Here, we consider a flat FRW universe whose its horizon entropy meets the Rényi entropy of nonextensive systems. In our model, the ordinary energy-momentum conservation law is not always valid. By applying the Clausius relation as well as the Cai-Kim temperature to the apparent horizon of a flat FRW universe, we obtain modified Friedmann equations. Fitting the model to the observational data on current accelerated universe, some values for the model parameters are also addressed. Our study shows that the current accelerating phase of universe expansion may be described by a geometrical fluid, originated from the non-extensive aspects of geometry, which models a varying dark energy source interacting with matter field in the Rastall way. Moreover, our results indicate that the probable non-extensive features of spacetime may also be used to model a varying dark energy source which does not interact with matter field, and is compatible with the current accelerated phase of universe.

The accelerated expansion of the Universe is one of the greatest challenges of modern physics. One candidate to explain this phenomenon is a new field called dark energy. In this work we have used the Tsallis nonextensive statistical formulation of the Friedmann equation to explore the BarbozaAlcaniz and Chevalier-Polarski-Linder parametric dark energy models and the Wang-Meng and Dalal vacuum decay models. After that, we have discussed the observational tests and the constraints concerning the Tsallis nonextensive parameter.PACS numbers: 98.80. Es, 98.80.Jk

Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there through non-gaussian statistical theories proposed by Tsallis and Kaniadakis. The effect of these nongaussian statistics in the cosmological context is change the strength of the gravitational constant.In this paper, we consider the wCDM model modified by the non-gaussian statistics and investigate the compatibility of these non-gaussian modification with the cosmological observations. In order to analyze in which extend the cosmological data constrain these non-extensive statistics, we use type Ia supernovae, baryon acoustic oscillations, Hubble expansion rate function and the linear growth of matter density perturbations data.There are theoretical evidences that the understanding of gravity has been greatly benefited from a possible connection to thermodynamics. Pioneering works of Bekenstein [1] and Hawking [2] have described this issue. For example, quantities as area and mass of black holes are associated with entropy and temperature respectively. Working on this subject, Jacobson [3] interpreted Einstein field equations as a thermodynamic identity. Padmanabhan [4] gave an interpretation of gravity as an equipartition theorem. Recently, Verlinde [5] brought an heuristic derivation of gravity, both Newtonian and relativistic, at least for static spacetime. The equipartition law of energy has also played an important role. The analysis of the dynamics of an inflationary universe ruled out by the entropic gravity concept was investigated in [6]. On the other hand, one can ask: what is the point of view of gravitational models coupled with thermostatistical theories and vice-versa?The concept introduced by Verlinde is analogous to Jacobson's [3] one, who proposed a thermodynamic derivation of Einstein's equations. The result has shown that the gravitation law derived by Newton can be interpreted as an entropic force originated by perturbations in the information "manifold" caused by the motion of a massive body when it moves away from the holographic screen. An holographic screen can be understood as a storage device for information which is constituted by bits. Bits are the smallest units of information. Verlinde used this idea together with the Unruh result [7] and he obtained Newton's second law. The idea of a entropic gravity/cosmology has been extensively investigated in different contexts, see [8,9] for recent results Moreover, assuming the holographic principle together with the equipartition law of energy, the Newton law of gravitation could be derived. The connection between nonextensive statistical theory and the entropic gravity models [10, 11] make us to realize an arguably bridge between nonextensivity and gravity theories. In this paper...

We apply The Batalin-Tyutin constraint formalism of converting a second class system into a first class system for the rotational quantisation of the SU(2) Skyrme model. We obtain the first class constraint and the Hamiltonian in the extended phase space. The vacuum functional is constructed and evaluated in the unitary gauge and a multiplier dependent gauge. Finally, we discuss the spectrum of the extended theory. The use of the BT formalism on the collective coordinates quantisation of the SU(2) Skyrme model leads an additional term in the usual quantum Hamiltonian that can improve the phenomenology predicted by the Skyrme model.

In this paper the SU(2) Skyrme model will be reformulated as a gauge theory and the hidden symmetry will be investigated and explored in the energy spectrum computation. To this end we purpose a new constraint conversion scheme, based on the symplectic framework with the introduction of Wess-Zumino (WZ) terms in an unambiguous way. It is a positive feature not present on the BFFT constraint conversion. The Dirac's procedure for the first-class constraints is employed to quantize this gauge invariant nonlinear system and the energy spectrum is computed. The finding out shows the power of the symplectic gauge-invariant formalism when compared with another constraint conversion procedures present on the literature.