9 research outputs found
Conditions for inflation in an initially inhomogeneous universe
Using a long wavelength iteration scheme to solve Einstein's equations near
the Big-Bang singularity of a universe driven by a massive scalar field, we
find how big initial quasi-isotropic inhomogeneities can be before they can
prevent inflation to set in.Comment: 9 pages, plain Tex, gr-qc/yymmnn
String-Dominated Cosmology
If string theory controls physics at the string scale, the dynamics of the
early universe before the GUT era will be governed by the low-energy string
equations of motion. Studying these equations for FRW spacetimes, we find that
depending on the initial conditions when the stringy era starts, and on the
time when it ends, there are a wide variety of qualitatively distinct types of
evolution. We classify these, and present the general solution to the equations
of motion
The Two--Point Correlation Function and the Size of Voids
Under the assumption of a void-filled Universe we investigate if the
characteristic scale of voids can be determined from existing surveys. We use
the Voronoi tessellation to create mock surveys and study the properties of the
first zero-crossing of the two-point correlation function for various survey
geometries. Our main conclusion is that the available data sets should be able
to discriminate between 5000 \kms and 12000 \kms voids, if one of these scales
actually characterizes the distribution of galaxies.Comment: uuencoded compressed postscript file with 6 figures included.
Accepted for publication in MNRA
A Comment on Junction and Energy Conditions in Thin Shells
This comment contains a suggestion for a slight modification of Israel's
covariant formulation of junction conditions between two spacetimes, placing
both sides on equal footing with normals having uniquely defined orientations.
The signs of mass energy densities in thin shells at the junction depend not
only on the orientations of the normals and it is useful therefore to discuss
the sign separately. Calculations gain in clarity by not choosing the
orientations in advance. Simple examples illustrate our point and complete
previous classifications of spherical thin shells in spherically symmetric
spacetimes relevant to cosmology.Comment: (Tex file + PS file with a figure) Tex errors were correcte
The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine
We study the propagator of a non-relativistic, non-interacting particle in
any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an
external, flat spacetime in which two spatial regions, at time and
at time , are connected by two temporal wormholes, one leading from
the past side of to t the future side of and the other from the
past side of to the future side of . We express the propagator
explicitly in terms of those for ordinary, flat spacetime and for the two
wormholes; and from that expression we show that the propagator satisfies
completeness and unitarity in the initial and final ``chronal regions''
(regions without closed timelike curves) and its propagation from the initial
region to the final region is unitary. However, within the time machine it
satisfies neither completeness nor unitarity. We also give an alternative proof
of initial-region-to-final-region unitarity based on a conserved current and
Gauss's theorem. This proof can be carried over without change to most any
non-relativistic time-machine spacetime; it is the non-relativistic version of
a theorem by Friedman, Papastamatiou and Simon, which says that for a free
scalar field, quantum mechanical unitarity follows from the fact that the
classical evolution preserves the Klein-Gordon inner product
Galerkin Method in the Gravitational Collapse: a Dynamical System Approach
We study the general dynamics of the spherically symmetric gravitational
collapse of a massless scalar field. We apply the Galerkin projection method to
transform a system of partial differential equations into a set of ordinary
differential equations for modal coefficients, after a convenient truncation
procedure, largely applied to problems of turbulence. In the present case, we
have generated a finite dynamical system that reproduces the essential features
of the dynamics of the gravitational collapse, even for a lower order of
truncation. Each initial condition in the space of modal coefficients
corresponds to a well definite spatial distribution of scalar field. Numerical
experiments with the dynamical system show that depending on the strength of
the scalar field packet, the formation of black-holes or the dispersion of the
scalar field leaving behind flat spacetime are the two main outcomes. We also
found numerical evidence that between both asymptotic states, there is a
critical solution represented by a limit cycle in the modal space with period
.Comment: 9 pages, revtex4, 10 ps figures; Phys. Rev. D, in pres