Behavior of Friedmann-Robertson-Walker Cosmological Models in Scalar-Tensor Gravity

We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory, where a scalar field is coupled to gravity. Matter is modelled by a $\gamma$-law perfect fluid, including false-vacuum energy as a special case. Through a change of variables, we reduce the field equations from fourth order to second order, and they become equivalent to a two-dimensional dynamical system. We then analyze the entire solution space of this dynamical system, and find that many qualitative features of these cosmologies can be gleaned, including standard non-inflationary or extended inflationary expansion, but also including bifurcations of stable or unstable expansion or contraction, noninflationary vacuum-energy dominated models, and several varieties of ``coasting," ``bouncing," ``hesitating," and ``vacillating" universes. It is shown that inflationary dogma, which states that a universe with curvature and dominated by inflationary matter will always approach a corresponding flat-space solution at late times, does not hold in general for the scalar-tensor theory, but rather that the occurence of inflation depends upon the initial energy of the scalar field relative to the expansion rate. In the case of flat space ($k=0$), the dynamical system formalism generates some previously known exact power-law solutions.Comment: Slight stylistic changes and some references added. This version to be published in {\sl Annals of Physics

Puncture of gravitating domain walls

We investigate the semi-classical instability of vacuum domain walls to processes where the domain walls decay by the formation of closed string loop boundaries on their worldvolumes. Intuitively, a wall which is initially spherical may `pop', so that a hole corresponding to a string boundary component on the wall, may form. We find instantons, and calculate the rates, for such processes. We show that after puncture, the hole grows exponentially at the same rate that the wall expands. It follows that the wall is never completely thermalized by a single expanding hole; at arbitrarily late times there is still a large, thin shell of matter which may drive an exponential expansion of the universe. We also study the situation where the wall is subjected to multiple punctures. We find that in order to completely annihilate the wall by this process, at least four string loops must be nucleated. We argue that this process may be relevant in certain brane-world scenarios, where the universe itself is a domain wall.Comment: 13 pages REVTeX, 3 .ps figures, added some references - version to appear in Physics Letters

Black Hole Boundary Conditions and Coordinate Conditions

This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further condition is necessary for the system to be well posed; the ``prescribed curvature conditions" are therefore proposed to complete the coordinate conditions at the black hole. These conditions lead to a system of two 2D elliptic differential equations on the inner boundary surface, which coexist nicely to the 3D equation for maximal slicing (or related slicing conditions). The overall 2D/3D system is argued to be well posed and globally well behaved. The importance of ``boundary conditions without boundary values" is emphasized. This paper is the first of a series. This revised version makes minor additions and corrections to the previous version.Comment: 13 pages LaTeX, revtex. No figure

S-Duality at the Black Hole Threshold in Gravitational Collapse

We study gravitational collapse of the axion/dilaton field in classical low energy string theory, at the threshold for black hole formation. A new critical solution is derived that is spherically symmetric and continuously self-similar. The universal scaling and echoing behavior discovered by Choptuik in gravitational collapse appear in a somewhat different form. In particular, echoing takes the form of SL(2,R) rotations (cf. S-duality). The collapse leaves behind an outgoing pulse of axion/dilaton radiation, with nearly but not exactly flat spacetime within it.Comment: 8 pages of LaTeX, uses style "revtex"; 1 figure, available in archive, or at ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-15.ep

Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field

We examine the gravitational collapse of a non-linear sigma model in spherical symmetry. There exists a family of continuously self-similar solutions parameterized by the coupling constant of the theory. These solutions are calculated together with the critical exponents for black hole formation of these collapse models. We also find that the sequence of solutions exhibits a Hopf-type bifurcation as the continuously self-similar solutions become unstable to perturbations away from self-similarity.Comment: 18 pages; one figure, uuencoded postscript; figure is also available at http://www.physics.ucsb.edu/people/eric_hirschman