417 research outputs found
Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices
This paper derives expressions for the growth rates for the random 2 x 2
matrices that result from solutions to the random Hill's equation. The
parameters that appear in Hill's equation include the forcing strength and
oscillation frequency. The development of the solutions to this periodic
differential equation can be described by a discrete map, where the matrix
elements are given by the principal solutions for each cycle. Variations in the
forcing strength and oscillation frequency lead to matrix elements that vary
from cycle to cycle. This paper presents an analysis of the growth rates
including cases where all of the cycles are highly unstable, where some cycles
are near the stability border, and where the map would be stable in the absence
of fluctuations. For all of these regimes, we provide expressions for the
growth rates of the matrices that describe the solutions.Comment: 22 pages, 3 figure
The Future Evolution of White Dwarf Stars Through Baryon Decay and Time Varying Gravitational Constant
Motivated by the possibility that the fundamental ``constants'' of nature
could vary with time, this paper considers the long term evolution of white
dwarf stars under the combined action of proton decay and variations in the
gravitational constant. White dwarfs are thus used as a theoretical laboratory
to study the effects of possible time variations, especially their implications
for the future history of the universe. More specifically, we consider the
gravitational constant to vary according to the parametric relation , where the time scale is the same order as
the proton lifetime. We then study the long term fate and evolution of white
dwarf stars. This treatment begins when proton decay dominates the stellar
luminosity, and ends when the star becomes optically thin to its internal
radiation.Comment: 12 pages, 10 figures, accepted to Astrophysics and Space Scienc
Inflationary cosmology in the central region of String/M-theory moduli space
The "central" region of moduli space of M- and string theories is where the
string coupling is about unity and the volume of compact dimensions is about
the string volume. Here we argue that in this region the non-perturbative
potential which is suggested by membrane instanton effects has the correct
scaling and shape to allow for enough slow-roll inflation, and to produce the
correct amplitude of CMB anisotropies. Thus, the well known theoretical
obstacles for achieving viable slow-roll inflation in the framework of
perturbative string theory are overcome. Limited knowledge of some generic
properties of the induced potential is sufficient to determine the simplest
type of consistent inflationary model and its predictions about the spectrum of
cosmic microwave background anisotropies: a red spectrum of scalar
perturbations, and negligible amount of tensor perturbations.Comment: 9 pages, 1 figur
The relativistic precession of the orbits
The relativistic precession can be quickly inferred from the nonlinear polar
orbit equation without actually solving it.Comment: Accepted for publication in Astrophysics & Space Scienc
Eccentricities of Planets in Binary Systems
The most puzzling property of the extrasolar planets discovered by recent
radial velocity surveys is their high orbital eccentricities, which are very
difficult to explain within our current theoretical paradigm for planet
formation. Current data reveal that at least 25% of these planets, including
some with particularly high eccentricities, are orbiting a component of a
binary star system. The presence of a distant companion can cause significant
secular perturbations in the orbit of a planet. At high relative inclinations,
large-amplitude, periodic eccentricity perturbations can occur. These are known
as "Kozai cycles" and their amplitude is purely dependent on the relative
orbital inclination. Assuming that every planet host star also has a (possibly
unseen, e.g., substellar) distant companion, with reasonable distributions of
orbital parameters and masses, we determine the resulting eccentricity
distribution of planets and compare it to observations? We find that
perturbations from a binary companion always appear to produce an excess of
planets with both very high (e>0.6) and very low (e<0.1) eccentricities. The
paucity of near-circular orbits in the observed sample implies that at least
one additional mechanism must be increasing eccentricities. On the other hand,
the overproduction of very high eccentricities observed in our models could be
combined with plausible circularization mechanisms (e.g., friction from
residual gas) to create more planets with intermediate eccentricities
(e=0.1-0.6).Comment: 8 pages, to appear in "Close Binaries in the 21st Century: New
Opportunities and Challenges", ed. A. Gimenez et al. (Springer
Natural Inflation From Fermion Loops
``Natural'' inflationary theories are a class of models in which inflation is
driven by a pseudo-Nambu-Goldstone boson. In this paper we consider two models,
one old and one new, in which the potential for inflation is generated by loop
effects from a fermion sector which explicitly breaks a global symmetry.
In both models, we retrieve the ``standard'' natural inflation potential,
, as a limiting case of the exact one-loop potential, but we
carry out a general analysis of the models including the limiting case.
Constraints from the COBE DMR observation and from theoretical consistency are
used to limit the parameters of the models, and successful inflation occurs
without the necessity of fine-tuning the parameters.Comment: (Revised) 15 pages, LaTeX (revTeX), 8 figures in uuencoded PostScript
format. Version accepted for publication in Phys. Rev. D 15. Corrected
definition of power spectrum and added three reference
The Long-Term Future of Extragalactic Astronomy
If the current energy density of the universe is indeed dominated by a
cosmological constant, then high-redshift sources will remain visible to us
only until they reach some finite age in their rest-frame. The radiation
emitted beyond that age will never reach us due to the acceleration of the
cosmic expansion rate, and so we will never know what these sources look like
as they become older. As a source image freezes on a particular time frame
along its evolution, its luminosity distance and redshift continue to increase
exponentially with observation time. The higher the current redshift of a
source is, the younger it will appear as it fades out of sight. For the popular
set of cosmological parameters, I show that a source at a redshift z=5-10 will
only be visible up to an age of 4-6 billion years. Arguments relating the
properties of high-redshift sources to present-day counterparts will remain
indirect even if we continue to monitor these sources for an infinite amount of
time. These sources will not be visible to us when they reach the current age
of the universe.Comment: Phys. Rev. D, in press (2001
The Imprint of Gravitational Waves on the Cosmic Microwave Background
Long-wavelength gravitational waves can induce significant temperature
anisotropy in the cosmic microwave background. Distinguishing this from
anisotropy induced by energy density fluctuations is critical for testing
inflationary cosmology and theories of large-scale structure formation. We
describe full radiative transport calculations of the two contributions and
show that they differ dramatically at angular scales below a few degrees. We
show how anisotropy experiments probing large- and small-angular scales can
combine to distinguish the imprint due to gravitational waves.Comment: 11 pages, Penn Preprint-UPR-
Duality Invariance of Cosmological Perturbation Spectra
I show that cosmological perturbation spectra produced from quantum
fluctuations in massless or self-interacting scalar fields during an
inflationary era remain invariant under a two parameter family of
transformations of the homogeneous background fields. This relates slow-roll
inflation models to solutions which may be far from the usual slow-roll limit.
For example, a scale-invariant spectrum of perturbations in a minimally
coupled, massless field can be produced by an exponential expansion with
, or by a collapsing universe with .Comment: 5 pages, Latex with Revtex. Hamiltonian formulation added and
discussion expanded. Version to appear in Phys Rev
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