Quasi Non-linear Evolution of Stochastic Bias

It is generally believed that the spatial distribution of galaxies does not trace that of the total mass. The understanding of the bias effect is therefore necessary to determine the cosmological parameters and the primordial density fluctuation spectrum from the galaxy survey. The deterministic description of bias may not be appropriate because of the various stochasticity of galaxy formation process. In nature, the biasing is epoch dependent and recent deep survey of the galaxy shows the large biasing at high redshift. Hence, we investigate quasi non-linear evolution of the stochastic bias by using the tree level perturbation method. Especially, the influence of the initial cross correlation on the evolution of the skewness and the bi-spectrum is examined in detail. We find that the non-linear bias can be generated dynamically. The small value of the initial cross correlation can bend the \dg-\dm relation effectively and easily lead to the negative curvature ($b_2<0$). We also propose a method to predict the bias, cross correlation and skewness at high redshift. As an illustration, the possibility of the large biasing at high redshift is discussed. Provided the present bias parameter as $b=1.5$ and $\Omega=1.0$, we predict the large scale bias as $b=4.63$ at $z=3$ by fitting the bi-spectrum to the Lick catalog data. Our results will be important for the future deep sky survey.Comment: 20 pages, 5 Encapsulated Postscript figures, aastex, final version to appear in Ap

Gravitational Wave Background from Neutrino-Driven Gamma-Ray Bursts

We discuss the gravitational wave background (GWB) from a cosmological population of gamma-ray bursts (GRBs). Among various emission mechanisms for the gravitational waves (GWs), we pay a particular attention to the vast anisotropic neutrino emissions from the accretion disk around the black hole formed after the so-called failed supernova explosions. The produced GWs by such mechanism are known as burst with memory, which could dominate over the low-frequency regime below \sim 10Hz. To estimate their amplitudes, we derive general analytic formulae for gravitational waveform from the axisymmetric jets. Based on the formulae, we first quantify the spectrum of GWs from a single GRB. Then, summing up its cosmological population, we find that the resultant value of the density parameter becomes roughly \Omega_{GW} \approx 10^{-20} over the wide-band of the low-frequency region, f\sim 10^{-4}-10^1Hz. The amplitude of GWB is sufficiently smaller than the primordial GWBs originated from an inflationary epoch and far below the detection limit.Comment: 6 pages, 4 figures, accepted for publication in MNRA

The hydrostatic equilibrium and Tsallis equilibrium for self-gravitating systems

Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We obtain a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium of self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions and Tsallis equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.Comment: 7 pages, 9 Reference

Solutions of gauge invariant cosmological perturbations in long-wavelength limit

We investigate gauge invariant cosmological perturbations in a spatially flat Friedman-Robertson-Walker universe with scalar fields. It is well known that the evolution equation for the gauge invariant quantities has exact solutions in the long-wavelength limit. We find that these gauge invariant solutions can be obtained by differentiating the background solution with respect to parameters contained in the background system. This method is very useful when we analyze the long-wavelength behavior of cosmological perturbation with multiple scalar fields.Comment: 17 pages, will appear in Classical and Quantum Gravit

A Closure Theory for Non-linear Evolution of Cosmological Power Spectra

We apply a non-linear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop results of standard perturbation theory and beyond that, it is still capable of treating the non-linear evolution of matter power spectra. We find the exact integral expressions for the solutions of closure equations. These analytic expressions coincide with the renormalized one-loop results presented by Crocce & Scoccimarro (2006,2007). By constructing the non-linear propagator, we analytically evaluate the non-linear matter power spectra based on the first-order Born approximation of the integral expressions and compare it with those of the renormalized perturbation theory.Comment: 22 pages, 4 figures, accepted for publication in Ap

Entropic Upper Bound on Gravitational Binding Energy

We prove that the gravitational binding energy {\Omega} of a self gravitating system described by a mass density distribution {\rho}(x) admits an upper bound B[{\rho}(x)] given by a simple function of an appropriate, non-additive Tsallis' power-law entropic functional Sq evaluated on the density {\rho}. The density distributions that saturate the entropic bound have the form of isotropic q-Gaussian distributions. These maximizer distributions correspond to the Plummer density profile, well known in astrophysics. A heuristic scaling argument is advanced suggesting that the entropic bound B[{\rho}(x)] is unique, in the sense that it is unlikely that exhaustive entropic upper bounds not based on the alluded Sq entropic measure exit. The present findings provide a new link between the physics of self gravitating systems, on the one hand, and the statistical formalism associated with non-additive, power-law entropic measures, on the other hand

Probing anisotropies of gravitational-wave backgroundswith a space-based interferometer II: Perturbative reconstruction of a low-frequency skymap

We present a perturbative reconstruction method to make a skymap of gravitational-wave backgrounds (GWBs) observed via space-based interferometer. In the presence of anisotropies in GWBs, the cross-correlated signals of observed GWBs are inherently time-dependent due to the non-stationarity of the gravitational-wave detector. Since the cross-correlated signal is obtained through an all-sky integral of primary signals convolving with the antenna pattern function of gravitational-wave detectors, the non-stationarity of cross-correlated signals, together with full knowledge of antenna pattern functions, can be used to reconstruct an intensity map of the GWBs. Here, we give two simple methods to reconstruct a skymap of GWBs based on the perturbative expansion in low-frequency regime. The first one is based on harmonic-Fourier representation of data streams and the second is based on "direct" time-series data. The latter method enables us to create a skymap in a direct manner. The reconstruction technique is demonstrated in the case of the Galactic gravitational wave background observed via planned space interferometer, LISA. Although the angular resolution of low-frequency skymap is rather restricted, the methodology presented here would be helpful in discriminating the GWBs of galactic origins by those of the extragalactic and/or cosmological origins.Comment: 23 pages, 12 figures, Phys.Rev.D (2005) in pres

Jeans' gravitational instability and nonextensive kinetic theory

The concept of Jeans gravitational instability is rediscussed in the framework of nonextensive statistics and its associated kinetic theory. A simple analytical formula generalizing the Jeans criterion is derived by assuming that the unperturbed self- gravitating collisionless gas is kinetically described by the $q$-parameterized class of power law velocity distributions. It is found that the critical values of wavelength and mass depend explicitly on the nonextensive $q$-parameter. The standard Jeans wavelength derived for a Maxwellian distribution is recovered in the limiting case $q$=1. For power-law distributions with cutoff, the instability condition is weakened with the system becoming unstable even for wavelengths of the disturbance smaller than the standard Jeans length $\lambda_J$.Comment: 5 pages, including 3 figures. Accepted for publication in A&