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We construct spherically symmetric and static solutions in F(R)$F(R)$ gravity coupled with electromagnetic fields. The solutions include new types of black holes with electric and magnetic charges. We show that the higher‐derivative terms make the curvature singularity much softer than that in the charged black holes in Einstein's general relativity. We calculate some thermodynamical quantities of the obtained black holes like entropy, Hawking radiation, and quasi‐local energy and we confirm that the black hole solutions satisfy the first law of thermodynamics. Finally, we study the stability analysis using the odd‐type mode and show that there are stable black hole solutions and the radial speed of the parity‐odd mode is unit, that is, the speed of light. The authors construct spherically symmetric and static solutions in F(R) gravity coupled with electromagnetic fields. The solutions include new types of black holes with electric and magnetic charges. It will be shown that the higher‐derivative terms make the curvature singularity much softer than that in the charged black holes in Einstein's general relativity. What follows are calculations of some thermodynamical quantities of the obtained black holes like entropy, Hawking radiation, and quasi‐local energy and the confirmation that the black hole solutions satisfy the first law of thermodynamics. Finally, the stability is analyzed using the odd‐type mode and it will be shown that there are stable black hole solutions and the radial speed of the parity‐odd mode is is just the speed of light. [ABSTRACT FROM AUTHOR]

Abstract In this work we study a modified version of f (R) gravity in which higher order kinetic terms of a scalar field are added in the action of vacuum f (R) gravity. This type of theory is a type of k -essence f (R) gravity, and it belongs to the general class of f (R , ϕ , X) theories of gravity, where ϕ is a scalar field and X = 1 2 ∂ μ ϕ ∂ μ ϕ. We focus on the inflationary phenomenology of the model, in the slow-roll approximation, and we investigate whether viable inflationary evolutions can be realized in the context of this theory. We use two approaches, firstly by imposing the slow-roll conditions and by using a non-viable vacuum f (R) gravity. As we demonstrate, the spectral index of the primordial scalar perturbations and the tensor-to-scalar ratio of the resulting theory can be compatible with the latest observational data. In the second approach, we fix the functional form of the Hubble rate as a function of the e -foldings number, and we modify well-known vacuum f (R) gravity reconstruction techniques, in order to find the k -essence f (R) gravity which can realize the given Hubble rate. Accordingly, we calculate the slow-roll indices and the corresponding observational indices, and we also provide general formulas of these quantities in the slow-roll approximation. As we demonstrate, viability can be obtained in this case too, however the result is strongly model dependent. In addition, we discuss when ghosts can occur in the theory, and we investigate under which conditions ghosts can be avoided by using a particular class of models. Finally, we qualitatively discuss the existence of inflationary attractors for the non-slow-roll theory, and we provide hints towards finding general de Sitter attractors for the theory at hand. [ABSTRACT FROM AUTHOR]

Energy conditions can play an important role in defining the cosmological evolution. Specifically acceleration/deceleration of cosmic fluid, as well as the emergence of Big Rip singularities, can be related to the constraints imposed by the energy conditions. Here we discuss this issue for f ( R ) gravity considering also conformal transformations. Cosmological solutions and equations of state can be classified according to energy conditions. The qualitative change of some energy conditions when transformation from the Jordan frame to the Einstein frame done is also observed. [ABSTRACT FROM AUTHOR]

We systematically review some standard issues and also the latest developments of modified gravity in cosmology, emphasizing on inflation, bouncing cosmology and late-time acceleration era. Particularly, we present the formalism of standard modified gravity theory representatives, like F ( R ) , F ( G ) and F ( T ) gravity theories, but also several alternative theoretical proposals which appeared in the literature during the last decade. We emphasize on the formalism developed for these theories and we explain how these theories can be considered as viable descriptions for our Universe. Using these theories, we present how a viable inflationary era can be produced in the context of these theories, with the viability being justified if compatibility with the latest observational data is achieved. Also we demonstrate how bouncing cosmologies can actually be described by these theories. Moreover, we systematically discuss several qualitative features of the dark energy era by using the modified gravity formalism, and also we critically discuss how a unified description of inflation with dark energy era can be described by solely using the modified gravity framework. Finally, we also discuss some astrophysical solutions in the context of modified gravity, and several qualitative features of these solutions. The aim of this review is to gather the different modified gravity techniques and form a virtual modified gravity “toolbox”, which will contain all the necessary information on inflation, dark energy and bouncing cosmologies in the context of the various forms of modified gravity. [ABSTRACT FROM AUTHOR]

Motivated by the fact that the pre-inflationary era may evolve in an exotic way, in this work we formalize anisotropic evolution in the context of modified gravity, focusing on pre-inflationary and near the vicinity of the inflationary epochs. We specialize on specific metrics like Bianchi and Taub and we formalize the inflationary theory in vacuum F (R) gravity, in F (R) gravity with an extra scalar field and in Gauss-Bonnet gravity. We discuss the qualitative effects of the anisotropies on the evolution of the Universe and also we consider several specific solutions, like the de Sitter solution, in both the isotropic and anisotropic contexts. Furthermore, several exotic modified gravity cosmological solutions, like the ones which contain finite time singularities, are also discussed in brief. [ABSTRACT FROM AUTHOR]

We investigate the Newton law in the unimodular F( R) gravity. In the standard F( R) gravity, due to the extra scalar mode, there often appear the large corrections to the Newton law and such models are excluded by the experiments and/or the observations. In the unimodular F( R) gravity, however, the extra scalar mode become not to be dynamical due to the unimodular constraint and there is not any correction to the Newton law. Even in the unimodular Einstein gravity, the Newton law is reproduced but the mechanism is a little bit different from that in the unimodular F( R) gravity. We also investigate the unimodular F( R) gravity in the covariant formulation. In the covariant formulation, we include the three-form field. We show that the three-form field could not have any unwanted property, like ghost nor correction to the Newton law. In the covariant formulation, however, the above extra scalar mode becomes dynamical and could give a correction to the Newton law. We also show that there are no difference in the Friedmann-Robertson-Walker (FRW) dynamics in the non-covariant and covariant formulation. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of various aspects of projectable F( R) Hořava-Lifshitz (HL) gravity. We show that some versions of F( R) HL gravity may have stable de Sitter solution and unstable flat-space solution. In this case, the problem of scalar graviton does not appear because flat space is not vacuum state. Generalizing the U(1) HL theory proposed in , we formulate U(1) extension of scalar theory and of F( R) Hořava-Lifshitz gravity. The Hamiltonian approach for such the theory is developed in full detail. It is demonstrated that its Hamiltonian structure is the same as for the non-relativistic covariant HL gravity. The spectrum analysis performed around the flat background indicates the consistency of the theory because it contains a graviton with only transverse polarization. Finally, we analyze the spatially flat FRW equations for U(1) invariant F( R) Hořava-Lifshitz gravity. [ABSTRACT FROM AUTHOR]

In this work we shall address the ghost issue of F (R , G) gravity, which is known to be plagued with ghost degrees of freedom. These ghosts occur due to the presence of higher than two derivatives in the field equations, and can arise even when considering cosmological perturbations, where superluminal modes may arise in the theory. If we consider the quantum theory, the ghosts generate the negative norm states, which give the negative probabilities, and therefore the ghosts are physically inconsistent. Motivated by the importance of F (R , G) gravity for providing viable inflationary and dark energy phenomenologies, in this work we shall provide a technique that can render F (R , G) gravity theories free from ghost degrees of freedom. This will be done by introducing two auxiliary scalar fields, and by employing the Lagrange multiplier technique, the theory is ghost free in the Einstein frame. Also the framework can be viewed as a reconstruction technique and can be used as a method in order to realize several cosmological evolutions of interest. We demonstrate how we can realize several cosmologically interesting phenomenologies by using the reconstruction technique. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d''Alembertian of the Ricci scalar, . Casting the dynamical equations into local form, we derive the fixed points of the dynamics and demonstrate the existence and stability of a one parameter family of dark energy solutions for a simple choice, . The effective EoS parameter is given by, and the stability of the solutions is guaranteed provided that . For and , the underlying system exhibits phantom and non-phantom behavior respectively; the de Sitter solution corresponds to . For a wide range of initial conditions, the system mimics dust like behavior before reaching the stable fixed point. The late time phantom phase is achieved without involving negative kinetic energy fields. A brief discussion on the entropy of de Sitter space in non-local model is included. [Copyright &y& Elsevier]

Abstract: We show that -gravity can, in general, give rise to cosmological viable models compatible with a matter-dominated epoch evolving into a late accelerated phase. We discuss the various representations of -gravity as an ideal fluid or a scalar–tensor gravity theory, taking into account conformal transformations. We point out that mathematical equivalence does not correspond, in several cases, to the physical equivalence of Jordan frame and Einstein frame. Finally, we show that wide classes of gravity models, including matter and accelerated phases, can be phenomenologically reconstructed by means of observational data. In principle, any popular quintessence models could be “reframed” as an -gravity model. [Copyright &y& Elsevier]

Abstract: Dark energy dynamics of the universe can be achieved by equivalent mathematical descriptions taking into account generalized fluid equations of state in General Relativity, scalar-tensor theories or modified gravity in Einstein or Jordan frames. The corresponding technique transforming equation of state description to scalar-tensor or modified gravity is explicitly presented. We show that such equivalent pictures can be discriminated by matching solutions with data capable of selecting the true physical frame. [Copyright &y& Elsevier]

In this article, we seek exact charged spherically symmetric black holes (BHs) with considering f (R) gravitational theory. This BH is characterized by convolution and error functions. Those two functions depend on a constant of integration which is responsible to make such a solution deviate from Einstein's general relativity (GR). The error function which constitutes the charge potential of the Maxwell field depends on the constant of integration and when this constant is vanishing we can not reproduce Reissner-Nordström BH in the lower order of f (R). This means that we can not reproduce Reissner-Nordström BH in lower-order–curvature theory, i.e., in GR limit f (R) = R , we can not get the well known charged BH. We study the physical properties of these BHs and show that it is asymptotically approached as a flat spacetime or approach AdS/dS spacetime. Also, we calculate the invariants of the BHS and show that the singularities are milder than those of BH's of GR. Additionally, we derive the stability condition through the use of geodesic deviation. Moreover, we study the thermodynamics of our BH and show the effect of the higher-order–curvature theory. Finally, we study the stability analysis using the odd-type mode and show that all the BHs are stable and have radial speed equal to one. [ABSTRACT FROM AUTHOR]

The detection of gravitational wave modes and polarizations could constitute an extremely important signature to discriminate among different theories of gravity. According to this statement, it is possible to prove that higher-order non-local gravity has formally the same gravitational spectrum of higher-order local gravity. In particular, we consider the cases of f (R , □ R , □ 2 R , ⋯ , □ n R) = R + ∑ i = 1 n α i R □ i R gravity, linear with respect to both R and □ i R and f (R , □ R) = R + α (□ R) 2 gravity, quadratic with respect to □ R , where it is demonstrated the graviton amplitude changes if compared with General Relativity. We also obtain the gravitational spectrum of higher-order non-local gravity f (R , □ − 1 R , □ − 2 R , ⋯ , □ − n R) = R + ∑ i = 1 n α i R □ − i R. In this case, we have three state of polarization and n + 3 oscillation modes. More in detail, it is possible to derive two transverse tensor (+) and (×) standard polarization modes of frequency ω 1 , massless and with 2-helicity; n + 1 further scalar modes of frequency ω 2 , ... , ω n + 2 , massive and with 0-helicity, each of which has the same mixed polarization, partly longitudinal and partly transverse. [ABSTRACT FROM AUTHOR]