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)

Kerr-de Sitter Universe

It is now widely accepted that the universe as we understand it is accelerating in expansion and fits the de Sitter model rather well. As such, a realistic assumption of black holes must place them on a de Sitter background and not Minkowski as is typically done in General Relativity. The most astrophysically relevant black hole is the uncharged, rotating Kerr solution, a member of the more general Kerr-Newman metrics. A generalization of the rotating Kerr black hole to a solution of the Einstein's equation with a cosmological constant $\Lambda$ was discovered by Carter \cite{DWDW}. It is typically referred to as the Kerr-de Sitter spacetime. Here, we discuss the horizon structure of this spacetime and its dependence on $\Lambda$. We recall that in a \La>0 universe, the term `extremal black hole' refers to a black hole with angular momentum $J > M^2$. We obtain explicit numerical results for the black hole's maximal spin value and get a distribution of admissible Kerr holes in the ($\Lambda$, spin) parameter space. We look at the conformal structure of the extended spacetime and the embedding of the 3-geometry of the spatial hypersurfaces. In analogy with Reissner-Nordstr\"{o}m -de Sitter spacetime, in particular by considering the Kerr-de Sitter causal structure as a distortion of the Reissner-Nordstr\"{o}m-de Sitter one, we show that spatial sections of the extended spacetime are 3-spheres containing 2-dimensional topologically spherical sections of the horizons of Kerr holes at the poles. Depending on how a $t=$ constant 3-space is defined these holes may be seen as black or white holes (four possible combinations).Comment: 20 pages, 9 figure

Light Propagation in Inhomogeneous Universes. III. Distributions of Image Separations

Using an analytical model, we compute the distribution of image separations resulting from gravitational lensing of distant sources, for 7 COBE-normalized CDM models with various combinations of Omega_0 and lambda_0. Our model assumes that multiple imaging results from strong lensing by individual galaxies. We model galaxies as nonsingular isothermal spheres, and take into account the finite angular size of the sources. Our model neglects the contribution of the background matter distribution, and assumes that lensing is entirely caused by galaxies. To test the validity of this assumption, we performed a series of ray-tracing experiments to study the effect of the background matter on the distribution of image separations. The analytical model predicts that the distributions of image separations are virtually indistinguishable for flat, cosmological constant models with different values of Omega_0. For models with no cosmological constant, the distributions of image separations do depend upon Omega_0, but this dependence is weak. We conclude that while the number of multiple-imaged sources can put strong constraints on the cosmological parameters, the distribution of image separations does not constrain the cosmological models in any significant way, and mostly provides constraints on the structure of the galaxies responsible for lensing.Comment: One Plain TeX file, with 12 postscript figures. Accepted for publication in The Astrophysical Journa

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