The exact three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential in the screening limit

The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann-Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values.Comment: 15 pages, 4 eps figure

CBR Anisotropy from Primordial Gravitational Waves in Two-Component Inflationary Cosmology

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early universe. We consider spatially flat, perturbed FRW models that begin with an inflationary phase, followed by a mixed phase containing both radiation and dust. The scale factor during the mixed phase takes the form $a(\eta)=c_1\eta^2+c_2\eta+c_3$, where $c_i$ are constants. During the mixed phase the universe smoothly transforms from being radiation to dust dominated. We find analytic expressions for the graviton mode function during the mixed phase in terms of spheroidal wave functions. This mode function is used to find an analytic expression for the multipole moments $\langle a_l^2\rangle$ of the two-point angular correlation function $C(\gamma)$ for the CBR anisotropy. The analytic expression for the multipole moments is written in terms of two integrals, which are evaluated numerically. The results are compared to multipoles calculated for models that are {\it completely} dust dominated at last-scattering. We find that the multipoles $\langle a_l^2\rangle$ of the CBR temperature perturbations for $l>10$ are significantly larger for a universe that contains both radiation and dust at last-scattering. We compare our results with recent, similar numerical work and find good agreement. The spheroidal wave functions may have applications to other problems of cosmological interest.Comment: 28 pgs + 6 postscript figures, RevTe

The Primordial Gravitational Wave Background in String Cosmology

We find the spectrum P(w)dw of the gravitational wave background produced in the early universe in string theory. We work in the framework of String Driven Cosmology, whose scale factors are computed with the low-energy effective string equations as well as selfconsistent solutions of General Relativity with a gas of strings as source. The scale factor evolution is described by an early string driven inflationary stage with an instantaneous transition to a radiation dominated stage and successive matter dominated stage. This is an expanding string cosmology always running on positive proper cosmic time. A careful treatment of the scale factor evolution and involved transitions is made. A full prediction on the power spectrum of gravitational waves without any free-parameters is given. We study and show explicitly the effect of the dilaton field, characteristic to this kind of cosmologies. We compute the spectrum for the same evolution description with three differents approachs. Some features of gravitational wave spectra, as peaks and asymptotic behaviours, are found direct consequences of the dilaton involved and not only of the scale factor evolution. A comparative analysis of different treatments, solutions and compatibility with observational bounds or detection perspectives is made.Comment: LaTeX, 50 pages with 2 figures. Uses epsfig and psfra

Gravitons and Lightcone Fluctuations

Gravitons in a squeezed vacuum state, the natural result of quantum creation in the early universe or by black holes, will introduce metric fluctuations. These metric fluctuations will introduce fluctuations of the lightcone. It is shown that when the various two-point functions of a quantized field are averaged over the metric fluctuations, the lightcone singularity disappears for distinct points. The metric averaged functions remain singular in the limit of coincident points. The metric averaged retarded Green's function for a massless field becomes a Gaussian which is nonzero both inside and outside of the classical lightcone. This implies some photons propagate faster than the classical light speed, whereas others propagate slower. The possible effects of metric fluctuations upon one-loop quantum processes are discussed and illustrated by the calculation of the one-loop electron self-energy.Comment: 18pp, LATEX, TUTP-94-1

Quantum Vacuum Instability Near Rotating Stars

We discuss the Starobinskii-Unruh process for the Kerr black hole. We show how this effect is related to the theory of squeezed states. We then consider a simple model for a highly relativistic rotating star and show that the Starobinskii-Unruh effect is absent.Comment: 17 Pages, (accepted by PRD), (previously incorrect header files have been corrected

Quintessence and Gravitational Waves

We investigate some aspects of quintessence models with a non-minimally coupled scalar field and in particular we show that it can behave as a component of matter with $-3 \lesssim P/\rho \lesssim 0$. We study the properties of gravitational waves in this class of models and discuss their energy spectrum and the cosmic microwave background anisotropies they induce. We also show that gravitational waves are damped by the anisotropic stress of the radiation and that their energy spectrum may help to distinguish between inverse power law potential and supergravity motivated potential. We finish by a discussion on the constraints arising from their density parameter \Omega_\GW.Comment: 21 pages, 18 figures, fianl version, accepted for publication in PR

Non Linear Current Response of a Many-Level Tunneling System: Higher Harmonics Generation

The fully nonlinear response of a many-level tunneling system to a strong alternating field of high frequency $\omega$ is studied in terms of the Schwinger-Keldysh nonequilibrium Green functions. The nonlinear time dependent tunneling current $I(t)$ is calculated exactly and its resonance structure is elucidated. In particular, it is shown that under certain reasonable conditions on the physical parameters, the Fourier component $I_{n}$ is sharply peaked at $n=\frac {\Delta E} {\hbar \omega}$, where $\Delta E$ is the spacing between two levels. This frequency multiplication results from the highly nonlinear process of $n$ photon absorption (or emission) by the tunneling system. It is also conjectured that this effect (which so far is studied mainly in the context of nonlinear optics) might be experimentally feasible.Comment: 28 pages, LaTex, 7 figures are available upon request from [email protected], submitted to Phys.Rev.

Noninteracting dark matter

Since an acceptable dark matter candidate may interact only weakly with ordinary matter and radiation, it is of interest to consider the limiting case where the dark matter interacts only with gravity and itself, the matter originating by the gravitational particle production at the end of inflation. We use the bounds on the present dark mass density and the measured large-scale fluctuations in the thermal cosmic background radiation to constrain the two parameters in a self-interaction potential that is a sum of quadratic and quartic terms in a single scalar dark matter field that is minimally coupled to gravity. In quintessential inflation, where the temperature at the end of inflation is relatively low, the field starts acting like cold dark matter relatively late, shortly before the epoch of equal mass densities in matter and radiation. This could have observable consequences for galaxy formation. We respond to recent criticisms of the quintessential inflation scenario, since these issues also apply to elements of the noninteracting dark matter picture.Comment: 37 pages, 3 figure

Van der Waals-Casimir-Polder interaction of an atom with a composite surface

We study the dispersion interaction of the van der Waals and Casimir-Polder (vdW-CP) type between a neutral atom and the surface of a metal by allowing for nonlocal electrodynamics, i.e. electron diffusion. We consider two models: (i) bulk diffusion, and (ii) diffusion in a surface charge layer. In both cases the transition to a semiconductor is continuous as a function of the conductivity, unlike the case of a local model. The relevant parameter is the electric screening length and depends on the carrier diffusion constant. We find that for distances comparable to the screening length, vdW-CP data can distinguish between bulk and surface diffusion, hence it can be a sensitive probe for surface states.Comment: v2: expanded references, statements on current status in the field. 10 pages, 6 figure

Magnetogenesis and the dynamics of internal dimensions

The dynamical evolution of internal space-like dimensions breaks the invariance of the Maxwell's equations under Weyl rescaling of the (conformally flat) four-dimensional metric. Depending upon the number and upon the dynamics of internal dimensions large scale magnetic fields can be created. The requirements coming from magnetogenesis together with the other cosmological constraints are examined under the assumption that the internal dimensions either grow or shrink (in conformal time) prior to a radiation dominated epoch. If the internal dimensions are growing the magnitude of the generated magnetic fields can seed the galactic dynamo mechanism.Comment: 27 in RevTex style, four figure