400 research outputs found
Fluctuations along supersymmetric flat directions during Inflation
We consider a set of scalar fields, consisting of a single flat direction and
one or several non-flat directions. We take our cue from the MSSM, considering
separately D-flat and F-flat directions, but our results apply to any
supersymmetric scenario containing flat directions. We study the field
fluctuations during pure de Sitter Inflation, following the evolution of the
infrared modes by numerically solving the appropriate Langevin equations. We
demonstrate that for the Standard Model U(1), SU(2) or SU(3) gauge couplings,
as well as for large enough Yukawa couplings, the fluctuations along the
non-flat directions effectively block the fluctuations along the flat
directions. The usual expected behaviour \propto N, with N the
number of efolds, may be strongly violated, depending on the coupling
strengths. As a consequence, those cosmological considerations, which are
derived assuming that during inflation flat directions fluctuate freely, should
be revised.Comment: 19 pages, 5 figures, Submitted to JCA
Non-linear inflationary perturbations
We present a method by which cosmological perturbations can be quantitatively
studied in single and multi-field inflationary models beyond linear
perturbation theory. A non-linear generalization of the gauge-invariant
Sasaki-Mukhanov variables is used in a long-wavelength approximation. These
generalized variables remain invariant under time slicing changes on long
wavelengths. The equations they obey are relatively simple and can be
formulated for a number of time slicing choices. Initial conditions are set
after horizon crossing and the subsequent evolution is fully non-linear. We
briefly discuss how these methods can be implemented numerically in the study
of non-Gaussian signatures from specific inflationary models.Comment: 10 pages, replaced to match JCAP versio
Quantitative bispectra from multifield inflation
After simplifying and improving the non-Gaussian formalism we developed in
previous work, we derive a quantitative expression for the three-point
correlator (bispectrum) of the curvature perturbation in general multiple-field
inflation models. Our result describes the evolution of non-Gaussianity on
superhorizon scales caused by the nonlinear influence of isocurvature
perturbations on the adiabatic perturbation during inflation. We then study a
simple quadratic two-field potential and find that when slow roll breaks down
and the field trajectory changes direction in field space, the non-Gaussianity
can become large. However, for the simple models studied to date, the magnitude
of this non-Gaussianity decays away after the isocurvature mode is converted
into the adiabatic mode.Comment: 7 pages, 1 figure. v4: Added remarks on momentum dependence, minor
textual changes, matches published versio
Simple route to non-Gaussianity in inflation
We present a simple way to calculate non-Gaussianity in inflation using fully
non-linear equations on long wavelengths with stochastic sources to take into
account the short-wavelength quantum fluctuations. Our formalism includes both
scalar metric and matter perturbations, combining them into variables which are
invariant under changes of time slicing in the long-wavelength limit. We
illustrate this method with a perturbative calculation in the single-field
slow-roll case. We also introduce a convenient choice of variables to
graphically present the full momentum dependence of the three-point correlator.Comment: 6 pages, 2 figures. v2: Updated formalism to version described in
astro-ph/0504508, leading to dropping of one unnecessary approximation. Final
results not significantly changed. Extended discussion of calculation and
added graphical presentation of full momentum dependence. References
corrected and added. v3: Final version, only small textual change
Analysis of wall mass transfer in a turbulent pipe flow combining extended POD and FIK identity
We combine extended proper orthogonal decomposition (EPOD) together with the Fukagata-Iwamoto-Kasagi (FIK) identity to quantify the role of individual coherent structures on the wall mass transfer in a turbulent pipe flow. Direct numerical simulation at a Reynolds number of 5300 (based on bulk velocity) is performed with the passive scalar released at the pipe inlet. The proper orthogonal decomposition (POD) eigenvalues show that the scalar field can be described by a more compact set of modes compared to the velocity field, and that these modes are skewed towards higher azimuthal wave numbers. POD modes for the scalar and EPOD modes for the velocity are visualized in the cross-stream plane to infer the capacity of each mode to transport scalar to and from the wall. A form of the FIK identity is derived for the wall mass transfer coefficient (Sherwood number, Sh) and employed to separate the contributions of the mean and fluctuating velocity and scalar fields. The FIK decomposition shows that the turbulent velocity/scalar correlations account for up to 65.8% of the total Sh. The contribution of each POD and EPOD mode to the Sh number is also computed; it is found that, using azimuthal wave numbers m=1–15 and POD modes n=1–10, it is possible to reconstruct 49% of the turbulent component of Sh, with the velocity modes containing only 31% of the turbulent kinetic energy. Quadrant analysis shows that these modes are related to ejection and sweep events near the wall, with the ejection events dominating
Reconstruction of large scale flow structures in a stirred tank from limited sensor data
We combine reduced order modelling and system identification to reconstruct the temporal evolution of large scale vortical structures behind the blades of a Rushton impeller. We performed Direct Numerical Simulations at Reynolds number 600 and employed proper orthogonal decomposition (POD) to extract the dominant modes and their temporal coefficients. We then applied the identification algorithm, N4SID, to construct an estimator that captures the relation between the velocity signals at sensor points (input) and the POD coefficients (output). We show that the first pair of modes can be very well reconstructed using the velocity time signal from even a single sensor point. A larger number of points improves accuracy and robustness, and also leads to better reconstruction for the second pair of POD modes. Application of the estimator derived at Re=600 to the flows at Re=500 and 700, shows that it is robust with respect to changes in operating conditions
Large non-Gaussianity in multiple-field inflation
We investigate non-Gaussianity in general multiple-field inflation using the
formalism we developed in earlier papers. We use a perturbative expansion of
the non-linear equations to calculate the three-point correlator of the
curvature perturbation analytically. We derive a general expression that
involves only a time integral over background and linear perturbation
quantities. We work out this expression explicitly for the two-field slow-roll
case, and find that non-Gaussianity can be orders of magnitude larger than in
the single-field case. In particular, the bispectrum divided by the square of
the power spectrum can easily be of O(1-10), depending on the model. Our result
also shows the explicit momentum dependence of the bispectrum. This conclusion
of large non-Gaussianity is confirmed in a semi-analytic slow-roll
investigation of a simple quadratic two-field model.Comment: 21 pages, 9 figures. v4: Minor textual changes to match published
version. In addition, and superseding the published version, a small error in
X and X-bar has been corrected; no significant changes to the final results.
Note that an extended (no slow roll) numerical treatment superseding section
V.D is available in astro-ph/051104
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