Non-Gaussianity of the density distribution in accelerating universes

According to recent observations, the existence of the dark energy has been considered. Even though we have obtained the constraint of the equation of the state for dark energy ($p = w \rho$) as $-1 \le w \le -0.78$ by combining WMAP data with other astronomical data, in order to pin down $w$, it is necessary to use other independent observational tools. For this purpose, we consider the $w$ dependence of the non-Gaussianity of the density distribution generated by nonlinear dynamics. To extract the non-Gaussianity, we follow a semi-analytic approach based on Lagrangian linear perturbation theory, which provides an accurate value for the quasi-nonlinear region. From our results, the difference of the non-Gaussianity between $w = -1$ and $w= -0.5$ is about 4% while that between $w = -1$ and $w= -0.8$ is about $0.9$. For the highly non-linear region, we estimate the difference by combining this perturbative approach with N-body simulation executed for our previous paper. From this, we can expect the difference to be more enhanced in the low-$z$ region, which suggests that the non-Gaussianity of the density distribution potentially plays an important role for extracting the information of dark energy.Comment: 15 pages, 4 figures, accepted for publication in JCAP; v2: smoothing scale has been change

The non-perturbative regime of cosmic structure formation

This paper focusses on the barely understood gap between the weakly nonlinear regime of structure formation and the onset of the virialized regime. While the former is accessed through perturbative calculations and the latter through virialization conditions incorporating dynamical stresses that arise in collisionless self-gravitating systems due to velocity dispersion forces, the addressed regime can only be understood through non-perturbative models. We here present an exact Lagrangian integral that provides a tool to access this regime. We derive a transport equation for the peculiar-gravitational field strength and integrate it along comoving trajectories of fluid elements. The so-obtained integral provides an exact expression that solves the longitudinal gravitational field equation in general. We argue that this integral provides a powerful approximation beyond the Lagrangian perturbative regime, and discuss its relation to known approximations, among them Lagrangian perturbation solutions including the Zel'dovich approximation and approximations for adhesive gravitational clustering, including the adhesion approximation. Furthermore, we propose an iteration scheme for a systematic analytical and numerical construction of trajectory fields. The integral may also be employed to improve inverse reconstruction techniques.Comment: 9 pages; matches published version in Astron. Astrophy

Improving the Lagrangian perturbative solution for cosmic fluid: Applying Shanks transformation

We study the behavior of Lagrangian perturbative solutions. For a spherical void model, the higher order the Lagrangian perturbation we consider, the worse the approximation becomes in late-time evolution. In particular, if we stop to improve until an even order is reached, the perturbative solution describes the contraction of the void. To solve this problem, we consider improving the perturbative solution using Shanks transformation, which accelerates the convergence of the sequence. After the transformation, we find that the accuracy of higher-order perturbation is recovered and the perturbative solution is refined well. Then we show that this improvement method can apply for a $\Lambda$CDM model and improved the power spectrum of the density field.Comment: 17 pages, 7 figures; accepted for publication in Phys.Rev.D; v2: Evolution of power spectrum in LCDM model is added; v3: References are correcte

Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations

We explore the initial conditions for cosmological N-body simulations suitable for calculating the skewness and kurtosis of the density field. In general, the initial conditions based on the perturbation theory (PT) provide incorrect second-order and higher-order growth. These errors implied by the use of the perturbation theory to set up the initial conditions in N-body simulations are called transients. Unless these transients are completely suppressed compared with the dominant growing mode, we can not reproduce the correct evolution of cumulants with orders higher than two, even though there is no problem with the numerical scheme. We investigate the impact of transients on the observable statistical quantities by performing $N$-body simulations with initial conditions based on Lagrangian perturbation theory (LPT). We show that the effects of transients on the kurtosis from the initial conditions, based on second-order Lagrangian perturbation theory (2LPT) have almost disappeared by $z\sim5$, as long as the initial conditions are set at $z > 30$. This means that for practical purposes, the initial conditions based on 2LPT are accurate enough for numerical calculations of skewness and kurtosis.Comment: 21 pages, 5 figures; accepted for publication in JCA

Thermodynamics of the self-gravitating ring model

We present the phase diagram, in both the microcanonical and the canonical ensemble, of the Self-Gravitating-Ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply a new iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state

Gravitational instability on the brane: the role of boundary conditions

An outstanding issue in braneworld theory concerns the setting up of proper boundary conditions for the brane-bulk system. Boundary conditions (BC's) employing regulatory branes or demanding that the bulk metric be nonsingular have yet to be implemented in full generality. In this paper, we take a different route and specify boundary conditions directly on the brane thereby arriving at a local and closed system of equations (on the brane). We consider a one-parameter family of boundary conditions involving the anisotropic stress of the projection of the bulk Weyl tensor on the brane and derive an exact system of equations describing scalar cosmological perturbations on a generic braneworld with induced gravity. Depending upon our choice of boundary conditions, perturbations on the brane either grow moderately (region of stability) or rapidly (instability). In the instability region, the evolution of perturbations usually depends upon the scale: small scale perturbations grow much more rapidly than those on larger scales. This instability is caused by a peculiar gravitational interaction between dark radiation and matter on the brane. Generalizing the boundary conditions obtained by Koyama and Maartens, we find for the Dvali-Gabadadze-Porrati model an instability, which leads to a dramatic scale-dependence of the evolution of density perturbations in matter and dark radiation. A different set of BC's, however, leads to a more moderate and scale-independent growth of perturbations. For the mimicry braneworld, which expands like LCDM, this class of BC's can lead to an earlier epoch of structure formation.Comment: 35 pages, 9 figures, an appendix and references added, version to be published in Classical and Quantum Gravit

Non-Gaussianity of the density distribution in accelerating universes II:N-body simulations

We explore the possibility of putting constraints on dark energy models with statistical property of large scale structure in the non-linear region. In particular, we investigate the $w$ dependence of non-Gaussianity of the smoothed density distribution generated by the nonlinear dynamics. In order to follow the non-linear evolution of the density fluctuations, we apply N-body simulations based on $P^3 M$ scheme. We show that the relative difference between non-Gaussianity of $w=-0.8$ model and that of $w=-1.0$ model is $0.67$ (skewness) and $1.2$ (kurtosis) for $R=8h^{-1}$ Mpc. We also calculate the correspondent quantities for $R=2h^{-1}$ Mpc, $3.0$ (skewness) and $4.5$ (kurtosis), and the difference turn out to be greater, even though non-linearity in this scale is so strong that the complex physical processes about galaxy formation affect the galaxy distribution. From this, we can expect that the difference can be tested by all sky galaxy surveys with the help of mock catalogs created by selection functions, which suggests that non-Gaussianity of the density distribution potentially plays an important role for extracting information on dark energy.Comment: 21 pages, 14 figure

Third-order perturbative solutions in the Lagrangian perturbation theory with pressure

Lagrangian perturbation theory for cosmological fluid describes structure formation in the quasi-nonlinear stage well. We present a third-order perturbative equation for Lagrangian perturbation with pressure in both the longitudinal and transverse modes. Then we derive the perturbative solution for simplest case.Comment: 11 pages, 1 figure; accepted for publication in Physical Review