No abstract

No abstract

No abstract

Maxwell's first derivation of the equilibrium distribution function for a dilute gas is generalized in the spirit of the nonextensive q-statistics proposed by Tsallis. As an application, the q-Doppler broadening of spectral lines due to the random thermal motion of the radiating atoms is derived.

We propose a novel cosmological scenario with the space-time emerging from a pure initial de Sitter stage and subsequently evolving into the radiation, matter and dark energy dominated epochs, thereby avoiding the initial singularity and providing a complete description of the expansion history and a natural solution to the horizon problem. The model is based on a dynamical vacuum energy density which evolves as a power series of the Hubble rate. The transit from the inflation into the standard radiation epoch is universal, giving a clue for a successful description of the graceful exit. Since the resulting late time cosmic history is very close to the concordance ΛCDM model, the new unified framework embodies a more complete past cosmic evolution than the standard cosmology.

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis". For q > 0, the q-transport equation satisfies an H-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' q-nonextensive velocity distribution.PACS numbers: 05.45.+b; 05.20.-y; 05.90.+m In 1988 Tsallis proposed a striking generalization of the Boltzmann-Gibbs entropy functional given by [1],

The thermodynamic behavior of vacuum decaying cosmologies is investigated within a manifestly covariant formulation. Such a process corresponds to a continuous irreversible energy flow from the vacuum component to the created matter constituents. It is shown that if the specific entropy per particle remains constant during the process, the equilibrium relations are preserved. In particular, if the vacuum decays into photons, the energy density ρ and average number density of photons n scale with the temperature as ρ ∼ T 4 and n ∼ T 3 . The temperature law is determined and a generalized Planckian type form of the spectrum, which is preserved in the course of the evolution, is also proposed. Some consequences of these results for decaying vacuum FRW type cosmologies as well as for models with "adiabatic" photon creation are discussed. PACS number(s): 98.80hw, 95.30.tg a

In the present mainstream cosmology, matter and spacetime emerged from a singularity and evolved through four distinct periods: early inflation, radiation, dark matter and late-time inflation (driven by dark energy). During the radiation and dark matter dominated stages, the universe is decelerating while the early and late-time inflations are accelerating stages. A possible connection between the accelerating periods remains unknown, and, even more intriguing, the best dark energy candidate powering the present accelerating stage (Λ-vacuum) is plagued with the cosmological constant and coincidence puzzles. Here we propose an alternative solution for such problems based on a large class of time-dependent vacuum energy density models in the form of power series of the Hubble rate, Λ = Λ(H). The proposed class of Λ(H)-decaying vacuum model provides: i) a new mechanism for inflation (different from the usual inflaton models), (ii) a natural mechanism for a graceful exit, which is universal for the whole class of models; iii) the currently accelerated expansion of the universe, iv) a mild dynamical dark energy at present; and v) a final de Sitter stage. Remarkably, the late-time cosmic expansion history of our class of models is very close to the concordance ΛCDM model, but above all it furnishes the necessary smooth link between the initial and final de Sitter stages through the radiation-and matter-dominated epochs.PACS numbers: