Local freedom in the gravitational field

In a cosmological context, the electric and magnetic parts of the Weyl tensor, E_{ab} and H_{ab}, represent the locally free curvature - i.e. they are not pointwise determined by the matter fields. By performing a complete covariant decomposition of the derivatives of E_{ab} and H_{ab}, we show that the parts of the derivative of the curvature which are locally free (i.e. not pointwise determined by the matter via the Bianchi identities) are exactly the symmetrised trace-free spatial derivatives of E_{ab} and H_{ab} together with their spatial curls. These parts of the derivatives are shown to be crucial for the existence of gravitational waves.Comment: New results on gravitational waves included; new references added; revised version (IOP style) to appear Class. Quantum Gra

Note on Signature Change and Colombeau Theory

Recent work alludes to various `controversies' associated with signature change in general relativity. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR

Gravity and Signature Change

The use of proper ``time'' to describe classical ``spacetimes'' which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.Comment: Plain TeX, 6 pages; to appear in GR

The Venus Balloon Project

On June 11 and 15, 1985, two instrumental balloons were released from the Soviet VEGA 1 and VEGA 2 spacecraft and deployed in the atmosphere of Venus. The VEGA probes flew by the planet on their way to a rendezvous with comet Halley in March 1986. Drifting with the wind at altitudes of 54 km, the balloons traveled one-third of the way around the planet during their 46-hour lifetimes. Sensors on-board the gondolas made periodic measurements of pressure, temperature, vertical wind velocity, cloud particle density, ambient light level, and frequency of lightning. The data were transmitted to Earth and received at the Deep Space Network (DSN) 64-m stations and at several large antennas in the USSR. Approximately 95 percent of the telemetry data were successfully decoded at the DSN complexes and in the Soviet Union, and were provided to the international science team for analysis. Very Long Baseline Interferometry (VLBI) data were acquired by 20 radio observatories around the world for the purpose of monitoring the Venus winds. The DSN 64-m subnet was part of a 15-station VLBI network organized by the Centre National d'Etudes Spatiales (CNES) of France. In addition, five antennas of the Soviet network participated. VLBI data from the CNES network are currently being processed at the Jet Propulsion Laboratory

Dynamics of Inflationary Universes with Positive Spatial Curvature

If the spatial curvature of the universe is positive, then the curvature term will always dominate at early enough times in a slow-rolling inflationary epoch. This enhances inflationary effects and hence puts limits on the possible number of e-foldings that can have occurred, independently of what happened before inflation began and in particular without regard for what may have happened in the Planck era. We use a simple multi-stage model to examine this limit as a function of the present density parameter $\Omega_0$ and the epoch when inflation ends.Comment: 9 Pages RevTex4. Revised and update

Electroweak Precision Data and Gravitino Dark Matter

Electroweak precision measurements can provide indirect information about the possible scale of supersymmetry already at the present level of accuracy. We review present day sensitivities of precision data in mSUGRA-type models with the gravitino as the lightest supersymmetric particle (LSP). The chi^2 fit is based on M_W, sin^2 theta_eff, (g-2)_mu, BR(b -> s gamma) and the lightest MSSM Higgs boson mass, M_h. We find indications for relatively light soft supersymmetry-breaking masses, offering good prospects for the LHC and the ILC, and in some cases also for the Tevatron.Comment: 4 pages, 1 figure. Talk given at the LCWS06 March 2006, Bangalore, India. References adde

A fully covariant description of CMB anisotropies

Starting from the exact non-linear description of matter and radiation, a fully covariant and gauge-invariant formula for the observed temperature anisotropy of the cosmic microwave background (CBR) radiation, expressed in terms of the electric ($E_{ab}$) and magnetic ($H_{ab}$) parts of the Weyl tensor, is obtained by integrating photon geodesics from last scattering to the point of observation today. This improves and extends earlier work by Russ et al where a similar formula was obtained by taking first order variations of the redshift. In the case of scalar (density) perturbations, $E_{ab}$ is related to the harmonic components of the gravitational potential $\Phi_k$ and the usual dominant Sachs-Wolfe contribution $\delta T_R/\bar{T}_R\sim\Phi_k$ to the temperature anisotropy is recovered, together with contributions due to the time variation of the potential (Rees-Sciama effect), entropy and velocity perturbations at last scattering and a pressure suppression term important in low density universes. We also explicitly demonstrate the validity of assuming that the perturbations are adiabatic at decoupling and show that if the surface of last scattering is correctly placed and the background universe model is taken to be a flat dust dominated Friedmann-Robertson-Walker model (FRW), then the large scale temperature anisotropy can be interpreted as being due to the motion of the matter relative to the surface of constant temperature which defines the surface of last scattering on those scales.Comment: 18 pages LaTeX, 1 figure. Submitted to Classical and Quantum Gravity. Also available at http://shiva.mth.uct.ac.za/preprints/9705.htm

Full one-loop amplitudes from tree amplitudes

We establish an efficient polynomial-complexity algorithm for one-loop calculations, based on generalized $D$-dimensional unitarity. It allows automated computations of both cut-constructible {\it and} rational parts of one-loop scattering amplitudes from on-shell tree amplitudes. We illustrate the method by (re)-computing all four-, five- and six-gluon scattering amplitudes in QCD at one-loop.Comment: 27 pages, revte

Locally extracting scalar, vector and tensor modes in cosmological perturbation theory

Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second- and higher-order because perturbative modes are sourced by products of lower-oder modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second-order. We perform much of our analysis using an index-free `vector-calculus' approach which makes manipulating tensor equations considerably simpler.Comment: 13 pages. Final version to appear in CQ