Damping of Tensor Modes in Cosmology

An analytic formula is given for the traceless transverse part of the anisotropic stress tensor due to free streaming neutrinos, and used to derive an integro-differential equation for the propagation of cosmological gravitational waves. The solution shows that anisotropic stress reduces the squared amplitude by 35.6 % for wavelengths that enter the horizon during the radiation-dominated phase, independent of any cosmological parameters. This decreases the tensor temperature and polarization correlation functions for these wavelengths by the same amount. The effect is less for wavelengths that enter the horizon at later times. At the longest wavelengths the decrease in the tensor correlation functions due to neutrino free streaming ranges from 10.7% for $\Omega_Mh^2=0.1$ to 9.0% for $\Omega_Mh^2=0.15$. An Appendix gives a general proof that tensor as well as scalar modes satisfy a conservation law for perturbations outside the horizon, even when the anisotropic stress tensor is not negligible.Comment: 14 pages. The original version of this paper has been expanded to deal with perturbations of any wavelength. While for wavelengths short enough to enter the horizon during radiation dominance, temperature and polarization correlations are damped by 35.6%, at the longest wavelengths the damping is from 9.0% to 11%. An added Appendix gives a general proof that tensor as well as scalar modes satisfy a conservation law outside the horizon, even during neutrino decoupling. Some references are also adde

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

Tunneling and propagation of vacuum bubbles on dynamical backgrounds

In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In particular, we provide semi-analytic and numerical results for the modified nucleation rate in FLRW backgrounds, as well as a parameter study of bubble walls propagating into inhomogeneous (LTB) or FLRW spacetimes, both in the thin-wall approximation. We show that in our model, matter in the background often prevents bubbles from successful expansion and forces them to collapse. For cases where they do expand, we give arguments why the effects on the interior spacetime are small for a wide range of reasonable parameters and discuss the limitations of the employed approximations.Comment: 29 pages, 8 figures, typos corrected, matches published versio

Testing metric-affine f(R)-gravity by relic scalar gravitational waves

We discuss the emergence of scalar gravitational waves in metric-affine f(R)-gravity. Such a component allows to discriminate between metric and metric-affine theories The intrinsic meaning of this result is that the geodesic structure of the theory can be discriminated. We extend the formalism of cross correlation analysis, including the additional polarization mode, and calculate the detectable energy density of the spectrum for cosmological relic gravitons. The possible detection of the signal is discussed against sensitivities of VIRGO, LIGO and LISA interferometers.Comment: 12 pages, 4 figure

A Note on Conserved Charges of Asymptotically Flat and Anti-de Sitter Spaces in Arbitrary Dimensions

The calculation of conserved charges of black holes is a rich problem, for which many methods are known. Until recently, there was some controversy on the proper definition of conserved charges in asymptotically anti-de Sitter (AdS) spaces in arbitrary dimensions. This paper provides a systematic and explicit Hamiltonian derivation of the energy and the angular momenta of both asymptotically flat and asymptotically AdS spacetimes in any dimension D bigger or equal to 4. This requires as a first step a precise determination of the asymptotic conditions of the metric and of its conjugate momentum. These conditions happen to be achieved in ellipsoidal coordinates adapted to the rotating solutions.The asymptotic symmetry algebra is found to be isomorphic either to the Poincare algebra or to the so(D-1, 2) algebra, as expected. In the asymptotically flat case, the boundary conditions involve a generalization of the parity conditions, introduced by Regge and Teitelboim, which are necessary to make the angular momenta finite. The charges are explicitly computed for Kerr and Kerr-AdS black holes for arbitrary D and they are shown to be in agreement with thermodynamical arguments.Comment: 27 pages; v2 : references added, minor corrections; v3 : replaced to match published version forthcoming in General Relativity and Gravitatio

Elastic electron deuteron scattering with consistent meson exchange and relativistic contributions of leading order

The influence of relativistic contributions to elastic electron deuteron scattering is studied systematically at low and intermediate momentum transfers ($Q^2\leq 30$ fm$^{-2}$). In a $(p/M)$-expansion, all leading order relativistic $\pi$-exchange contributions consistent with the Bonn OBEPQ models are included. In addition, static heavy meson exchange currents including boost terms and lowest order $\rho\pi\gamma$-currents are considered. Sizeable effects from the various relativistic two-body contributions, mainly from $\pi$-exchange, have been found in form factors, structure functions and the tensor polarization $T_{20}$. Furthermore, static properties, viz. magnetic dipole and charge quadrupole moments and the mean square charge radius are evaluated.Comment: 15 pages Latex including 5 figures, final version accepted for publication in Phys.Rev.C Details of changes: (i) The notation of the curves in Figs. 1 and 2 have been clarified with respect to left and right panels. (ii) In Figs. 3 and 4 an experimental point for T_20 has been added and a corresponding reference [48] (iii) At the end of the text we have added a paragraph concerning the quality of the Bonn OBEPQ potential

Gravitational Coupling and Dynamical Reduction of The Cosmological Constant

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner, a decaying mechanism is presented in which the conformal factor appears as a dynamical field and plays a key role to relax a large effective cosmological constant. Moreover, we argue that this model also provides a possible explanation for the coincidence problem.Comment: To appear in GR

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

How does the electromagnetic field couple to gravity, in particular to metric, nonmetricity, torsion, and curvature?

The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in the laboratory or by observing outer space. (ii) One desires to test out alternatives to Einstein's gravitational theory, in particular those of a gauge-theoretical nature, like Einstein-Cartan theory or metric-affine gravity. A clean discussion requires a reflection on the foundations of electrodynamics. If one bases electrodynamics on the conservation laws of electric charge and magnetic flux, one finds Maxwell's equations expressed in terms of the excitation H=(D,H) and the field strength F=(E,B) without any intervention of the metric or the linear connection of spacetime. In other words, there is still no coupling to gravity. Only the constitutive law H= functional(F) mediates such a coupling. We discuss the different ways of how metric, nonmetricity, torsion, and curvature can come into play here. Along the way, we touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld, Heisenberg-Euler, Plebanski), linear ones, including the Abelian axion (Ni), and find a method for deriving the metric from linear electrodynamics (Toupin, Schoenberg). Finally, we discuss possible non-minimal coupling schemes.Comment: Latex2e, 26 pages. Contribution to "Testing Relativistic Gravity in Space: Gyroscopes, Clocks, Interferometers ...", Proceedings of the 220th Heraeus-Seminar, 22 - 27 August 1999 in Bad Honnef, C. Laemmerzahl et al. (eds.). Springer, Berlin (2000) to be published (Revised version uses Springer Latex macros; Sec. 6 substantially rewritten; appendices removed; the list of references updated