326 research outputs found
Characteristics of Cosmic Time
The nature of cosmic time is illuminated using Hamilton-Jacobi theory for
general relativity. For problems of interest to cosmology, one may solve for
the phase of the wavefunctional by using a line integral in superspace. Each
contour of integration corresponds to a particular choice of time hypersurface,
and each yields the same answer. In this way, one can construct a covariant
formalism where all time hypersurfaces are treated on an equal footing. Using
the method of characteristics, explicit solutions for an inflationary epoch
with several scalar fields are given. The theoretical predictions of double
inflation are compared with recent galaxy data and large angle microwave
background anisotropies.Comment: 20 pages, RevTex using Latex 2.09, Submitted to Physical Review D Two
figures included in fil
Solving the Hamilton-Jacobi Equation for General Relativity
We demonstrate a systematic method for solving the Hamilton-Jacobi equation
for general relativity with the inclusion of matter fields. The generating
functional is expanded in a series of spatial gradients. Each term is
manifestly invariant under reparameterizations of the spatial coordinates
(``gauge-invariant''). At each order we solve the Hamiltonian constraint using
a conformal transformation of the 3-metric as well as a line integral in
superspace. This gives a recursion relation for the generating functional which
then may be solved to arbitrary order simply by functionally differentiating
previous orders. At fourth order in spatial gradients, we demonstrate solutions
for irrotational dust as well as for a scalar field. We explicitly evolve the
3-metric to the same order. This method can be used to derive the Zel'dovich
approximation for general relativity.Comment: 13 pages, RevTeX, DAMTP-R93/2
Coordinate-free Solutions for Cosmological Superspace
Hamilton-Jacobi theory for general relativity provides an elegant covariant
formulation of the gravitational field. A general `coordinate-free' method of
integrating the functional Hamilton-Jacobi equation for gravity and matter is
described. This series approximation method represents a large generalization
of the spatial gradient expansion that had been employed earlier. Additional
solutions may be constructed using a nonlinear superposition principle. This
formalism may be applied to problems in cosmology.Comment: 11 pages, self-unpacking, uuencoded tex file, to be published in
Physical Review D (1997
Initial Hypersurface Formulation: Hamilton-Jacobi Theory for Strongly Coupled Gravitational Systems
Strongly coupled gravitational systems describe Einstein gravity and matter
in the limit that Newton's constant G is assumed to be very large. The
nonlinear evolution of these systems may be solved analytically in the
classical and semiclassical limits by employing a Green function analysis.
Using functional methods in a Hamilton-Jacobi setting, one may compute the
generating functional (`the phase of the wavefunctional') which satisfies both
the energy constraint and the momentum constraint. Previous results are
extended to encompass the imposition of an arbitrary initial hypersurface. A
Lagrange multiplier in the generating functional restricts the initial fields,
and also allows one to formulate the energy constraint on the initial
hypersurface. Classical evolution follows as a result of minimizing the
generating functional with respect to the initial fields. Examples are given
describing Einstein gravity interacting with either a dust field and/or a
scalar field. Green functions are explicitly determined for (1) gravity, dust,
a scalar field and a cosmological constant and (2) gravity and a scalar field
interacting with an exponential potential. This formalism is useful in solving
problems of cosmology and of gravitational collapse.Comment: 30 pages Latex (IOP) file with 2 IOP style files, to be published in
Classical and Quantum Gravity (1998
On the Perturbative Solutions of Bohmian Quantum Gravity
In this paper we have solved the Bohmian equations of quantum gravity,
perturbatively. Solutions up to second order are derived explicitly, but in
principle the method can be used in any order. Some consequences of the
solution are disscused.Comment: 14 Pages, RevTeX. To appear in Phys. Rev.
The Cosmic Microwave Background Bispectrum and Inflation
We derive an expression for the non-Gaussian cosmic-microwave-background
(CMB) statistic defined recently by Ferreira, Magueijo, and G\'orski in
terms of the slow-roll-inflation parameters and . This result
shows that a nonzero value of in COBE would rule out single-field
slow-roll inflation. A sharp change in the slope of the inflaton potential
could increase the predicted value of , but not significantly. This
further suggests that it will be difficult to account for such a detection in
multiple-field models in which density perturbations are produced by quantum
fluctuations in the scalar field driving inflation. An Appendix shows how to
evaluate an integral that is needed in our calculation as well as in more
general calculations of CMB bispectra.Comment: 10 pages, no figure
Lodoxamide as Adjuvant Therapy in Patients with Dry Eye
Dry eye, due to its impaired function of tear film becomes more susceptible to all
kinds of airborne allergens. Due to air pollution this is more marked in urban areas,
and is compounded by the modern way of life. There are various standard topical medications
which alleviate allergic reaction of the eye, but many of them must be administered
with caution and only on short term due to their potentially hazardous side effects.
The purpose of this work is to assess the efficacy of lodoxamide, a new antiallergic medication
for topical use, whose advantage is low or absent risk of adverse side effects, in alleviating
local allergic reactions of the eye in patients with dry eye. Research has shown
that, compared to treatment with eye lubricants alone (artificial tears), treatment with
artificial tears combined with lodoxamide has resulted in more marked decrease in the
signs of inflammation, and to the lesser extent to the reduction of the symptoms as well
The Zel'dovich Approximation and the Relativistic Hamilton-Jacobi Equation
Beginning with a relativistic action principle for the irrotational flow of
collisionless matter, we compute higher order corrections to the Zel'dovich
approximation by deriving a nonlinear Hamilton-Jacobi equation for the velocity
potential. It is shown that the velocity of the field may always be derived
from a potential which however may be a multi-valued function of the space-time
coordinates. In the Newtonian limit, the results are nonlocal because one must
solve the Newton-Poisson equation. By considering the Hamilton-Jacobi equation
for general relativity, we set up gauge-invariant equations which respect
causality. A spatial gradient expansion leads to simple and useful results
which are local --- they require only derivatives of the initial gravitational
potential.Comment: 25 pages, DAMTP R94/6, ALBERTA THY/06-9
Long wavelength iteration of Einstein's equations near a spacetime singularity
We clarify the links between a recently developped long wavelength iteration
scheme of Einstein's equations, the Belinski Khalatnikov Lifchitz (BKL) general
solution near a singularity and the antinewtonian scheme of Tomita's. We
determine the regimes when the long wavelength or antinewtonian scheme is
directly applicable and show how it can otherwise be implemented to yield the
BKL oscillatory approach to a spacetime singularity. When directly applicable
we obtain the generic solution of the scheme at first iteration (third order in
the gradients) for matter a perfect fluid. Specializing to spherical symmetry
for simplicity and to clarify gauge issues, we then show how the metric behaves
near a singularity when gradient effects are taken into account.Comment: 35 pages, revtex, no figure
Hamilton-Jacobi Solutions for Strongly-Coupled Gravity and Matter
A Green's function method is developed for solving strongly-coupled gravity
and matter in the semiclassical limit. In the strong-coupling limit, one
assumes that Newton's constant approaches infinity. As a result, one may
neglect second order spatial gradients, and each spatial point evolves like an
homogeneous universe. After constructing the Green's function solution to the
Hamiltonian constraint, the momentum constraint is solved using functional
methods in conjunction with the superposition principle for Hamilton-Jacobi
theory. Exact and approximate solutions are given for a dust field or a scalar
field interacting with gravity.Comment: 26 pages Latex (IOP) file with 2 IOP style files, to be published in
Classical and Quantum Gravity (1998
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