Correspondence between f(G) gravity and holographic dark energy via power-law solution

In this paper, we discuss cosmological application of holographic Dark Energy (HDE) in the framework of f(G) modified gravity. For this purpose, we construct f(G) model with the inclusion of HDE and a well-known power law form of the scale factor a(t). The reconstructed f(G) is found to satisfy a sufficient condition for a realistic modified gravity model. We find quintessence behavior of effective equation of state (EoS) parameter ω _DE through energy conditions in this context. Moreover, we observe that the squared speed of sound $v_{s}^{2}$ remains negative, which indicates the instability of HDE f(G) model.     

Holographic f(T) gravity model

We try to study the corresponding relation between f(T) gravity and holographic dark energy (HDE). A kind of energy density from f(T) is introduced which has the same role as HDE density. A f(T) model according to the HDE model is calculated. We find out a torsion scalar T based on the scalar factor is assumed by Capoziello et al. (Phys. Lett. B 639:135, 2006). The effective torsion equation of state, deceleration parameter of the holographic f(T)-gravity model are calculated.     

Cosmology of f(T) gravity in a holographic dark energy and nonisotropic background

It is shown that the acceleration of the universe can be understood by considering a f(T) gravity models. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. For these f(T) gravity models, a variant of the accelerating cosmology reconstruction program is developed. We consider spatially homogenous and anisotropic Bianchi type I universe in the context of f(T) gravity. The de Sitter, power-law and general exponential solutions are assumed for the scale factor in each spatial direction and the corresponding cosmological models are reconstructed. We reconstruct f(T) theories from two different holographic dark energy models in different time durations. For the holographic dark energy model, the dark energy dominated era with new setting up is chosen for reconstruction, and the Ricci dark energy model, radiation, matter and dark energy dominated time durations are all investigated. Finally we have obtained a modified gravity action consistent with the holographic dark energy scenario.     

New agegraphic dark energy in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

In this paper, we study a cosmological application of the new agegraphic dark energy density in the f(R) gravity framework. We employ the new agegraphic model of dark energy to obtain the equation of state for the new agegraphic energy density in a spatially flat universe. Our calculations show, taking n<0, that it is possible to have w _Λ crossing −1. This implies that one can generate a phantom-like equation of state from a new agegraphic dark energy model in a flat universe in the modified gravity cosmology framework. Also, we develop a reconstruction scheme for the modified gravity with f(R) action.     

A holographic reconstruction scheme for f(R) gravity and the study of stability and thermodynamic consequences

The present paper reports a study of the reconstruction of f(R) gravity from holographic Ricci dark energy, a specific case of Nojiri–Odintsov holographic DE (ref Nojiri and Odinstov, 2005a), in the presence of bulk viscosity. The reconstructed equation of state (EoS) parameter w_R was found to have a transition from quintessence to phantom in the absence of the bulk viscosity. Thus, the behaviour of w_R for this reconstruction scheme was identified as “quintom” in the absence of the bulk viscosity. However, in the case of the bulk viscous scenario w_R behaves like “quintessence”. Furthermore, the generalized second law of thermodynamics was tested in the case of the reconstructed f(R) gravity. Finally, the stability of this model against small perturbations was demonstrated with the aid of squared speed of sound.     

Wormhole model with a hybrid shape function in f(R,T) gravity

In the present article we propose a new hybrid shape function for wormhole (WH)s in the modified f(R, T) gravity. The proposed shape function satisfied the conditions of WH geometry. Geometrical behavior of WH solutions are discussed in both anisotropic and isotropic cases respectively. Also, the stability of this model is obtained by determining the equilibrium condition. The radial null energy condition and weak energy condition are validated in the proposed shape function indicating the absence of exotic matter in modified f(R, T) gravity.     

Generalized second law of thermodynamics in QCD ghost f(G) gravity

Considering power-law for of scale factor in a flat FRW universe we reported a reconstruction scheme for f(G) gravity based on QCD ghost dark energy. We reconstructed the effective equation of state parameter and observed “quintessence” behavior of the equation of state parameter. Furthermore, considering dynamical apparent horizon as the enveloping horizon of the universe we have observed that the generalized second law of thermodynamics is valid for this reconstructed f(G) gravity.     

Cosmological evolution for dark energy models in f(T) gravity

In this paper, we investigate the behavior of equation of state parameter and energy density for dark energy in the framework of f(T) gravity. For this purpose, we use anisotropic LRS Bianchi type I universe model. The behavior of accelerating universe is discussed for some well-known f(T) models. It is found that the universe takes a transition between phantom and non-phantom phases for f(T) models except exponential and logarithmic models. We conclude that our results are relativity analogous to the results of FRW universe.     

Reconstruction of f(R,T) gravity in anisotropic cosmological models of accelerating universe

In this paper, we search the existence of Bianchi type I cosmological model in f(R,T) gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. We obtain the gravitational field equations in the metric formalism, and reconstruct the corresponding f(R,T) functions. Attention is attached to the special case, f(R,T)=f ₁(R)+f ₂(T) and two examples are assumed for this model. In the first example, we consider the unification of matter dominated and accelerated phases with f(R) gravity in anisotropic universe, and in the second instance, model of f(R,T) gravity with transition of matter dominated phase to the acceleration phase is obtained. In both cases, f(R,T) is proportional to a power of R with exponents depending on the input parameters.     

Power-law and logarithmic entropy-corrected Ricci viscous dark energy and dynamics of scalar fields

In this work, I consider the logarithmic-corrected and the power-law corrected versions of the holographic dark energy (HDE) model in the non-flat FRW universe filled with a viscous Dark Energy (DE) interacting with Dark Matter (DM). I propose to replace the infra-red cut-off with the inverse of the Ricci scalar curvature R. I obtain the equation of state (EoS) parameter ω _Λ , the deceleration parameter q and the evolution of energy density parameter $\varOmega_{D}'$ in the presence of interaction between DE and DM for both corrections. I study the correspondence of the logarithmic entropy corrected Ricci Dark Dnergy (LECRDE) and power-law entropy corrected Ricci Dark Energy (PLECRDE) models with the the Modified Chaplygin Gas (MCG) and some scalar fields including tachyon, K-essence, dilaton and quintessence. I also make comparisons with previous results.     

Cosmology from induced matter model applied to 5D f(R,T) theory

It is well known that the universe is undergoing a phase of accelerated expansion. Plenty of models have already been created with the purpose of describing what causes this non-expected cosmic feature. Among them, one could quote the extradimensional and the f(R,T) gravity models. In this work, in the scope of unifying Kaluza-Klein extradimensional model with f(R,T) gravity, cosmological solutions for density and pressure of the universe are obtained from the induced matter model application. Particular solutions for vacuum quantum energy and radiation are also shown.     

Generalized teleparallel gravity via some scalar field dark energy models

We consider generalized teleparallel gravity in the flat FRW universe with a viable power-law f(T) model. We construct its equation of state and deceleration parameters which give accelerated expansion of the universe in quintessence era for the obtained scale factor. Further, we develop correspondence of f(T) model with scalar field models such as, quintessence, tachyon, K-essence and dilaton. The dynamics of scalar field as well as scalar potential of these models indicate the expansion of the universe with acceleration in the f(T) gravity scenario.     

The generalized second law of thermodynamics for the interacting in f(T) gravity

We study the validity of the generalized second law (GSL) of gravitational thermodynamics in a non-flat FRW universe containing the interacting in f(T) gravity. We consider that the boundary of the universe to be confined by the dynamical apparent horizon in FRW universe. In general, we discuss the effective equation of state, deceleration parameter and GLS in this framewok. Also, we find that the interacting-term Q modifies these quantities and in particular, the evolution of the total entropy, results in an increases on the GLS of thermodynamic, by a factor $4\pi R_{A}^{3} Q/3$ . By using a viable f(T) gravity with an exponential dependence on the torsion, we develop a model where the interaction term is related to the total energy density of matter. Here, we find that a crossing of phantom divide line is possible for the interacting-f(T) model.     

Pilgrim dark energy in f(T,T G ) cosmology

We work on the reconstruction scenario of pilgrim dark energy (PDE) in f(T,T _G ). In PDE model it is assumed that a repulsive force that is accelerating the Universe is phantom type with (w _DE f(T,T _G ) models and correspondingly evaluate equation of state parameter for various choices of scale factor. Also, we assume polynomial form of f(T,T _G ) in terms of cosmic time and reconstruct H and w _DE in this manner. Through discussion, it is concluded that PDE shows aggressive phantom-like behavior for s=?2 in f(T,T _G ) gravity.     

Bulk viscous cosmological models in f(R,T) theory of gravity

We have constructed Locally Rotationally Symmetric Bianchi type I (LRSBI) cosmological models in the f(R,T) theory of gravity when the source of gravitation is the bulk viscous fluid. The models are constructed for f(R,T)=R+2f(T) and f(R,T)=f ₁(R)+f ₂(T). We found that in the first case the model degenerates into effective stiff fluid model of the universe. In the second case we obtained degenerate effective stiff fluid model as well as general bulk viscous models of the universe. Some physical and kinematical properties of the models are also discussed.     

Anisotropic cosmological models in f(R,T) gravity according to holographic and new agegraphic dark energy

The paper deals with a spatially homogeneous and anisotropic universe filled with perfect fluid and dark energy components. We consider the f(R,T) theory according to holographic and new agegraphic dark energy in the Bianchi type I universe. In this study, we concentrate on two particular models of f(R,T) gravity namely, R+2f(T) and f(R)+λT. We conclude that the derived f(R,T) models can represent phantom or quintessence regimes of the universe.     

LRS Bianchi type-I cosmological model in f(R,T) theory of gravity

The exact solutions of the field equations in respect of LRS Bianchi type-I space time filled with perfect fluid in the framework of f(R,T) gravity (Harko et al., arXiv: [gr-qc], 2011) are derived. The physical behavior of the model is studied. In fact, the possibility of reconstruction of the LRS Bianchi type-I cosmology with an appropriate choice of a function f(T) has been proved in f(R,T) gravity.     

Cosmological implications of exponential harmonic field with collisional matter

We have studied the evolution of cosmological parameters by considering exponential harmonic field with collisional matter. A comparison has been made with the behavior of these parameters in the presence of ordinary matter and the model \(\Lambda CDM\). We have also compared the evolution of these parameters with the ones obtained in the modified gravity f(R) and f(R, T) theory case. The results are in line with those of the modified gravity so that the harmonic exponential field can be used to explain why the Universe has gone from the deceleration phase to the acceleration phase.     

Revisiting the coincidence problem in f(R) gravitation

The energy densities of dark matter (DM) and dark energy (DE) are of the same order at the present epoch despite the fact that both these quantities have contrasting characteristics and are presumed to have evolved distinctively with cosmic evolution. This is a major issue in standard ΛCDM cosmology and is termed “The Coincidence Problem” which hitherto cannot be explained by any fundamental theory. In this spirit, Bisabr (2010) reported a cosmological scenario in f(R) gravity where DM and DE interact and exchange energy with each other and therefore evolve dependently. We investigate the efficiency and model independancy of the technique reported in Bisabr (2010) in addressing the Coincidence problem with the help of two f(R) gravity models with model parameters constrained from various observations. Our result confirm the idea that not all scalar-tensor gravity theories and models can circumvent the Coincidence Problem and any cosmological scenario with interacting fluids is highly model dependent and hence alternate model independent theories and ideas should be nominated to solve this mystery.