247 research outputs found
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
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
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.
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
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
Small Deviations from Gaussianity and The Galaxy Cluster Abundance Evolution
We raise the hypothesis that the density fluctuations field which originates
the growth of large scale structures is a combination of two or more
distributions. By applying the statistical analysis of finite mixture
distributions to a specific combination of Gaussian plus non-Gaussian random
fields, we studied the case where just a small departure from Gaussianity is
allowed. Our results suggest that even a very small level of non-Gaussianity
may introduce significant changes in the cluster abundance evolution rate.Comment: 10 pages with 2 figures, accepted for publication in Ap
On generation of metric perturbations during preheating
We consider the generation of the scalar mode of the metric perturbations
during preheating stage in a two field model with the potential . We discuss two possible
sources of such perturbations: a) due to the coupling between the perturbation
of the matter field and the background part of the matter field
, b) due to non-linear fluctuations in a condensate of
``particles'' of the field . Both types of the metric perturbations are
assumed to be small, and estimated using the linear theory of the metric
perturbations. We estimate analytically the upper limit of the amplitude of the
metric perturbations for all scales in the limit of so-called broad resonance,
and show that the large scale metric perturbations are very small, and taking
them into account does not influence the standard picture of the production of
the metric perturbations in inflationary scenario.Comment: This version is to be published in PRD, new references added and
typos correcte
Inflation, Symmetry, and B-Modes
We examine the role of using symmetry and effective field theory in
inflationary model building. We describe the standard formulation of starting
with an approximate shift symmetry for a scalar field, and then introducing
corrections systematically in order to maintain control over the inflationary
potential. We find that this leads to models in good agreement with recent
data. On the other hand, there are attempts in the literature to deviate from
this paradigm by invoking other symmetries and corrections. In particular: in a
suite of recent papers, several authors have made the claim that standard
Einstein gravity with a cosmological constant and a massless scalar carries
conformal symmetry. They further claim that such a theory carries another
hidden symmetry; a global SO(1,1) symmetry. By deforming around the global
SO(1,1) symmetry, they are able to produce a range of inflationary models with
asymptotically flat potentials, whose flatness is claimed to be protected by
these symmetries. These models tend to give rise to B-modes with small
amplitude. Here we explain that these authors are merely introducing a
redundancy into the description, not an actual conformal symmetry. Furthermore,
we explain that the only real (global) symmetry in these models is not at all
hidden, but is completely manifest when expressed in the Einstein frame; it is
in fact the shift symmetry of a scalar field. When analyzed systematically as
an effective field theory, deformations do not generally produce asymptotically
flat potentials and small B-modes, but other types of potentials with B-modes
of appreciable amplitude. Such simple models typically also produce the
observed red spectral index, Gaussian fluctuations, etc. In short: simple
models of inflation, organized by expanding around a shift symmetry, are in
excellent agreement with recent data.Comment: 9 pages in double column format. V2: Updated to coincide with version
published in Physics Letters
Robertson-Walker fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter
Einstein's equations for a Robertson-Walker fluid source endowed with
rotation Einstein's equations for a Robertson-Walker fluid source endowed with
rotation are presented upto and including quadratic terms in angular velocity
parameter. A family of analytic solutions are obtained for the case in which
the source angular velocity is purely time-dependent. A subclass of solutions
is presented which merge smoothly to homogeneous rotating and non-rotating
central sources. The particular solution for dust endowed with rotation is
presented. In all cases explicit expressions, depending sinusoidally on polar
angle, are given for the density and internal supporting pressure of the
rotating source. In addition to the non-zero axial velocity of the fluid
particles it is shown that there is also a radial component of velocity which
vanishes only at the poles. The velocity four-vector has a zero component
between poles
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