208 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
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
Evolution of Non-linear Fluctuations in Preheating after Inflation
We investigate the evolution of the non-linear long wavelength fluctuations
during preheating after inflation. By using the separate universe approach, the
temporal evolution of the power spectrum of the scalar fields and the curvature
variable is obtained numerically. We found that the amplitude of the large
scale fluctuations is suppressed after non-linear evolution during preheating.Comment: To be published in Class. Quantum Gra
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
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
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
Wilkinson Microwave Anisotropy Probe 7-yr constraints on fNL with a fast wavelet estimator
A new method to constrain the local non-linear coupling parameter fNL based
on a fast wavelet decomposition is presented. Using a multiresolution wavelet
adapted to the HEALPix pixelization, we have developed a method that is 10^2
times faster than previous estimators based on isotropic wavelets and 10^3
faster than the KSW bispectrum estimator, at the resolution of the Wilkinson
Microwave Anisotropy Probe (WMAP) data. The method has been applied to the WMAP
7-yr V+W combined map, imposing constraints on fNL of -69 < fNL < 65 at the 95
per cent CL. This result has been obtained after correcting for the
contribution of the residual point sources which has been estimated to be fNL =
7 +/- 6. In addition, a Gaussianity analysis of the data has been carried out
using the third order moments of the wavelet coefficients, finding consistency
with Gaussianity. Although the constrainsts imposed on fNL are less stringent
than those found with optimal estimators, we believe that a very fast method,
as the one proposed in this work, can be very useful, especially bearing in
mind the large amount of data that will be provided by future experiments, such
as the Planck satellite. Moreover, the localisation of wavelets allows one to
carry out analyses on different regions of the sky. As an application, we have
separately analysed the two hemispheres defined by the dipolar modulation
proposed by Hoftuft et al. (2009). We do not find any significant asymmetry
regarding the estimated value of fNL in those hemispheres.Comment: 8 pages, 5 figures. Submitted and Accepted for publication in MNRA
The Andante Regime of Scalar Field Dynamics
The andante regime of scalar field dynamics in the chaotic inflationary
Universe is defined as the epoch when the field is rolling moderately slowly
down its interaction potential, but at such a rate that first-order corrections
to the slow-roll approximation become important. These conditions should apply
towards the end of inflation as the field approaches the global minimum of the
potential. Solutions to the Einstein-scalar field equations for the class of
power law potentials are found in this regime in
terms of the inverse error function.Comment: 11 pages of plain Latex, FNAL-Pub-94/226-
Inflation with Non-minimal Gravitational Couplings and Supergravity
We explore in the supergravity context the possibility that a Higgs scalar
may drive inflation via a non-minimal coupling to gravity characterised by a
large dimensionless coupling constant. We find that this scenario is not
compatible with the MSSM, but that adding a singlet field (NMSSM, or a variant
thereof) can very naturally give rise to slow-roll inflation. The inflaton is
necessarily contained in the doublet Higgs sector and occurs in the D-flat
direction of the two Higgs doublets.Comment: 13 pages, 1 figur
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