508 research outputs found
Evolution of Cosmological Perturbations in the Long Wavelength Limit
The relation between the long wavelength limit of solutions to the
cosmological perturbation equations and the perturbations of solutions to the
exactly homogeneous background equations is investigated for scalar
perturbations on spatially flat cosmological models. It is shown that a
homogeneous perturbation coincides with the long wavelength limit of some
inhomogeneous perturbation only when the former satisfies an additional
condition corresponding to the momentum constraint if the matter consists only
of scalar fields. In contrast, no such constraint appears if the fundamental
variables describing the matter contain a vector field as in the case of a
fluid. Further, as a byproduct of this general analysis, it is shown that there
exist two universal exact solutions to the perturbation equations in the long
wavelength limit, which are expressed only in terms of the background
quantities. They represent adiabatic growing and decaying modes, and correspond
to the well-known exact solutions for perfect fluid systems and scalar field
systems.Comment: 16 pages, no figure, submitted to PR
Evolution of Cosmological Perturbations in the Universe dominated by Multiple Scalar Fields
By efforts of several authors, it is recently established that the dynamical
behavior of the cosmological perturbation on superhorizon scales is well
approximated in terms of that in the long wavelength limit, and the latter can
be constructed from the evolution of corresponding exactly homogeneous
universe. Using these facts, we investigate the evolution of the cosmological
perturbation on superhorizon scales in the universe dominated by oscillating
multiple scalar fields which are generally interacting with each other, and the
ratio of whose masses is incommensurable. Since the scalar fields oscillate
rapidly around the local minimum of the potential, we use the action angle
variables. We found that this problem can be formulated as the canonical
perturbation theory in which the perturbed part appearing as the result of the
expansion of the universe and the interaction of the scalar fields is bounded
by the negative power ot time. We show that by constructing the canonical
transformations properly, the transformed hamiltonian becomes simple enough to
be solved. As the result of the invetigation using the long wavelength limit
and the canonical perturbation theory, under the sufficiently general
conditions, we prove that for the adiabatic growing mode the Bardeen parameter
stays constant and that for all the other modes the Bardeen parameter decays.
From the viewpoint of the ergodic theory, it is discussed that as for the
Bardeen parameter, the sigularities appear probabilistically. This analysis
serves the understanding of the evolution of the cosmological perturbations on
superhorizon scales during reheating.Comment: 31 Pages; Latex, No figure
Cosmological Perturbations with Multiple Fluids and Fields
We consider the evolution of perturbed cosmological spacetime with multiple
fluids and fields in Einstein gravity. Equations are presented in gauge-ready
forms, and are presented in various forms using the curvature (\Phi or
\phi_\chi) and isocurvature (S_{(ij)} or \delta \phi_{(ij)}) perturbation
variables in the general background with K and \Lambda. We clarify the
conditions for conserved curvature and isocurvature perturbations in the
large-scale limit. Evolutions of curvature perturbations in many different
gauge conditions are analysed extensively. In the multi-field system we present
a general solution to the linear order in slow-roll parameters.Comment: 19 pages, 6 figures, revised thoroughly; published version in Class.
Quant. Gra
Evolution of Second-Order Cosmological Perturbations and Non-Gaussianity
We present a second-order gauge-invariant formalism to study the evolution of
curvature perturbations in a Friedmann-Robertson-Walker universe filled by
multiple interacting fluids. We apply such a general formalism to describe the
evolution of the second-order curvature perturbations in the standard
one-single field inflation, in the curvaton and in the inhomogeneous reheating
scenarios for the generation of the cosmological perturbations. Moreover, we
provide the exact expression for the second-order temperature anisotropies on
large scales, including second-order gravitational effects and extend the
well-known formula for the Sachs-Wolfe effect at linear order. Our findings
clarify what is the exact non-linearity parameter f_NL entering in the
determination of higher-order statistics such as the bispectrum of Cosmic
Microwave Background temperature anisotropies. Finally, we compute the level of
non-Gaussianity in each scenario for the creation of cosmological
perturbations.Comment: 14 pages, LaTeX file. Further comments adde
Quantized gravitational waves in the Milne universe
The quantization of gravitational waves in the Milne universe is discussed.
The relation between positive frequency functions of the gravitational waves in
the Milne universe and those in the Minkowski universe is clarified.
Implications to the one-bubble open inflation scenario are also discussed.Comment: 26 pages, 1 figure, revtex. submitted to Phys. Rev. D1
Metric perturbations at reheating: the use of spherical symmetry
We consider decay of the inflaton with a quartic potential coupled to other
fields, including gravity, but restricted to spherical symmetry. We describe
analytically an early, quasilinear regime, during which inflaton fluctuations
and the metric functions are driven by nonlinear effects of the decay products.
We present a detailed study of the leading nonlinear effects in this regime.
Results of the quasilinear approximation, in its domain of applicability, are
found to be consistent with those of fully nonlinear lattice studies. We
discuss how these results may be promoted to the full three dimensions.Comment: 18 pages, revtex, 2 figure
Self Excitation of the Tunneling Scalar Field in False Vacuum Decay
A method to determine the quantum state of a scalar field after
-symmetric bubble nucleation has been developed recently. The method has
an advantage that it concisely gives us a clear picture of the resultant
quantum state. In particular, one may interpret the excitations as a particle
creation phenomenon just as in the case of particle creation in curved
spacetime. As an application, we investigate in detail the spectrum of quantum
excitations of the tunneling field when it undergoes false vacuum decay. We
consider a tunneling potential which is piece-wise quadratic, hence is simple
enough to allow us an analytical treatment. We find a strong dependence of the
excitation spectrum upon the shape of the potential on the true vacuum side. We
then discuss features of the excitation spectrum common to general tunneling
potentials not restricted to our simple model.Comment: 24 pages, uuencoded compressed postscript fil
Quantum fluctuations and CMB anisotropies in one-bubble open inflation models
We first develop a method to calculate a complete set of mode functions which
describe the quantum fluctuations generated in one-bubble open inflation
models. We consider two classes of models. One is a single scalar field model
proposed by Bucher, Goldhaber and Turok and by us as an example of the open
inflation scinario, and the other is a two-field model such as the
``supernatural'' inflation proposed by Linde and Mezhlumian. In both cases we
assume the difference in the vacuum energy density between inside and outside
the bubble is negligible. There are two kinds of mode functions. One kind has
usual continuous spectrum and the other has discrete spectrum with
characteristic wavelengths exceeding the spatial curvature scale. The latter
can be further devided into two classes in terms of its origin. One is called
the de Sitter super-curvature mode, which arises due to the global spacetime
structure of de Sitter space, and the other is due to fluctuations of the
bubble wall. We calculate the spectrum of quantum fluctuations in these models
and evaluate the resulting large angular scale CMB anisotropies. We find there
are ranges of model parameters that are consistent with observed CMB
anisotropies.Comment: 22 pages revtex file, 12 postscript figures, tarred, gzippe
Cosmological perturbations from varying masses and couplings
We study the evolution of perturbations during the domination and decay of a
massive particle species whose mass and decay rate are allowed to depend on the
expectation value of a light scalar field. We specialize in the case where the
light field is slow-rolling, showing that during a phase of inhomogeneous
mass-domination and decay the isocurvature perturbation of the light field is
converted into a curvature perturbation with an efficiency which is nine times
larger than when the mass is fixed. We derive a condition on the annihilation
cross section and on the decay rate for the domination of the massive particles
and we show that standard model particles cannot dominate the universe before
nucleosynthesis. We also compare this mechanism with the curvaton model.
Finally, observational signatures are discussed. A cold dark matter
isocurvature mode can be generated if the dark matter is produced out of
equilibrium by both the inflaton and the massive particle species decay.
Non-Gaussianities are present: they are chi-square deviations. However, they
might be too small to be observable.Comment: 21 pages, 4 figures, published versio
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