Exact Nonperturbative Unitary Amplitudes for 1->N Transitions

I present an extension to arbitrary N of a previously proposed field theoretic model, in which unitary amplitudes for $1->8$ processes were obtained. The Born amplitude in this extension has the behavior $A(1->N)^{tree}\ =\ g^{N-1}\ N!$ expected in a bosonic field theory. Unitarity is violated when $|A(1->N)|>1$, or when $N>\N_crit\simeq e/g.$ Numerical solutions of the coupled Schr\"odinger equations shows that for weak coupling and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}. The very small size of the coefficient 1/\g2 , indicative of a very weak exponential suppression, is not in accord with standard discussions based on saddle point analysis, which give a coefficient $\sim 1.\$ The weak dependence on $N$ could have experimental implications in theories where the exponential suppression is weak (as in this model). Non-perturbative contributions to few-point correlation functions in this theory would arise at order $K\ \simeq\ \left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}$in an expansion in powers of$\g2.$Comment: 11 pages, 3 figures (not included

Update on tests of the Cen A neutron-emission model of highest energy cosmic rays

We propose that neutron emission from Cen A dominates the cosmic ray sky at the high end of the spectrum. Neutrons that are able to decay generate proton diffusion fronts, whereas those that survive decay produce a spike in the direction of the source. We use recent data reported by the Pierre Auger Collaboration to normalize the injection spectrum and estimate the required luminosity in cosmic rays. We find that such a luminosity, L_{CR} ~ 5 x 10^{40} erg/s, is considerably smaller than the bolometric luminosity of Cen A, L_{bol} ~ 10^{43} erg/s. We compute the incoming current flux density as viewed by an observer on Earth and show that the anisotropy amplitude is in agreement with data at the 1\sigma level. Regardless of the underlying source model, our results indicate that after a decade of data taking the Pierre Auger Observatory will be able to test our proposal.Comment: To be published in PR

Reionization Revisited: Secondary CMB Anisotropies and Polarization

Secondary CMB anisotropies and polarization provide a laboratory to study structure formation in the reionized epoch. We consider the kinetic Sunyaev-Zel'dovich effect from mildly nonlinear large-scale structure and show that it is a natural extension of the perturbative Vishniac effect. If the gas traces the dark matter to overdensities of order 10, as expected from simulations, this effect is at least comparable to the Vishniac effect at arcminute scales. On smaller scales, it may be used to study the thermal history-dependent clustering of the gas. Polarization is generated through Thomson scattering of primordial quadrupole anisotropies, kinetic (second order Doppler) quadrupole anisotropies and intrinsic scattering quadrupole anisotropies. Small scale polarization results from the density and ionization modulation of these sources. These effects generically produce comparable E and B-parity polarization, but of negligible amplitude (0.001-0.01 uK) in adiabatic CDM models. However, the primordial and kinetic quadrupoles are observationally comparable today so that a null detection of B-polarization would set constraints on the evolution and coherence of the velocity field. Conversely, a detection of a cosmological B-polarization even at large angles does not necessarily imply the presence of gravity waves or vorticity. For these calculations, we develop an all-sky generalization of the Limber equation that allows for an arbitrary local angular dependence of the source for both scalar and symmetric trace-free tensor fields on the sky.Comment: 14 pages, 12 figures, minor changes and typo fixes reflect published versio

Lagrangian and Hamiltonian for the Bondi-Sachs metrics

We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the Einstein vacuum equations in a closed form. Following the Dirac approach to constrained systems we investigate the related Hamiltonian formulation.Comment: 8 page

Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing

We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her with the previously found constraints, these form a sufficient number of second class constraints so that the phase space is reduced to one pair of canonically conjugate variables: \Ac_2\and\Sc^2. The formalism is related to both the Bondi-Sachs and the Newman-Penrose methods of studying the gravitational field at null infinity. Asymptotic solutions in the vicinity of null infinity which exclude logarithmic behavior require the connection to fall off like $1/r^3$ after the Minkowski limit. This, of course, gives the previous results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off more slowly leads to logarithmic behavior which leaves null infinity intact, allows for meaningful gravitational radiation, but the peeling theorem does not extend to $\Psi_1$ in the terminology of Newman-Penrose. The conclusions are in agreement with those of Chrusciel, MacCallum, and Singleton. This work was begun as a preliminary study of a reduced phase space for quantization of general relativity.Comment: magnification set; pagination improved; 20 pages, plain te

Weak Gravitational Flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy-galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy-galaxy lensing, examining isothermal sphere and Navarro, Frenk & White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in 2-D projection on the sky, and in 3-D in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence-flexion cross-correlations, and find that the signal is an effective probe of structure on non-linear scales.Comment: 17 pages, including 12 figures, submitted to MNRA

The Goldberg-Sachs theorem in linearized gravity

The Goldberg-Sachs theorem has been very useful in constructing algebraically special exact solutions of Einstein vacuum equation. Most of the physical meaningful vacuum exact solutions are algebraically special. We show that the Goldberg-Sachs theorem is not true in linearized gravity. This is a remarkable result, which gives light on the understanding of the physical meaning of the linearized solutions.Comment: 6 pages, no figures, LaTeX 2