20,250 research outputs found
Oscillations in the Primordial Bispectrum: Mode Expansion
We consider the presence of oscillations in the primordial bispectrum,
inspired by three different cosmological models; features in the primordial
potential, resonant type non-Gaussianities and deviation from the standard
Bunch Davies vacuum. In order to put constraints on their bispectra, a logical
first step is to put these into factorized form which can be achieved via the
recently proposed method of polynomial basis expansion on the tetrahedral
domain. We investigate the viability of such an expansion for the oscillatory
bispectra and find that one needs an increasing number of orthonormal mode
functions to achieve significant correlation between the expansion and the
original spectrum as a function of their frequency. To reduce the number of
modes required, we propose a basis consisting of Fourier functions
orthonormalized on the tetrahedral domain. We show that the use of Fourier mode
functions instead of polynomial mode functions can lead to the necessary
factorizability with the use of only 1/5 of the total number of modes required
to reconstruct the bispectra with polynomial mode functions. Moreover, from an
observational perspective, the expansion has unique signatures depending on the
orientation of the oscillation due to a resonance effect between the mode
functions and the original spectrum. This effect opens the possibility to
extract informa- tion about both the frequency of the bispectrum as well as its
shape while considering only a limited number of modes. The resonance effect is
independent of the phase of the reconstructed bispectrum suggesting Fourier
mode extraction could be an efficient way to detect oscillatory bispectra in
the data.Comment: 17 pages, 12 figures. Matches published versio
Classical {\it vs.}\ Landau-Ginzburg Geometry of Compactification
We consider superstring compactifications where both the classical
description, in terms of a Calabi-Yau manifold, and also the quantum theory is
known in terms of a Landau-Ginzburg orbifold model. In particular, we study
(smooth) Calabi-Yau examples in which there are obstructions to parametrizing
all of the complex structure cohomology by polynomial deformations thus
requiring the analysis based on exact and spectral sequences. General arguments
ensure that the Landau-Ginzburg chiral ring copes with such a situation by
having a nontrivial contribution from twisted sectors. Beyond the expected
final agreement between the mathematical and physical approaches, we find a
direct correspondence between the analysis of each, thus giving a more complete
mathematical understanding of twisted sectors. Furthermore, this approach shows
that physical reasoning based upon spectral flow arguments for determining the
spectrum of Landau-Ginzburg orbifold models finds direct mathematical
justification in Koszul complex calculations and also that careful point- field
analysis continues to recover suprisingly much of the stringy features.Comment: 14
Three-Body Recombination in One Dimension
We study the three-body problem in one dimension for both zero and finite
range interactions using the adiabatic hyperspherical approach. Particular
emphasis is placed on the threshold laws for recombination, which are derived
for all combinations of the parity and exchange symmetries. For bosons, we
provide a numerical demonstration of several universal features that appear in
the three-body system, and discuss how certain universal features in three
dimensions are different in one dimension. We show that the probability for
inelastic processes vanishes as the range of the pair-wise interaction is taken
to zero and demonstrate numerically that the recombination threshold law
manifests itself for large scattering length.Comment: 15 pages 7 figures Submitted to Physical Review
Extracting New Physics from the CMB
We review how initial state effects generically yield an oscillatory
component in the primordial power spectrum of inflationary density
perturbations. These oscillatory corrections parametrize unknown new physics at
a scale and are potentially observable if the ratio is
sufficiently large. We clarify to what extent present and future CMB data
analysis can distinguish between the different proposals for initial state
corrections.Comment: Invited talk by B. Greene at the XXII Texas Symposium on Relativistic
Astrophysics, Stanford University, 13-17 December 2004, (TSRA04-0001), 8
pages, LaTeX, some references added, added paragraph at the end of section 2
and an extra note added after the conclusions regarding modifications to the
large k power spectra deduced from galaxy survey
Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries
At special loci in their moduli spaces, Calabi-Yau manifolds are endowed with
discrete symmetries. Over the years, such spaces have been intensely studied
and have found a variety of important applications. As string compactifications
they are phenomenologically favored, and considerably simplify many important
calculations. Mathematically, they provided the framework for the first
construction of mirror manifolds, and the resulting rational curve counts.
Thus, it is of significant interest to investigate such manifolds further. In
this paper, we consider several unexplored loci within familiar families of
Calabi-Yau hypersurfaces that have large but unexpected discrete symmetry
groups. By deriving, correcting, and generalizing a technique similar to that
of Candelas, de la Ossa and Rodriguez-Villegas, we find a calculationally
tractable means of finding the Picard-Fuchs equations satisfied by the periods
of all 3-forms in these families. To provide a modest point of comparison, we
then briefly investigate the relation between the size of the symmetry group
along these loci and the number of nonzero Yukawa couplings. We include an
introductory exposition of the mathematics involved, intended to be accessible
to physicists, in order to make the discussion self-contained.Comment: 54 pages, 3 figure
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