Реферат: In the present work, we review some general aspects of modified gravity theories, investigating mathematical and physical properties and, more specifically, the feature of viable and realistic models able to reproduce the dark energy epoch and the early-time inflation. We will discuss the black hole solutions in generalized theories of gravity: it is of fundamental interest to understand how properties and laws of black holes in General Relativity can be addressed in the framework of modified theories. In particular, we will discuss the energy issue and the possibility to derive the First Law of thermodynamics from the field equations. Then, in the analysis of cosmological solutions, we will pay a particular attention to the occurrence of finite-time future singularities and to the possibility to avoid them in $\mathcal F(R,G)$-gravity. Furthermore, realistic models of $F(R)$-gravity will be analyzed in the detail. A general feature occurring in matter era will be shown, namely the high derivatives of Hubble parameter may be influenced by the high frequency oscillation of the dark energy and some correction term is required in order to stabilize the theory at high redshift. The inflationary scenario is also carefully analyzed and an unified description of the universe is risen. In the final part of the work, we will have a look at the last developments in modified gravity, namely we will investigate cosmological and black hole solutions in a covariant field theory of gravity and we will introduce the extended \"teleparallel\" $F(T)$-gravity theories. A nice application to the dark matter problem will be presented.
Loop Quantum Corrections to Statefinder Parameters of Dark Energy
Реферат: In this paper, we have calculated the statefinder parameters for the Friedmann-Robertson-Walker (FRW) Universe in the gravitational framework of loop quantum cosmology (LQC). As examples, we study two types of dark energy models namely Holographic dark energy and New Age graphic dark energy.
Reconstruction of f(T) and f(R) gravity according to (m,n)-type holographic dark energy
Ключевые слова: теории гравитации*модели гравитации*голографическая темная энергия*модифицированная гравитация*
Реферат: Motivated by earlier works, we extend them by considering a newly proposed model of (m, n)-type holographic dark energy in f(R) and f(T) gravity theories, where R and T represent Ricci scalar and torsion scalar respectively. Specifically, we reconstruct the two later gravity models and discuss their viability and cosmography. The obtained gravity models are free from ghosts, consistent with local solar system tests, and describe effective positive gravitational constant.
Реферат: We consider the thermodynamics and Geometrothermodynamics of the Myers-Perry black holes in five dimensions for three different cases, depending on the values of the angular momenta. We follow Davies approach to study the thermodynamics of black holes and find a non-trivial thermodynamic structure in all cases, which is fully reproduced by the analysis performed with the techniques of Geometrothermodynamics. Moreover, we observe that in the cases when only one angular momentum is present or the two angular momenta are fixed to be equal, i.e. when the thermodynamic system is two dimensional, there is a complete agreement between the divergences of the generalized susceptibilities and the singularities of the equilibrium manifold, whereas when the two angular momenta are fully independent, that is, when the thermodynamic system is three dimensional, additional singularities in the curvature appear. However, we prove that such singularities are due to the changing from a stable phase to an unstable one.
Einstein gravity with Gauss-Bonnet entropic corrections
Реферат: A toy model of Einstein gravity with a Gauss-Bonnet classically \"entropic\" term mimicking a quantum correction is considered. The static black hole solution due to Tomozawa is found and generalized with the inclusion of nontrivial horizon topology, and its entropy is evaluated, deriving the first law by equations of motion. As a result the Bekenstein-Hawking area law turns out to be corrected by a logarithmic area term. A Misner-Sharp expression for the mass of a black hole is found. Within a Friedmann-Lemaitre-Robertson-Walker cosmological setting, the model is used in order to derive modified Friedmann equations. Such new equations are shown to reproduce the first law with the same formal entropy and quasilocal energy of the static case, but here within a Friedmann-Lemaitre-Robertson-Walker space-time interpreted as a dynamical cosmological black hole. A detailed analysis of cosmological solutions is presented, and it is shown that the presence of the correction term provides regular solutions and interesting phases of acceleration and deceleration, as well as, with negligible matter, exact de Sitter solutions.
Holographic, new agegraphic and ghost dark energy models in fractal cosmology
Ключевые слова: модели темной энергии*фрактальная космология*уравнения состояния параметров модели*модель Вселенной*
Реферат: We investigate the holographic, new agegraphic, and ghost dark energy models in the framework of fractal cosmology. We consider a fractal flat Friedmann-Robertson-Walker universe filled with dark energy and matter. We obtain the deceleration and equation of state parameters of the selected dark energy models in the ultraviolet regime and discuss their implications in the early universe.
Noether gauge symmetry for Bianchi type I model in f(T) gravity
Реферат: In this paper, we present the Noether symmetries of a class of the Bianchi type I anisotropic model in the context of f(T) gravity. By solving the system of equations obtained from the Noether symmetry condition, we obtain the form of f(T) as a teleparallel form. This analysis shows that teleparallel gravity has the maximum number of Noether symmetries. We derive the symmetry generators and show that there are five kinds of symmetries, including time and scale invariance under metric coefficients. We classify the symmetries and we obtain the corresponding invariants.
Inhomogeneous Viscous Fluids in a Friedmann-Robertson-Walker (FRW) Universe
Реферат: We give a brief review of some aspects of inhomogeneous viscous fluids in a flat Friedmann-Robertson-Walker Universe. In general, it is pointed out that several fluid models may bring the future Universe evolution to become singular, with the appearance of the so-called Big Rip scenario. We investigate the effects of fluids coupled with dark matter in a de Sitter Universe, by considering several cases. Due to this coupling, the coincidence problem may be solved, and if the de Sitter solution is stable, the model is also protected against the Big Rip singularity.
Holographic superconductors with Weyl Corrections via gauge/gravity duality
Реферат: In this paper, we analytically investigate the properties of Weyl\'s corrected p-wave holographic superconductors by the matching method. The relation between the critical temperature Tc and the charge density p has been obtained as Tc p and the dependence of the expectation value of the condensation operator on the temperature has been found analytically in the form. The critical exponent of the condensation also comes out to be 1/2, which is the universal value in the mean field theory and which has nothing to do with the Weyl coupling gamma. Our results are in very good agreement with the existing numerical results and have been obtained using the variational method.
Noether Gauge Symmetry Approach in Quintom Cosmology
Автор(ы): Aslam A.*Jamil M.*Momeni D.*Myrzakulov R.*Rashid M. A.*Raza M.*
Реферат: literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.