Non-Gaussian effects on quantum entropies

AbstractA deduction of generalized quantum entropies within the non-Gaussian frameworks, Tsallis and Kaniadakis, is derived using a generalized combinatorial method and the so-called q and κ calculus. In agreement with previous results, we also show that for the Tsallis formulation the q-quantum entropy is well-defined for values of the nonextensive parameter q lying in the interval [0,2]

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

Current lookback time-redshift bounds on dark energy

We investigate observational constraints on dark energy models from lookback time (LT) estimates of 32 old passive galaxies distributed over the redshift interval $0.11 \leq z \leq 1.84$. To build up our LT sample we combine the age measurements for these 32 objects with estimates of the total age of the Universe, as obtained from current CMB data. We show that LT data may provide bounds on the cosmological parameters with accuracy competitive with type Ia Supernova methods. In order to break possible degeneracies between models parameters, we also discuss the bounds when our lookback time versus redshift sample is combined with with the recent measurement of the baryonic acoustic oscillation peak and the derived age of the Universe from current CMB measurements.Comment: 6 pages, 4 figures, LaTe

Age Constraints on Brane Models of Dark Energy

Inspired by recent developments in particle physics, the so-called brane world cosmology seems to provide an alternative explanation for the present dark energy problem. In this paper, we use the estimated age of high-$z$ objects to constrain the value of the cosmological parameters in some particular scenarios based on this large scale modification of gravity. We show that such models are compatible with these observations for values of the crossover distance between the 4 and 5 dimensions of the order of $r_c \leq 1.67H_o^{-1}$.Comment: 4 pages, 2 figures, 1 table, to appear in Phys. Rev.

Non-extensive statistics and the stellar polytrope index

We use physical constrains imposed from the H-Theorem and from the negative nature of the heat capacity of self-gravitating thermodynamically isolated systems to investigate some possible limits on the stellar polytrope index $n$ within the domain of a classical non-extensive kinetic theory.Comment: 4 pages, 2 figures, LaTe

Dark Matter and Dark Energy

I briefly review our current understanding of dark matter and dark energy. The first part of this paper focusses on issues pertaining to dark matter including observational evidence for its existence, current constraints and the `abundance of substructure' and `cuspy core' issues which arise in CDM. I also briefly describe MOND. The second part of this review focusses on dark energy. In this part I discuss the significance of the cosmological constant problem which leads to a predicted value of the cosmological constant which is almost $10^{123}$ times larger than the observed value \la/8\pi G \simeq 10^{-47}GeV$^4$. Setting \la to this small value ensures that the acceleration of the universe is a fairly recent phenomenon giving rise to the `cosmic coincidence' conundrum according to which we live during a special epoch when the density in matter and \la are almost equal. Anthropic arguments are briefly discussed but more emphasis is placed upon dynamical dark energy models in which the equation of state is time dependent. These include Quintessence, Braneworld models, Chaplygin gas and Phantom energy. Model independent methods to determine the cosmic equation of state and the Statefinder diagnostic are also discussed. The Statefinder has the attractive property \atridot/a H^3 = 1 for LCDM, which is helpful for differentiating between LCDM and rival dark energy models. The review ends with a brief discussion of the fate of the universe in dark energy models.Comment: 40 pages, 11 figures, Lectures presented at the Second Aegean Summer School on the Early Universe, Syros, Greece, September 2003, New References added Final version to appear in the Proceeding

Global Structure of Deffayet (Dvali-Gabadadze-Porrati) Cosmologies

We detail the global structure of the five-dimensional bulk for the cosmological evolution of Dvali-Gabadadze-Porrati braneworlds. The picture articulated here provides a framework and intuition for understanding how metric perturbations leave (and possibly reenter) the brane universe. A bulk observer sees the braneworld as a relativistically expanding bubble, viewed either from the interior (in the case of the Friedmann-Lemaitre-Robertson-Walker phase) or the exterior (the self-accelerating phase). Shortcuts through the bulk in the first phase can lead to an apparent brane causality violation and provide an opportunity for the evasion of the horizon problem found in conventional four-dimensional cosmologies. Features of the global geometry in the latter phase anticipate a depletion of power for linear metric perturbations on large scales.Comment: 15 pages, 4 figures, RevTeX. References adde

A parametric model for dark energy

Determining the mechanism behind the current cosmic acceleration constitutes a major question nowadays in theoretical physics. If the dark energy route is taken, this problem may potentially bring to light new insights not only in Cosmology but also in high energy physics theories. Following this approach, we explore in this paper some cosmological consequences of a new time-dependent parameterization for the dark energy equation of state (EoS), which is a well behaved function of the redshift $z$ over the entire cosmological evolution, i.e., $z\in [-1,\infty)$. This parameterization allows us to divide the parametric plane $(w_0,w_1)$ in defined regions associated to distinct classes of dark energy models that can be confirmed or excluded from a confrontation with current observational data. A statistical analysis involving the most recent observations from type Ia supernovae, baryon acoustic oscillation peak, Cosmic Microwave Background shift parameter and Hubble evolution $H(z)$ is performed to check the observational viability of the EoS parameterization here proposed.Comment: 6 pages, 3 figures, LaTe

Observational constraints on the time-dependence of dark energy

One of the most important questions nowadays in physics concerns the nature of the so-called dark energy. It is also a consensus among cosmologists that such a question will not be answered on the basis only of observational data. However, it is possible to diminish the range of possibilities for this dark component by comparing different dark energy scenarios and finding which models can be ruled out by current observations. In this paper, by asssuming three distinct parametrizations for the low-redshift evolution of the dark energy equation of state (EOS), we consider the possibility of discriminating between evolving dark energy and $\Lambda$CDM models from a joint analysis involving the most recent radio sources gravitational lensing sample, namely, the Cosmic All Sky Survey (CLASS) statistical data and the recently published \emph{gold} SNe Ia sample. It is shown that this particular combination of observational data restricts considerably the dark energy parameter space, which enables possible distinctions between time-dependent and constant EOS's.Comment: 5 pages, 1 figure, to appear in Nuclear Physics

Negative heat capacity and non-extensive kinetic theory

The negative nature of the heat capacity $C_V$ of thermodynamically isolated self-gravitating systems is rediscussed in the framework of a non-extensive kinetic theory. It is found that the dependence of $C_V$ on the non-extensive parameter $q$ gives rise to a negative branch with the critical value corresponding to $q = 5/3$ ($C_V\to - \infty$).Comment: 7 pages, 1 figure, revised version to appear in Phys. Lett.