Is nonperturbative inflatino production during preheating a real threat to cosmology?

We discuss toy models where supersymmetry is broken due to non-vanishing time-varying vacuum expectation value of the inflaton field during preheating. We discuss the production of inflatino the superpartner of inflaton due to vacuum fluctuations and then we argue that they do not survive until nucleosynthesis and decay along with the inflaton to produce a thermal bath after preheating. Thus the only relevant remnant is the helicity \pm 3/2 gravitinos which can genuinely cause problem to nucleosynthesis.Comment: 10 pages, Updates to match the accepted version in Phys. Rev.

The Formation of Cosmic Structures in a Light Gravitino Dominated Universe

We analyse the formation of cosmic structures in models where the dark matter is dominated by light gravitinos with mass of $100$ eV -- 1 keV, as predicted by gauge-mediated supersymmetry (SUSY) breaking models. After evaluating the number of degrees of freedom at the gravitinos decoupling ($g_*$), we compute the transfer function for matter fluctuations and show that gravitinos behave like warm dark matter (WDM) with free-streaming scale comparable to the galaxy mass scale. We consider different low-density variants of the WDM model, both with and without cosmological constant, and compare the predictions on the abundances of neutral hydrogen within high-redshift damped Ly--$\alpha$ systems and on the number density of local galaxy clusters with the corresponding observational constraints. We find that none of the models satisfies both constraints at the same time, unless a rather small $\Omega_0$ value (\mincir 0.4) and a rather large Hubble parameter (\magcir 0.9) is assumed. Furthermore, in a model with warm + hot dark matter, with hot component provided by massive neutrinos, the strong suppression of fluctuation on scales of \sim 1\hm precludes the formation of high-redshift objects, when the low--$z$ cluster abundance is required. We conclude that all different variants of a light gravitino DM dominated model show strong difficulties for what concerns cosmic structure formation. This gives a severe cosmological constraint on the gauge-mediated SUSY breaking scheme.Comment: 28 pages,Latex, submitted for publication to Phys.Rev.

Supergravity Inflation Free from Harmful Relics

We present a realistic supergravity inflation model which is free from the overproduction of potentially dangerous relics in cosmology, namely moduli and gravitinos which can lead to the inconsistencies with the predictions of baryon asymmetry and nucleosynthesis. The radiative correction turns out to play a crucial role in our analysis which raises the mass of supersymmetry breaking field to intermediate scale. We pay a particular attention to the non-thermal production of gravitinos using the non-minimal Kahler potential we obtained from loop correction. This non-thermal gravitino production however is diminished because of the relatively small scale of inflaton mass and small amplitudes of hidden sector fields.Comment: 10 pages, revtex, 1 eps figure, references added, conclusion section expande

On the exact gravitational lens equation in spherically symmetric and static spacetimes

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 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.Comment: REVTEX, 11 pages, 12 eps-figures, figures partly improved, minor revision

Energy conditions, traversable wormholes and dust shells

Firstly, we review the pointwise and averaged energy conditions, the quantum inequality and the notion of the ``volume integral quantifier'', which provides a measure of the ``total amount'' of energy condition violating matter. Secondly, we present a specific metric of a spherically symmetric traversable wormhole in the presence of a generic cosmological constant, verifying that the null and the averaged null energy conditions are violated, as was to be expected. Thirdly, a pressureless dust shell is constructed around the interior wormhole spacetime by matching the latter geometry to a unique vacuum exterior solution. In order to further minimize the usage of exotic matter, we then find regions where the surface energy density is positive, thereby satisfying all of the energy conditions at the junction surface. An equation governing the behavior of the radial pressure across the junction surface is also deduced. Lastly, taking advantage of the construction, specific dimensions of the wormhole, namely, the throat radius and the junction interface radius, and estimates of the total traversal time and maximum velocity of an observer journeying through the wormhole, are also found by imposing the traversability conditions.Comment: 11 pages, 3 figures, Revtex

Double Inflation in Supergravity and the Large Scale Structure

The cosmological implication of a double inflation model with hybrid + new inflations in supergravity is studied. The hybrid inflation drives an inflaton for new inflation close to the origin through supergravity effects and new inflation naturally occurs. If the total e-fold number of new inflation is smaller than $\sim 60$, both inflations produce cosmologically relevant density fluctuations. Both cluster abundances and galaxy distributions provide strong constraints on the parameters in the double inflation model assuming $\Omega_0=1$ standard cold dark matter scenario. The future satellite experiments to measure the angular power spectrum of the cosmic microwave background will make a precise determination of the model parameters possible.Comment: 19 pages (RevTeX file

Inflationary Cosmology with Five Dimensional SO(10)

We discuss inflationary cosmology in a five dimensional SO(10) model compactified on $S^1/(Z_2\times Z_2')$, which yields $SU(3)_c\times SU(2)_L\times U(1)_Y\times U(1)_X$ below the compactification scale. The gauge symmetry $SU(5)\times U(1)_X$ is preserved on one of the fixed points, while ``flipped'' $SU(5)'\times U(1)'_X$ is on the other fixed point. Inflation is associated with $U(1)_X$ breaking, and is implemented through $F$-term scalar potentials on the two fixed points. A brane-localized Einstein-Hilbert term allows both branes to have positive tensions during inflation. The scale of $U(1)_X$ breaking is fixed from $\delta T/T$ measurements to be around $10^{16}$ GeV, and the scalar spectral index $n=0.98-0.99$. The inflaton field decays into right-handed neutrinos whose subsequent out of equilibrium decay yield the observed baryon asymmetry via leptogenesis.Comment: 1+19 pages, improved discussion of 5D cosmology, Version to appear in PR

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example