Cosmological evolution with a logarithmic correction in the dark energy entropy

In a thermodynamical model of cosmological FLRW event horizons for the dark energy (DE), we consider a logarithmic corrective term in the entropy to which corresponds a new term in the DE density. This model of $\Lambda (t)$ in an interacting two-component cosmology with cold dark matter (DM) as second component leads to a system of coupled equations, yielding, after numerical resolution, the evolutions of $\Lambda (t)$, the Hubble $H(t)$, vacuum density $\Omega \_{\Lambda}(t)$, deceleration $q(t)$ and statefinder $R(t)$ and $S(t)$ parameters. Its results, compatible with an initial inflation and the current observations of the so-called "concordance model", predict a graceful exit of early inflation and the present acceleration and solve in the same time the age and coincidence problems. Moreover they account for the low-$l$ CMBR power spectrum suppression.Comment: 17 pages, 3 figures, submitted to JCA

SnIa Constraints on the event-horizon Thermodynamical model of Dark Energy

We apply the thermodynamical model of the cosmological event horizon of the spatially flat FLRW metrics to the study of the recent accelerated expansion phase and to the coincidence problem. This model, called "ehT model" hereafter, led to a dark energy (DE) density $\Lambda$ varying as $r^{-2},$ where $r$ is the proper radius of the event horizon. Recently, another model motivated by the holographic principle gave an independent justification of the same relation between $\Lambda$ and $r$. We probe the theoretical results of the ehT model with respect to the SnIa observations and we compare it to the model deduced from the holographic principle, which we call "LHG model" in the following.Our results are in excellent agreement with the observations for $H\_{0}=64kms^{-1}Mpc^{-1}$, and $\Omega \_{\Lambda }^{0}=0.63\_{-0.01}^{+0.1}$, which leads to $q\_{0}=-0.445$ and $z\_{T}\simeq 0.965$

Invariance of the relativistic one-particle distribution function

The one-particle distribution function is of importance both in non-relativistic and relativistic statistical physics. In the relativistic framework, Lorentz invariance is possibly its most fundamental property. The present article on the subject is a contrastive one: we review, discuss critically, and, when necessary, complete, the treatments found in the standard literature

Cosmological energy in a thermo-horizon and the first law

We consider a cosmological horizon, named thermo-horizon, to which are associated a temperature and an entropy of Bekenstein-Hawking and which obeys the first law for an energy flow calculated through the corresponding limit surface. We point out a contradiction between the first law and the definition of the total energy contained inside the horizon. This contradiction is removed when the first law is replaced by a Gibbs' equation for a vacuum-like component associated to the event horizon

Active gravitational mass and the invariant characterization of Reissner-Nordstrom spacetime

We analyse the concept of active gravitational mass for Reissner-Nordstrom spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do.Comment: 6 pages Latex, to appear in General Relativity and Gravitatio

Entropy-Corrected Holographic Dark Energy

The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called ``entropy-corrected holographic dark energy'' (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called ``entropy-corrected agegraphic dark energy'' (ECADE).Comment: 11 pages, 2 tables, revtex4; v2: references adde

Relativistic Brownian Motion

Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special relativity, we review, here, recent progress in the phenomenological description of relativistic diffusion processes. After a brief historical overview, we will summarize basic concepts from the Langevin theory of nonrelativistic Brownian motions and discuss relevant aspects of relativistic equilibrium thermostatistics. The introductory parts are followed by a detailed discussion of relativistic Langevin equations in phase space. We address the choice of time parameters, discretization rules, relativistic fluctuation-dissipation theorems, and Lorentz transformations of stochastic differential equations. The general theory is illustrated through analytical and numerical results for the diffusion of free relativistic Brownian particles. Subsequently, we discuss how Langevin-type equations can be obtained as approximations to microscopic models. The final part of the article is dedicated to relativistic diffusion processes in Minkowski spacetime. Due to the finiteness of velocities in relativity, nontrivial relativistic Markov processes in spacetime do not exist; i.e., relativistic generalizations of the nonrelativistic diffusion equation and its Gaussian solutions must necessarily be non-Markovian. We compare different proposals that were made in the literature and discuss their respective benefits and drawbacks. The review concludes with a summary of open questions, which may serve as a starting point for future investigations and extensions of the theory.Comment: review article, 159 pages, references updated, misprints corrected, App. A.4. correcte