The dispersion relations for electrostatic plane-wave propagation in a collisionless thermal plasma are discussed in the context of the nonextensive statistics proposed by Tsallis. Analytic formulas both for the undamped (Bohm-Gross) and Landau damped waves are derived and compared with the standard results. In the extensive limiting case $\mathrm{}(q=1\mathrm{}),$ the classical dispersion relations based on the Maxwellian distribution are recovered. It is shown that the experimental results points to a class of Tsallis’s velocity distribution described by a nonextensive q-parameter smaller than unity.

In order to shed some light on the current discussion about $f(R)$-gravity theories we derive and discuss the bounds imposed by the energy conditions on a general $f(R)$ functional form. The null and strong energy conditions in this framework are derived from Raychaudhuri’s equation along with the requirement that gravity is attractive, whereas the weak and dominant energy conditions are stated from a comparison with the energy conditions that can be obtained in a direct approach via an effective energy-momentum tensor for $f(R)$ gravity. As a concrete application of the energy conditions to locally homogeneous and isotropic $f(R)$ cosmology, the recent estimated values of the deceleration and jerk parameters are used to examine the bounds from the weak energy condition on the parameters of two families of $f(R)$-gravity theories.

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without a dark energy matter component. If gravity is governed by a $f(R)$ theory, a number of issues should be reexamined in this framework, including the violation of causality problem on nonlocal scale. We examine the question as to whether the $f(R)$ gravity theories permit space-times in which the causality is violated. We show that the field equations of these $f(R)$ gravity theories do not exclude solutions with breakdown of causality for a physically well-motivated perfect-fluid matter content. We demonstrate that every perfect-fluid Gödel-type solution of a generic $f(R)$ gravity satisfying the condition $df/dR>0$ is necessarily isometric to the Gödel geometry, and therefore presents violation of causality. This result extends a theorem on Gödel-type models, which has been established in the context of general relativity. We also derive an expression for the critical radius $r_c$ (beyond which the causality is violated) for an arbitrary $f(R)$ theory, making apparent that the violation of causality depends on both the $f(R)$ gravity theory and the matter content. As an illustration, we concretely take a recent $f(R)$ gravity theory that is free from singularities of the Ricci scalar and is cosmologically viable, and show that this theory accommodates noncausal as well as causal Gödel-type solutions.

In general relativity, the energy conditions are invoked to restrict general energy-momentum tensors $T_{\mu \nu }$ on physical grounds. We show that in the standard Friedmann–Lemaître–Robertson–Walker (FLRW) approach to cosmological modeling where the equation of state of the cosmological fluid is unknown, the energy conditions provide model-independent bounds on the behavior of the distance modulus of cosmic sources as a function of the redshift. We use both the gold and the legacy samples of current type Ia supenovae to carry out a model-independent analysis of the energy conditions violation in the context of standard cosmology.