558 research outputs found
Numerical Quantum Field Theory on the Continuum and a New Look at Perturbation Theory
The Source Galerkin method finds approximate solutions to the functional
differential equations of field theories in the presence of external sources.
While developing this process, it was recognized that approximations of the
spectral representations of the Green's functions by Sinc function expansions
are an extremely powerful calculative tool. Specifically, this understanding
makes it not only possible to apply the Source Galerkin method to higher
dimensional field theories, but also leads to a new approach to perturbation
theory calculations in scalar and fermionic field theories. This report
summarizes the methodologies for solving quantum field theories with the Source
Galerkin method and for performing perturbation theory calculations using Sinc
approximations.Comment: Lattice2001(theorydevelop
Inflaton Fragmentation and Oscillon Formation in Three Dimensions
Analytical arguments suggest that a large class of scalar field potentials
permit the existence of oscillons -- pseudo-stable, non-topological solitons --
in three spatial dimensions. In this paper we numerically explore oscillon
solutions in three dimensions. We confirm the existence of these field
configurations as solutions to the Klein-Gorden equation in an expanding
background, and verify the predictions of Amin and Shirokoff for the
characteristics of individual oscillons for their model. Further, we
demonstrate that significant numbers of oscillons can be generated via
fragmentation of the inflaton condensate, consistent with the analysis of Amin.
These emergent oscillons can easily dominate the post-inflationary universe.
Finally, both analytic and numerical results suggest that oscillons are stable
on timescales longer than the post-inflationary Hubble time. Consequently, the
post-inflationary universe can contain an effective matter-dominated phase,
during which it is dominated by localized concentrations of scalar field
matter.Comment: See http://easther.physics.yale.edu/downloads.html for numerical
codes. Visualizations available at http://www.mit.edu/~mamin/oscillons.html
and http://easther.physics.yale.edu/fields.html V2 Minor fixes to reference
lis
PSpectRe: A Pseudo-Spectral Code for (P)reheating
PSpectRe is a C++ program that uses Fourier-space pseudo-spectral methods to
evolve interacting scalar fields in an expanding universe. PSpectRe is
optimized for the analysis of parametric resonance in the post-inflationary
universe, and provides an alternative to finite differencing codes, such as
Defrost and LatticeEasy. PSpectRe has both second- (Velocity-Verlet) and
fourth-order (Runge-Kutta) time integrators. Given the same number of spatial
points and/or momentum modes, PSpectRe is not significantly slower than finite
differencing codes, despite the need for multiple Fourier transforms at each
timestep, and exhibits excellent energy conservation. Further, by computing the
post-resonance equation of state, we show that in some circumstances PSpectRe
obtains reliable results while using substantially fewer points than a finite
differencing code. PSpectRe is designed to be easily extended to other problems
in early-universe cosmology, including the generation of gravitational waves
during phase transitions and pre-inflationary bubble collisions. Specific
applications of this code will be pursued in future work.Comment: 22 pages; source code for PSpectRe available:
http://easther.physics.yale.edu v2 Typos fixed, minor improvements to
wording; v3 updated as per referee comment
Entropy of Anisotropic Universe and Fractional Branes
We obtain the entropy of a homogeneous anisotropic universe applicable, by
assumption, to the fractional branes in the universe in the model of Chowdhury
and Mathur. The entropy for the 3 or 4 charge fractional branes thus obtained
is not of the expected form E^{{3/2}} or E^2. One way the expected form is
realised is if p \to \rho for the transverse directions and if the compact
directions remain constant in size. These conditions are likely to be enforced
by brane decay and annihilation, and by the S, T, U dualities. T duality is
also likely to exclude high entropic cases, found in the examples, which arise
due to the compact space contracting to zero size. Then the 4 charge fractional
branes may indeed provide a detailed realisation of the maximum entropic
principle we proposed recently to determine the number (3 + 1) of large
spacetime dimensions.Comment: Version 2: 21 pages. More discussion and references added. To appear
in General Relativity and Gravitatio
Inflation as a Probe of Short Distance Physics
We show that a string-inspired Planck scale modification of general
relativity can have observable cosmological effects. Specifically, we present a
complete analysis of the inflationary perturbation spectrum produced by a
phenomenological Lagrangian that has a standard form on large scales but
incorporates a string-inspired short distance cutoff, and find a deviation from
the standard result. We use the de Sitter calculation as the basis of a
qualitative analysis of other inflationary backgrounds, arguing that in these
cases the cutoff could have a more pronounced effect, changing the shape of the
spectrum. Moreover, the computational approach developed here can be used to
provide unambiguous calculations of the perturbation spectrum in other
heuristic models that modify trans-Planckian physics and thereby determine
their impact on the inflationary perturbation spectrum. Finally, we argue that
this model may provide an exception to constraints, recently proposed by Tanaka
and Starobinsky, on the ability of Planck-scale physics to modify the
cosmological spectrum.Comment: revtex, 8 pages, eps figures included, references adde
Delayed Reheating and the Breakdown of Coherent Oscillations
We analyze the evolution of the perturbations in the inflaton field and
metric following the end of inflation. We present accurate analytic
approximations for the perturbations, showing that the coherent oscillations of
the post-inflationary condensate necessarily break down long before any current
phenomenological constraints require the universe to become radiation
dominated. Further, the breakdown occurs on length-scales equivalent to the
comoving post-inflationary horizon size. This work has implications for both
the inflationary "matching" problem, and the possible generation of a
stochastic gravitational wave background in the post-inflationary universe.Comment: 18 pages, 5 figures, v2: references added, extended discussion in
section
A Back-reaction Induced Lower Bound on the Tensor-to-Scalar Ratio
There are large classes of inflationary models, particularly popular in the
context of string theory and brane world approaches to inflation, in which the
ratio of linearized tensor to scalar metric fluctuations is very small. In such
models, however, gravitational waves produced by scalar modes cannot be
neglected. We derive the lower bound on the tensor-to-scalar ratio by
considering the back-reaction of the scalar perturbations as a source of
gravitational waves. These results show that no cosmological model that is
compatible with a metric scalar amplitude of can have a ratio
of the tensor to scalar power spectra less than at
recombination and that higher-order terms leads to logarithmic growth for r
during radiation domination. Our lower bound also applies to non-inflationary
models which produce an almost scale-invariant spectrum of coherent
super-Hubble scale metric fluctuations.Comment: 5 pages, version 3, minor changes from version
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