Superheavy dark matter and ultrahigh energy cosmic rays

The phase of inflationary expansion in the early universe produces superheavy relics in a mass window between 10^{12} GeV and 10^{14} GeV. Decay or annihilation of these superheavy relics can explain the observed ultrahigh energy cosmic rays beyond the Greisen-Zatsepin-Kuzmin cutoff. We emphasize that the pattern of cosmic ray arrival directions with energies beyond 20 EeV will decide between the different proposals for the origin of ultrahigh energy cosmic rays.Comment: Based on an invited talk given by RD at Theory Canada 1, Vancouver, June 2-5, 200

Remarks on probability theory and TMJ diagnosis

On the basis of the classic concepts of events and probability theory, this article analyzes some recently introduced diagnostic probability concepts as they pertain to temporomandibular joint (TMJ) diseases and disorders.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74644/1/j.1365-2842.1992.tb01486.x.pd

Type IIB Solutions with Interpolating Supersymmetries

We study type IIB supergravity solutions with four supersymmetries that interpolate between two types widely considered in the literature: the dual of Becker and Becker's compactifications of M-theory to 3 dimensions and the dual of Strominger's torsion compactifications of heterotic theory to 4 dimensions. We find that for all intermediate solutions the internal manifold is not Calabi-Yau, but has SU(3) holonomy in a connection with a torsion given by the 3-form flux. All 3-form and 5-form fluxes, as well as the dilaton, depend on one function appearing in the supersymmetry spinor, which satisfies a nonlinear differential equation. We check that the fields corresponding to a flat bound state of D3/D5-branes lie in our class of solutions. The relations among supergravity fields that we derive should be useful in studying new gravity duals of gauge theories, as well as possibly compactifications.Comment: 27pp, v2 REVTeX4, typographical fixes and minor clarifications, v3 added ref, modified discussion of RR axion slightl

Approximate k-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number {\kappa}. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C_{s} from the valence energy spectrum of particle and also for pseudospin symmetry constant C_{ps} from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter {\alpha}. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when {\alpha} becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.Comment: 21 pages, 6 figure

The Fall of Stringy de Sitter

Kachru, Kallosh, Linde, & Trivedi recently constructed a four-dimensional de Sitter compactification of IIB string theory, which they showed to be metastable in agreement with general arguments about de Sitter spacetimes in quantum gravity. In this paper, we describe how discrete flux choices lead to a closely-spaced set of vacua and explore various decay channels. We find that in many situations NS5-brane meditated decays which exchange NSNS 3-form flux for D3-branes are comparatively very fast.Comment: 35 pp (11 pp appendices), 5 figures, v3. fixed minor typo

A generic estimate of trans-Planckian modifications to the primordial power spectrum in inflation

We derive a general expression for the power spectra of scalar and tensor fluctuations generated during inflation given an arbitrary choice of boundary condition for the mode function at a short distance. We assume that the boundary condition is specified at a short-distance cutoff at a scale $M$ which is independent of time. Using a particular prescription for the boundary condition at momentum $p = M$, we find that the modulation to the power spectra of density and gravitational wave fluctuations is of order $(H/M)$, where $H$ is the Hubble parameter during inflation, and we argue that this behavior is generic, although by no means inevitable. With fixed boundary condition, we find that the shape of the modulation to the power spectra is determined entirely by the deviation of the background spacetime from the de Sitter limit.Comment: 15 pages (RevTeX), 2 figure

Supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian Screened Coulomb potential via Hamiltonian hierarchy inspired variational method

The supersymmetric solutions of PT-symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schrodinger equation for the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy inspired variational method is used to obtain the approximate energy eigenvalues and corresponding wave functions.Comment: 13 page

(Re)constructing Dimensions

Compactifying a higher-dimensional theory defined in R^{1,3+n} on an n-dimensional manifold {\cal M} results in a spectrum of four-dimensional (bosonic) fields with masses m^2_i = \lambda_i, where - \lambda_i are the eigenvalues of the Laplacian on the compact manifold. The question we address in this paper is the inverse: given the masses of the Kaluza-Klein fields in four dimensions, what can we say about the size and shape (i.e. the topology and the metric) of the compact manifold? We present some examples of isospectral manifolds (i.e., different manifolds which give rise to the same Kaluza-Klein mass spectrum). Some of these examples are Ricci-flat, complex and K\"{a}hler and so they are isospectral backgrounds for string theory. Utilizing results from finite spectral geometry, we also discuss the accuracy of reconstructing the properties of the compact manifold (e.g., its dimension, volume, and curvature etc) from measuring the masses of only a finite number of Kaluza-Klein modes.Comment: 23 pages, 3 figures, 2 references adde

A theoretical and empirical investigation of nutritional label use

Due in part to increasing diet-related health problems caused, among others, by obesity, nutritional labelling has been considered important, mainly because it can provide consumers with information that can be used to make informed and healthier food choices. Several studies have focused on the empirical perspective of nutritional label use. None of these studies, however, have focused on developing a theoretical economic model that would adequately describe nutritional label use based on a utility theoretic framework. We attempt to fill this void by developing a simple theoretical model of nutritional label use, incorporating the time a consumer spends reading labels as part of the food choice process. The demand equations of the model are then empirically tested. Results suggest the significant role of several variables that flow directly from the model which, to our knowledge, have not been used in any previous empirical work