Takayuki Tatekawa

Cosmic structures via Bose–Einstein condensation and its collapse

We develop our novel model of cosmology based on Bose–Einstein condensation. This model unifies the dark energy and the dark matter, and predicts the multiple collapse of condensation, followed by the final acceleration regime of cosmic expansion. We first explore the generality of this model, especially the constraints on the boson mass and condensation conditions. We further argue the robustness of this model over a wide range of parameters of mass, self-coupling constant and the condensation rate. Then the dynamics of BEC collapse and the preferred scale of the collapse are studied. Finally, we describe possible observational tests of our model, especially the periodicity of the collapses and the gravitational wave associated with them.

The effect of modified gravity on weak lensing

Abstract We study the effect of modified gravity on weak lensing in a class of scalar-tensor theory that includes f ( R ) gravity as a special case. These models are designed to satisfy local gravity constraints by having a large scalar-field mass in a region of high curvature. Matter density perturbations in these models are enhanced at small redshifts because of the presence of a coupling Q that characterizes the strength between dark energy and non-relativistic matter. We compute a convergence power spectrum of weak lensing numerically and show that the spectral index and the amplitude of the spectrum in the linear regime can be significantly modified compared to the ΛCDM model for large values of | Q | of the order of unity. Thus weak lensing provides a powerful tool to constrain such large coupling scalar-tensor models including f ( R ) gravity.

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 an iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state.

Origin of scaling structure and non-Gaussian velocity distribution in a self-gravitating ring model

Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems, such as galaxies and interstellar molecular clouds. We study the origin of these properties using a one-dimensional ring model that we propose in this paper. In this simple model, N particles are moving, on a circular ring fixed in three-dimensional space, with mutual interaction of gravity. This model is suitable for the accurate symplectic integration method by which we argue the phase transition in this system. Especially, in between the extended phase and the collapsed phase, we find an interesting phase (halo phase) that has negative specific heat at the intermediate energy scale. Moreover, in this phase, there appear scaling properties and nonthermal and non-Gaussian velocity distributions. In contrast, these peculiar properties are never observed in other gas and core phases. Particles in each phase have a typical time scale of motions determined by the cutoff length xi, the ring radius R, and the total energy E. Thus all relaxation patterns of the system are determined by these three time scales.

Second-order matter density perturbations and skewness in scalar?tensor modified gravity models

We study second-order cosmological perturbations in scalar–tensor models of dark energy that satisfy local gravity constraints, including f(R) gravity. We derive equations for matter fluctuations under a sub-horizon approximation and clarify conditions under which first-order perturbations in the scalar field can be neglected relative to second-order matter and velocity perturbations. We also compute the skewness of the matter density distribution and find that the difference from the ΛCDM (CDM: cold dark matter) model is less than a few per cent even if the growth rate of first-order perturbations is significantly different from that in the ΛCDM model. This shows that the skewness provides a model-independent test for the picture of gravitational instability from Gaussian initial perturbations including scalar–tensor modified gravity models.

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 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 cannot 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. 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~5, 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.

Extending Lagrangian perturbation theory to a fluid with velocity dispersion

We formulate a perturbative approximation to gravitational instability, based on Lagrangian hydrodynamics in Newtonian cosmology. We take account of the ‘pressure’ effect of a fluid, which is kinematically caused by velocity dispersion, to aim the hydrodynamical description beyond shell crossing. Master equations in the Lagrangian description are derived and solved perturbatively up to second order. Then, as an illustration, power spectra of density fluctuations are computed in a one-dimensional model from the Lagrangian approximations and Eulerian linear perturbation theory for comparison. We find that the results by the Lagrangian approximations are different from those by the Eulerian theory in the weakly non-linear regime at scales smaller than the Jeans length. We also show the validity of the perturbative Lagrangian approximations by consulting the difference between the first-order and second-order approximations.

Universal non-Gaussian velocity distribution in violent gravitational processes.

We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N -body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasistationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity distribution, which is a democratic (equal-weighted) superposition of many Gaussian distributions (DT distribution). This is deeply related with the local virial equilibrium and the linear mass-temperature relation which characterize the system. We show the robustness of this distribution function against various initial conditions which leads to the violent gravitational process. The DT distribution has a positive correlation with the energy fluctuation of the system. On the other hand, the coherent motion such as the radial motion in the spherical collapse and the rotation with the angular momentum suppress the appearance of the DT distribution.

Primordial fractal density perturbations and structure formation in the universe: One-dimensional collisionless sheet model

The two-point correlation function of galaxy distribution shows that structure in the present universe is scale-free up to a certain scale (at least several tens of Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze the time evolution of fractal density perturbations in an Einstein-de Sitter universe, and study how the perturbation evolves and what kind of nonlinear structure will result. We assume a one-dimensional collisionless sheet model with initial Cantor-type fractal perturbations. The nonlinear structure seems to approach some attractor with a unique fractal dimension, which is independent of the fractal dimensions of initial perturbations. A discrete self-similarity in the phase space is also found when the universal nonlinear fractal structure is reached.

Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion

We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This perturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein-de Sitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.