Light-like Signals in General relativity and Cosmology

The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penrose's hierarchical classification of the geometry induced on the null hypersurface history of the surface by its imbedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Results are accompanied by illustrative examples using cosmological models, vacuum space-times, the de sitter univers and Minkowskian space-time.Comment: 21 pages, latex, no figure

Gravitational wave generation from bubble collisions in first-order phase transitions: an analytic approach

Gravitational wave production from bubble collisions was calculated in the early nineties using numerical simulations. In this paper, we present an alternative analytic estimate, relying on a different treatment of stochasticity. In our approach, we provide a model for the bubble velocity power spectrum, suitable for both detonations and deflagrations. From this, we derive the anisotropic stress and analytically solve the gravitational wave equation. We provide analytical formulae for the peak frequency and the shape of the spectrum which we compare with numerical estimates. In contrast to the previous analysis, we do not work in the envelope approximation. This paper focuses on a particular source of gravitational waves from phase transitions. In a companion article, we will add together the different sources of gravitational wave signals from phase transitions: bubble collisions, turbulence and magnetic fields and discuss the prospects for probing the electroweak phase transition at LISA.Comment: 48 pages, 14 figures. v2 (PRD version): calculation refined; plots redone starting from Fig. 4. Factor 2 in GW energy spectrum corrected. Main conclusions unchanged. v3: Note added at the end of paper to comment on the new results of 0901.166

Improved limits on short-wavelength gravitational waves from the cosmic microwave background

The cosmic microwave background (CMB) is affected by the total radiation density around the time of decoupling. At that epoch, neutrinos comprised a significant fraction of the radiative energy, but there could also be a contribution from primordial gravitational waves with frequencies greater than ~ 10^-15 Hz. If this cosmological gravitational wave background (CGWB) were produced under adiabatic initial conditions, its effects on the CMB and matter power spectrum would mimic massless non-interacting neutrinos. However, with homogenous initial conditions, as one might expect from certain models of inflation, pre big-bang models, phase transitions and other scenarios, the effect on the CMB would be distinct. We present updated observational bounds for both initial conditions using the latest CMB data at small scales from the South Pole Telescope (SPT) in combination with Wilkinson Microwave Anisotropy Probe (WMAP), current measurements of the baryon acoustic oscillations, and the Hubble parameter. With the inclusion of the data from SPT the adiabatic bound on the CGWB density is improved by a factor of 1.7 to 10^6 Omega_gw < 8.7 at the 95% confidence level (C.L.), with weak evidence in favor of an additional radiation component consistent with previous analyses. The constraint can be converted into an upper limit on the tension of horizon-sized cosmic strings that could generate this gravitational wave component, with Gmu < 2 10^-7 at 95% C.L., for string tension Gmu. The homogeneous bound improves by a factor of 3.5 to 10^6 Omega_gw < 1.0 at 95% C.L., with no evidence for such a component from current data.Comment: 5 pages, 3 figure

Wave and Particle Scattering Properties of High Speed Black Holes

The light-like limit of the Kerr gravitational field relative to a distant observer moving rectilinearly in an arbitrary direction is an impulsive plane gravitational wave with a singular point on its wave front. By colliding particles with this wave we show that they have the same focussing properties as high speed particles scattered by the original black hole. By colliding photons with the gravitational wave we show that there is a circular disk, centered on the singular point on the wave front, having the property that photons colliding with the wave within this disk are reflected back and travel with the wave. This result is approximate in the sense that there are observers who can see a dim (as opposed to opaque) circular disk on their sky. By colliding plane electromagnetic waves with the gravitational wave we show that the reflected electromagnetic waves are the high frequency waves.Comment: Latex file, 22 pages, 1 figure, accepted for publication in Classical and Quantum Gravit

Space missions to detect the cosmic gravitational-wave background

It is thought that a stochastic background of gravitational waves was produced during the formation of the universe. A great deal could be learned by measuring this Cosmic Gravitational-wave Background (CGB), but detecting the CGB presents a significant technological challenge. The signal strength is expected to be extremely weak, and there will be competition from unresolved astrophysical foregrounds such as white dwarf binaries. Our goal is to identify the most promising approach to detect the CGB. We study the sensitivities that can be reached using both individual, and cross-correlated pairs of space based interferometers. Our main result is a general, coordinate free formalism for calculating the detector response that applies to arbitrary detector configurations. We use this general formalism to identify some promising designs for a GrAvitational Background Interferometer (GABI) mission. Our conclusion is that detecting the CGB is not out of reach.Comment: 22 pages, 7 figures, IOP style, References Adde

Detecting Vanishing Dimensions Via Primordial Gravitational Wave Astronomy

Lower-dimensionality at higher energies has manifold theoretical advantages as recently pointed out. Moreover, it appears that experimental evidence may already exists for it - a statistically significant planar alignment of events with energies higher than TeV has been observed in some earlier cosmic ray experiments. We propose a robust and independent test for this new paradigm. Since (2+1)-dimensional spacetimes have no gravitational degrees of freedom, gravity waves cannot be produced in that epoch. This places a universal maximum frequency at which primordial waves can propagate, marked by the transition between dimensions. We show that this cut-off frequency may be accessible to future gravitational wave detectors such as LISA.Comment: Somewhat expanded version with discussions that could not fit into the PRL version; references adde

Improved rain rate and drop size retrievals from airborne Doppler radar

Satellite remote sensing of rain is important for quantifying the hydrological cycle, atmospheric energy budget, and cloud and precipitation processes; however, radar retrievals of rain rate are sensitive to assumptions about the raindrop size distribution. The upcoming EarthCARE satellite will feature a 94 GHz Doppler radar alongside lidar and radiometer instruments, presenting opportunities for enhanced retrievals of the raindrop size distribution. We demonstrate the capability to retrieve rain rate as a function of drop size and drop number concentration from airborne 94 GHz Doppler radar measurements using CAPTIVATE, the variational retrieval algorithm developed for EarthCARE. For a range of rain regimes observed during the Tropical Composition, Cloud and Climate Coupling field campaign, we explore the contributions of mean Doppler velocity and path-integrated attenuation (PIA) measurements to the retrieval of rain rate, and the retrievals are evaluated against independent measurements from an independent 9.6 GHz Doppler radar. The retrieved drop number concentrations vary over 5 orders of magnitude between very light rain from melting ice and warm rain from liquid clouds. In light rain conditions mean Doppler velocity facilitates estimates of rain rate without PIA, suggesting the possibility of EarthCARE rain rate estimates over land; in moderate warm rain, drop number concentration can be retrieved without mean Doppler velocity, with possible applications to CloudSat

Gravitational Waves from Mesoscopic Dynamics of the Extra Dimensions

Recent models which describe our world as a brane embedded in a higher dimensional space introduce new geometrical degrees of freedom: the shape and/or size of the extra dimensions, and the position of the brane. These modes can be coherently excited by symmetry breaking in the early universe even on ``mesoscopic'' scales as large as 1 mm, leading to detectable gravitational radiation. Two sources are described: relativistic turbulence caused by a first-order transition of a radion potential, and Kibble excitation of Nambu-Goldstone modes of brane displacement. Characteristic scales and spectral properties are estimated and the prospects for observation by LISA are discussed. Extra dimensions with scale between 10 \AA and 1 mm, which enter the 3+1-D era at cosmic temperatures between 1 and 1000 TeV, produce backgrounds with energy peaked at observed frequencies in the LISA band, between $10^{-1}$ and $10^{-4}$ Hz. The background is detectable above instrument and astrophysical foregrounds if initial metric perturbations are excited to a fractional amplitude of $10^{-3}$ or more, a likely outcome for the Nambu-Goldstone excitations.Comment: Latex, 5 pages, plus one figure, final version to appear in Phys. Rev. Let

Detecting the Earliest Galaxies Through Two New Sources of 21cm Fluctuations

The first galaxies that formed at a redshift ~20-30 emitted continuum photons with energies between the Lyman-alpha and Lyman limit wavelengths of hydrogen, to which the neutral universe was transparent except at the Lyman-series resonances. As these photons redshifted or scattered into the Lyman-alpha resonance they coupled the spin temperature of the 21cm transition of hydrogen to the gas temperature, allowing it to deviate from the microwave background temperature. We show that the fluctuations in the radiation emitted by the first galaxies produced strong fluctuations in the 21cm flux before the Lyman-alpha coupling became saturated. The fluctuations were caused by biased inhomogeneities in the density of galaxies, along with Poisson fluctuations in the number of galaxies. Observing the power-spectra of these two sources would probe the number density of the earliest galaxies and the typical mass of their host dark matter halos. The enhanced amplitude of the 21cm fluctuations from the era of Lyman-alpha coupling improves considerably the practical prospects for their detection.Comment: 11 pages, 7 figures, ApJ, published. Normalization fixed in top panels of Figures 4-