Spherical collapse with dark energy

I discuss the work of Maor and Lahav [1], in which the inclusion of dark energy into the spherical collapse formalism is reviewed. Adopting a phenomenological approach, I consider the consequences of - a) allowing the dark energy to cluster, and, b) including the dark energy in the virialization process. Both of these issues affect the final state of the system in a fundamental way. The results suggest a potentially differentiating signature between a true cosmological constant and a dynamic form of dark energy. This signature is unique in the sense that it does not depend on a measurement of the value of the equation of state of dark energy.Comment: To appear in the proceedings of the ``Peyresq Physics 10" Workshop, 19 - 24 June 2005, Peyresq, Franc

Inverse flux quantum periodicity of magnetoresistance oscillations in two-dimensional short-period surface superlattices

Transport properties of the two-dimensional electron gas (2DEG) are considered in the presence of a perpendicular magnetic field $B$ and of a {\it weak} two-dimensional (2D) periodic potential modulation in the 2DEG plane. The symmetry of the latter is rectangular or hexagonal. The well-known solution of the corresponding tight-binding equation shows that each Landau level splits into several subbands when a rational number of flux quanta $h/e$ pierces the unit cell and that the corresponding gaps are exponentially small. Assuming the latter are closed due to disorder gives analytical wave functions and simplifies considerably the evaluation of the magnetoresistivity tensor $\rho_{\mu\nu}$. The relative phase of the oscillations in $\rho_{xx}$ and $\rho_{yy}$ depends on the modulation periods involved. For a 2D modulation with a {\bf short} period $\leq 100$ nm, in addition to the Weiss oscillations the collisional contribution to the conductivity and consequently the tensor $\rho_{\mu\nu}$ show {\it prominent peaks when one flux quantum $h/e$ passes through an integral number of unit cells} in good agreement with recent experiments. For periods $300- 400$ nm long used in early experiments, these peaks occur at fields 10-25 times smaller than those of the Weiss oscillations and are not resolved

Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequences

Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results to distributions with unbounded support and removing normality assumption

Cosmological Tracking Solutions

A substantial fraction of the energy density of the universe may consist of quintessence in the form of a slowly-rolling scalar field. Since the energy density of the scalar field generally decreases more slowly than the matter energy density, it appears that the ratio of the two densities must be set to a special, infinitesimal value in the early universe in order to have the two densities nearly coincide today. Recently, we introduced the notion of tracker fields to avoid this initial conditions problem. In the paper, we address the following questions: What is the general condition to have tracker fields? What is the relation between the matter energy density and the equation-of-state of the universe imposed by tracker solutions? And, can tracker solutions explain why quintessence is becoming important today rather than during the early universe

Shear viscosity of hot scalar field theory in the real-time formalism

Within the closed time path formalism a general nonperturbative expression is derived which resums through the Bethe-Salpter equation all leading order contributions to the shear viscosity in hot scalar field theory. Using a previously derived generalized fluctuation-dissipation theorem for nonlinear response functions in the real-time formalism, it is shown that the Bethe-Salpeter equation decouples in the so-called (r,a) basis. The general result is applied to scalar field theory with pure lambda*phi**4 and mixed g*phi**3+lambda*phi**4 interactions. In both cases our calculation confirms the leading order expression for the shear viscosity previously obtained in the imaginary time formalism.Comment: Expanded introduction and conclusions. Several references and a footnote added. Fig.5 and its discussion in the text modified to avoid double counting. Signs in Eqs. (45) and (53) correcte

Power-law entropy-corrected HDE and NADE in Brans-Dicke cosmology

Considering the power-law corrections to the black hole entropy, which appear in dealing with the entanglement of quantum fields inside and outside the horizon, the holographic energy density is modified accordingly. In this paper we study the power-law entropy-corrected holographic dark energy in the framework of Brans-Dicke theory. We investigate the cosmological implications of this model in detail. We also perform the study for the new agegraphic dark energy model and calculate some relevant cosmological parameters and their evolution. {As a result we find that this model can provide the present cosmic acceleration and even the equation of state parameter of this model can cross the phantom line $w_D=-1$ provided the model parameters are chosen suitably}.Comment: 14 pages, 2 figure, accepted by IJT

Genesis of Dark Energy: Dark Energy as Consequence of Release and Two-stage Tracking Cosmological Nuclear Energy

Recent observations on Type-Ia supernovae and low density ($\Omega_{m} = 0.3$) measurement of matter including dark matter suggest that the present-day universe consists mainly of repulsive-gravity type `exotic matter' with negative-pressure often said `dark energy' ($\Omega_{x} = 0.7$). But the nature of dark energy is mysterious and its puzzling questions, such as why, how, where and when about the dark energy, are intriguing. In the present paper the authors attempt to answer these questions while making an effort to reveal the genesis of dark energy and suggest that `the cosmological nuclear binding energy liberated during primordial nucleo-synthesis remains trapped for a long time and then is released free which manifests itself as dark energy in the universe'. It is also explained why for dark energy the parameter $w = - {2/3}$. Noting that $w = 1$ for stiff matter and $w = {1/3}$ for radiation; $w = - {2/3}$ is for dark energy because $"-1"$ is due to `deficiency of stiff-nuclear-matter' and that this binding energy is ultimately released as `radiation' contributing $"+ {1/3}"$, making $w = -1 + {1/3} = - {2/3}$. When dark energy is released free at $Z = 80$, $w = -{2/3}$. But as on present day at $Z = 0$ when radiation strength has diminished to $\delta \to 0$, $w = -1 + \delta{1/3} = - 1$. This, thus almost solves the dark-energy mystery of negative pressure and repulsive-gravity. The proposed theory makes several estimates /predictions which agree reasonably well with the astrophysical constraints and observations. Though there are many candidate-theories, the proposed model of this paper presents an entirely new approach (cosmological nuclear energy) as a possible candidate for dark energy.Comment: 17 pages, 4 figures, minor correction

Holographic dark energy in a non-flat universe with Granda-Oliveros cut-off

Motivated by Granda and Oliveros (GO) model, we generalize their work to the non-flat case. We obtain the evolution of the dark energy density, the deceleration and the equation of state parameters for the holographic dark energy model in a non-flat universe with GO cut-off. In the limiting case of a flat universe, i.e. $k = 0$, all results given in GO model are obtained.Comment: 11 pages, 5 figure

Interacting polytropic gas model of phantom dark energy in non-flat universe

By introducing the polytropic gas model of interacting dark energy, we obtain the equation of state for the polytropic gas energy density in a non-flat universe. We show that for even polytropic index by choosing $K>Ba^{\frac{3}{n}}$, one can obtain $\omega^{\rm eff}_{\Lambda}<-1$, which corresponds to a universe dominated by phantom dark energy.Comment: 7 page

Constraining the dark energy with galaxy clusters X-ray data

The equation of state characterizing the dark energy component is constrained by combining Chandra observations of the X-ray luminosity of galaxy clusters with independent measurements of the baryonic matter density and the latest measurements of the Hubble parameter as given by the HST key project. By assuming a spatially flat scenario driven by a "quintessence" component with an equation of state $p_x = \omega \rho_x$ we place the following limits on the cosmological parameters $\omega$ and $\Omega_{\rm{m}}$: (i) $-1 \leq \omega \leq -0.55$ and $\Omega_{\rm m} = 0.32^{+0.027}_{-0.014}$ (1$\sigma$) if the equation of state of the dark energy is restricted to the interval $-1 \leq \omega < 0$ (\emph{usual} quintessence) and (ii) $\omega = -1.29^{+0.686}_{-0.792}$ and $\Omega_{\rm{m}} = 0.31^{+0.037}_{-0.034}$ ($1\sigma$) if $\omega$ violates the null energy condition and assume values $< -1$ (\emph{extended} quintessence or ``phantom'' energy). These results are in good agreement with independent studies based on supernovae observations, large-scale structure and the anisotropies of the cosmic background radiation.Comment: 6 pages, 4 figures, LaTe