Electromagnetic Propagators in Hyperbolic Robertson-Walker Cosmologies

Green functions (retarded, advanced, Feynman and Dyson propagators) are calculated for the electromagnetic field in Robertson-Walker cosmologies with hyperbolic 3-manifolds as spacelike slices. The starting point is the Proca equation, i.e., the Maxwell field with a finite photon mass for infrared regularization, in a static cosmology with simply connected hyperbolic 3-sections. The time and space components of the resolvent kernel are scalar and vectorial point-pair invariants, respectively, and this symmetry allows for an explicit evaluation in the spectral representation. It is found that the quantum propagators have a logarithmic infrared singularity, which drops out in the zero curvature limit. Retarded and advanced Green functions remain well defined in the limit of zero photon mass, and they admit a simple generalization, by conformal scaling, to expanding 3-spaces. In cosmologies with multiply connected hyperbolic 3-manifolds as spacelike sections, the four enumerated propagators are constructed by means of Poincare series. The spectral decomposition of the Green functions is given in terms of Eisenstein series for a certain class of open hyperbolic 3-spaces, including those with Schottky covering groups corresponding to solid handle-bodies as spacelike slices

Superluminal cascade spectra of TeV c-ray sources

Abstract Astrophysical radiation sources are scrutinized in search of superluminal c-rays. The tachyonic spectral densities generated by ultra-relativistic electrons in uniform motion are fitted to the high-energy spectra of Galactic supernova remnants, such as RX J0852.0À4622 and the pulsar wind nebulae in G0.9+0.1 and MSH 15-52. The superluminal spectral maps of the unidentified TeV c-ray sources HESS J1303À631, TeV J2032+4130 and HESS J1825À137 are inferred from EGRET, HEGRA and HESS data. Tachyonic cascade spectra are quite capable of generating the spectral curvature seen in double-logarithmic plots, as well as the extended spectral plateaus defined by EGRET flux points in the GeV band. The curvature of the TeV spectra is intrinsic, caused by the Boltzmann factor in the source densities. The spectral averaging with thermal and exponentially cut power-law electron densities can be done in closed form, and systematic high-and low-temperature expansions of the superluminal spectral densities are derived. Estimates on the electron/proton populations generating the tachyon flux are obtained from the spectral fits, such as power-law indices, temperature and source counts. The cutoff temperatures of the source densities suggest ultra-high-energy protons in MSH 15-52, HESS J1825À137 and TeV J2032+4130

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms

TACHYONS IN ROBERTSON–WALKER COSMOLOGY

Superluminal signal transfer is studied in the context of a preferred cosmic frame of reference provided by the galactic background. The receding galaxies constitute a frame of absolute rest, in which the energy of tachyons (faster-than-light particles) is unambiguously defined as a positive quantity. The causality violation which arises in relativistic tachyonic theories is avoided. We define interactions of particles and tachyons in terms of elastic head-on collisions and energy-momentum conservation. To compare the theory developed with existing relativistic theories, tachyons are studied at first in a Minkowski universe, and the causality of a superluminal communication process is analyzed. Then we discuss the dynamics of tachyons in a Robertson-Walker universe with linear expansion factor and negatively curved three-space. We point out the consequences that the space expansion has on tachyons, like a finite life-time in the frame of absolute rest, and multiple images in the rest frames of moving observers

Electromagnetic Radiation in Multiply Connected Robertson-Walker Cosmologies

Maxwell's equations on a topologically nontrivial cosmological background are studied. The cosmology is locally determined by a Robertson-Walker line element, but the spacelike slices are open hyperbolic manifolds, whose topology and geometry may vary in time. In this context the spectral resolution of Maxwell's equations in terms of horospherical elementary waves generated at infinity of hyperbolic space is given. The wave fronts are orthogonal to bundles of unstable geodesic rays, and the eikonal of geometric optics appears just as the phase of the horospherical waves. This fact is used to attach to the unstable geodesic rays a quantum mechanical momentum. In doing so the quantized energy-momentum tensor of the radiation field is constructed in a geometrically and dynamically transparent way, without appealing to the intricacies of the second quantization. In particular Planck's radiation formula, and the bearing of the multiply connected topology on the fluctuations in the temperature of the background radiation is discussed

Classical and Quantum Dispersion in Robertson-Walker Cosmologies

The instability of world lines in Robertson-Walker universes of negative spatial curvature is investigated. A probabilistic description of this instability, similar to the Liouville equation, is developed, but in a manifestly covariant, non-Hamiltonian form. To achieve this the concept of a horospherical geodesic flow of expanding bundles of parallel world lines is introduced. An invariant measure and a covariant evolution equation for the probability density on which this flow acts is constructed. The orthogonal surfaces to these bundles of trajectories are horospheres, closed surfaces in three-space, touching the boundary at infinity of hyperbolic space, where the flow lines emerge. These horospheres are just the wave fronts of spherical waves, which constitute a complete set of eigenfunctions of the Klein-Gordon equation. This fact suggests that the evolution of the quantum mechanical density with the classical one be compared, and asymptotic identity in the asymptotically flat region is found. This leads, furthermore, to the study of the time behavior of the dispersion of the energy and the coordinates and the energy-time uncertainty relation, and identity in the late stage of the cosmic evolution is again found. In an example it is finally demonstrated that this identity can persist in the early phase of the expansion with a rapidly varying scale factor, provided the fields are conformally coupled to the curvature

High-index asymptotics of spherical Bessel products averaged with modulated Gaussian power laws

Abstract. Bessel integrals of type l (k)k 2 dk are investigated, where the kernel g(k) is a modulated Gaussian power-law distribution k μ e −ak 2 −(b+iω)k , and the j (m) l are multiple derivatives of spherical Bessel functions. These integrals define the multipole moments of Gaussian random fields on the unit sphere, arising in multipole fits of temperature and polarization power spectra of the cosmic microwave background. Two methods allowing efficient numerical calculation of these integrals are presented, covering Bessel indices l in the currently accessible multipole range 0 ≤ l ≤ 10 4 and beyond. The first method is based on a representation of spherical Bessel functions by Lommel polynomials. Gaussian power-law averages can then be calculated in closed form as finite Hankel series of parabolic cylinder functions, which allow highprecision evaluation. The second method is asymptotic, covering the high-l regime, and is applicable to general distribution functions g(k) in the integrand; it is based on the uniform Nicholson approximation of the Bessel derivatives in conjunction with an integral representation of squared Airy functions. A numerical comparison of these two methods is performed, employing Gaussian power laws and Kummer distributions to average the Bessel products

Subexponential decay in Fermi-LAT pulsar spectra: The case for tachyonic Cherenkov radiation

Tachyonic Cherenkov fits are performed to the Fermi-LAT γ-ray spectra of the Vela pulsar, PSR J1709 − 4429 and Geminga. The high-energy spectral tails of these pulsars exhibit pronounced subexponential Weibull decay, which can be modeled in a permeable spacetime by a frequency-dependent tachyon mass. The scaling exponent of the tachyon mass defines the Weibull shape parameter of the energy flux, and it also determines whether the radiation is sub- or superluminal. The negative mass-square in the tachyonic Maxwell-Proca equations gives rise to a longitudinal flux component. The radiation is generated by an ultra-relativistic thermal electron plasma via the inertial Cherenkov effect. The transversal and longitudinal γ-ray emission from Geminga is slightly superluminal, whereas γ-rays from the Vela pulsar and PSR J1709 − 4429 are subluminal despite the negative tachyonic mass-square in the dispersion relations

Tachyonic synchrotron radiation from c-ray pulsars

Abstract Superluminal radiation emitted by electrons orbiting in strong magnetic fields is investigated. We show that electrons gyrating in the surface fields of rotation-powered neutron stars can radiate superluminal quanta (tachyons) via the synchrotron mechanism. The tachyonic luminosity of c-ray pulsars is inferred from COMPTEL and EGRET observations, and so is the magnetospheric electron population generating this radiation. In the surface fields, electromagnetic synchrotron radiation in the c-ray band is suppressed by a quantum cutoff, but not so tachyonic c-radiation. This provides an exceptional opportunity to search for tachyon radiation, unspoiled by electromagnetic emission. Estimates of the superluminal power radiated and the tachyonic count rates are obtained for each of the seven established c-ray pulsars, the Crab and Vela pulsars, as well as PSR B1706À44, Geminga, PSR B1055À52, B1951+32, and B1509À58. Detection mechanisms such as tachyonic ionization and Compton scattering are analyzed with regard to superluminal c-rays