The pregalactic cosmic gravitational wave background

An outline is given that estimates the expected gravitational wave background, based on plausible pregalactic sources. Some cosmologically significant limits can be put on incoherent gravitational wave background arising from pregalactic cosmic evolution. The spectral region of cosmically generated and cosmically limited radiation is, at long periods, P greater than 1 year, in contrast to more recent cosmological sources, which have P approx. 10 to 10(exp -3)

Light Propagation in inhomogeneous Universes

Using a multi-plane lensing method that we have developed, we follow the evolution of light beams as they propagate through inhomogeneous universes. We use a P3M code to simulate the formation and evolution of large-scale structure. The resolution of the simulations is increased to sub-Megaparsec scales by using a Monte Carlo method to locate galaxies inside the computational volume according to the underlying particle distribution. The galaxies are approximated by isothermal spheres, with each morphological type having its own distribution of masses and core radii. The morphological types are chosen in order to reproduce the observed morphology-density relation. This algorithm has an effective resolution of 9 orders of magnitudes in length, from the size of superclusters down to the core radii of the smallest galaxies. We consider cold dark matter models normalized to COBE, and perform a large parameter survey by varying the cosmological parameters Omega_0, lambda_0, H_0, and n (the tilt of the primordial power spectrum). The values of n are chosen by imposing particular values or sigma_8, the rms mass fluctuation at a scale of 8/h Mpc. We use the power spectrum given by Bunn & White. This is the largest parameter survey ever done is this field.Comment: 3 pages, gzip'ed tar file, including TeX source (not Latex). To be published in a periodical of the Yukawa Institute for Theoretical Physics (1998

Hyperbolicity and Constrained Evolution in Linearized Gravity

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them ({\it unconstrained} evolution). Since computational solution of differential equations introduces almost inevitable errors, it is clearly "more correct" to introduce a scheme which actively maintains the constraints by solution ({\it constrained} evolution). This has shown promise in computational settings, but the analysis of the resulting mixed elliptic hyperbolic method has not been completely carried out. We present such an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves. We begin with a study of the hyperbolicity of the unconstrained Einstein equations. (Because the study of hyperbolicity deals only with the highest derivative order in the equations, linearization loses no essential details.) We then give explicit analytical construction of the effect of initial data setting and constrained evolution for linearized gravitational waves. While this is clearly a toy model with regard to constrained evolution, certain interesting features are found which have relevance to the full nonlinear Einstein equations.Comment: 18 page

Intercommutation of Semilocal Strings and Skyrmions

We study the intercommuting of semilocal strings and Skyrmions, for a wide range of internal parameters, velocities and intersection angles by numerically evolving the equations of motion. We find that the collisions of strings and strings, strings and Skyrmions, and Skyrmions and Skyrmions, all lead to intercommuting for a wide range of parameters. Even the collisions of unstable Skyrmions and strings leads to intercommuting, demonstrating that the phenomenon of intercommuting is very robust, extending to dissimilar field configurations that are not stationary solutions. Even more remarkably, at least for the semilocal U(2) formulation considered here, all intercommutations trigger a reversion to U(1) Nielsen-Olesen strings.Comment: 4 pages, 4 figures. Fixed typos, added reference

Super-Extremal Spinning Black Holes via Accretion

A Kerr black hole with mass $M$ and angular momentum $J$ satisfies the extremality inequality $|J| \le M^2$. In the presence of matter and/or gravitational radiation, this bound needs to be reformulated in terms of local measurements of the mass and the angular momentum directly associated with the black hole. The isolated and dynamical horizon framework provides such quasi-local characterization of black hole mass and angular momentum. With this framework, it is possible in axisymmetry to reformulate the extremality limit as $|J| \le 2\,M_H^2$, with $M_H$ the irreducible mass of the black hole computed from its apparent horizon area and $J$ obtained using approximate rotational Killing vectors on the apparent horizon. The $|J| \le 2\,M_H^2$ condition is also equivalent to requiring a non-negative black hole surface gravity. We present numerical experiments of an accreting black hole that temporarily violates this extremality inequality. The initial configuration consists of a single, rotating black hole surrounded by a thick, shell cloud of negative energy density. For these numerical experiments, we introduce a new matter-without-matter evolution method.Comment: 11 pages, 10 figure

Big Bang nucleosynthesis and the Quark-Hadron transition

An examination and brief review is made of the effects of quark-hadron transistion induced fluctuations on Big Bang nucleosynthesis. It is shown that cosmologically critical densities in baryons are difficult to reconcile with observation, but the traditional baryon density constraints from homogeneous calculations might be loosened by as much as 50 percent, to 0.3 of critical density, and the limit on the number of neutrino flavors remains about N(sub nu) is less than or approximately 4. To achieve baryon densities of greater than or approximately 0.3 of critical density would require initial density contrasts R is much greater the 10(exp 3), whereas the simplest models for the transition seem to restrict R to less than of approximately 10(exp 2)

Measuring emission coordinates in a pulsar-based relativistic positioning system

A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed repetition period in its rest frame.) The positioning system uses the fact that an event in spacetime can be fully described by emission coordinates: the proper emission time of each pulse measured at the event. The proper emission time of each pulse from four different pulsars---interpolated as necessary---provides the four spacetime coordinates of the reception event in the emission coordinate system. If more than four pulsars are available, the redundancy can improve the accuracy of the determination and/or resolve degeneracies resulting from special geometrical arrangements of the sources and the event. We introduce a robust numerical approach to measure the emission coordinates of an event in any arbitrary spacetime geometry. Our approach uses a continuous solution of the eikonal equation describing the backward null cone from the event. The pulsar proper time at the instant the null cone intersects the pulsar world line is one of the four required coordinates. The process is complete (modulo degeneracies) when four pulsar world lines have been crossed by the light cone. The numerical method is applied in two different examples: measuring emission coordinates of an event in Minkowski spacetime using pulses from four pulsars stationary in the spacetime; and measuring emission coordinates of an event in Schwarzschild spacetime using pulses from four pulsars freely falling toward a static black hole. These numerical simulations are merely exploratory, but with improved resolution and computational resources the method can be applied to more pertinent problems. For instance one could measure the emission coordinates, and therefore the trajectory, of the Earth.Comment: 9 pages, 2 figures, v3: replaced with version accepted by Phys. Rev.