow{L}l\gamma \gamma$ $(\overrightarrow{\mu }e\gamma \gamma ,$ $\overrightarrow{\tau }e\gamma \gamma ,$ and $\overrightarrow{\tau }\mu \gamma \gamma )$ are proposed as new probes of R-parity-violating supersymmetry. Non-penguin diagrams with a sneutrino that decays into two photons via a triangle graph might trigger such decays even in the absence of the corresponding radiative decays into one photon only, e.g. $\overrightarrow{\mu }e\gamma .$ Thus, processes of the type $\overrightarrow{L}l\gamma \gamma$ may provide an independent probe of new flavor physics.

We discuss the phenomenology of the lightest ${\mathrm{SU}\left(3\right)\mathrm{}}_C$ singlet and nonsinglet technihadrons in the straw man model of low-scale technicolor (TCSM). The technihadrons are assumed to be those arising in top-color-assisted technicolor models in which top-color is broken by technifermion condensates. We improve upon the description of the color-singlet sector presented in our earlier paper introducing the TCSM [K. Lane, Phys. Rev. D 60, 075007 (1999)]. These improvements are most important for subprocess energies well below the masses of the ${\rho }_T$ and ${\omega }_T$ vector technihadrons and, therefore, apply especially to $e^{+}{e}^{-}$ colliders such as CERN LEP and a low-energy linear collider. In the color-octet sector, we consider mixing of the gluon, the coloron $V_8$ from top-color breaking, and four isosinglet color-octet technirho mesons ${\rho }_{T8\mathrm{}}.$ We assume, as expected in walking technicolor, that these ${\rho }_{T8\mathrm{}}$ decay into $\overline{q}q,gg,$ and $g{\pi }_T$ final states, but not into ${\pi }_T{\pi }_T,$ where ${\pi }_T$ is a technipion. All the TCSM production and decay processes discussed here are included in the event generator PYTHIA. We present several simulations appropriate for the Fermilab Tevatron collider, and suggest benchmark model lines for further experimental investigation.

We calculate the masses of the lowest lying eigenstates of improved SU(2) and SU(3) lattice gauge theory in 2+1 dimensions using an analytic variational approach. The ground state is approximated by a one plaquette trial state and mass gaps are calculated in the symmetric and antisymmetric sectors by minimizing over a suitable basis of rectangular states.