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

Perturbative analysis of wave interactions in nonlinear systems

This work proposes a new way for handling obstacles to asymptotic integrability in perturbed nonlinear PDEs within the method of Normal Forms - NF - for the case of multi-wave solutions. Instead of including the whole obstacle in the NF, only its resonant part is included, and the remainder is assigned to the homological equation. This leaves the NF intergable and its solutons retain the character of the solutions of the unperturbed equation. We exploit the freedom in the expansion to construct canonical obstacles which are confined to te interaction region of the waves. Fo soliton solutions, e.g., in the KdV equation, the interaction region is a finite domain around the origin; the canonical obstacles then do not generate secular terms in the homological equation. When the interaction region is infifnite, or semi-infinite, e.g., in wave-front solutions of the Burgers equation, the obstacles may contain resonant terms. The obstacles generate waves of a new type, which cannot be written as functionals of the solutions of the NF. When an obstacle contributes a resonant term to the NF, this leads to a non-standard update of th wave velocity.Comment: 13 pages, including 6 figure

Gauge-invariant Formulation of the Second-order Cosmological Perturbations

Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the non-linear effects of the Einstein equations.Comment: 5 pages, no figure. RevTeX; short letter version of gr-qc/0605108; some details of explanations are adde

Effects of nucleus initialization on event-by-event observables

In this work we present a study of the influence of nucleus initializations on the event-by-event elliptic flow coefficient, $v_2$. In most Monte-Carlo models, the initial positions of the nucleons in a nucleus are completely uncorrelated, which can lead to very high density regions. In a simple, yet more realistic model where overlapping of the nucleons is avoided, fluctuations in the initial conditions are reduced. However, $v_2$ distributions are not very sensitive to the initialization choice.Comment: 4 pages, 5 figures, to appear in the Bras. Jour. Phy

Remarks on the Theory of Cosmological Perturbation

It is shown that the power spectrum defined in the Synchronous Gauge can not be directly used to calculate the predictions of cosmological models on the large-scale structure of universe, which should be calculated directly by a suitable gauge-invariant power spectrum or the power spectrum defined in the Newtonian Gauge.Comment: 13 pages, 1 figure, minor changes, to be published in Chinese Physics Letter

Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation

By considering the long-wave limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple scale method in obtaining uniform perturbative series.Comment: 15 pages, RevTex, no figures (to appear in Phys. Rev. E

Coarse graining scale and effectiveness of hydrodynamic modeling

Some basic questions about the hydrodynamical approach to relativistic heavy ion collisions are discussed aiming to clarify how far we can go with such an approach to extract useful information on the properties and dynamics of the QCD matter created. We emphasize the importance of the coarse-graining scale required for the hydrodynamic modeling which determines the space-time resolution and the associated limitations of collective flow observables. We show that certain kinds of observables can indicate the degree of inhomogeneity of the initial condition under less stringent condition than the local thermal equilibrium subjected to the coarse-graining scale compatible to the scenario.Comment: 12 pages, 4 figures, Quark Matter 201