LambdaCDM epoch reconstruction from F(R,G) and modified Gauss-Bonnet gravities

Dark energy cosmology is considered in a modified Gauss-Bonnet model of gravity with and without a scalar field. It is shown that these generalizations of General Relativity endow it with a very rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence or phantom cosmic acceleration, with the possibility to describe the transition from a decelerating to an accelerating phase explicitly. It is demonstrated here that these modified GB and scalar-GB theories are perfectly viable as cosmological models. They can describe the LambdaCDM cosmological era without any need for a cosmological constant. Specific properties of these theories of gravity in different particular cases, such as the de Sitter one, are studied.Comment: 14 page

Oscillations of the F(R) dark energy in the accelerating universe

Oscillations of the $F(R)$ dark energy around the phantom divide line, $\omega_{DE}=-1$, both during the matter era and also in the de Sitter epoch are investigated. The analysis during the de Sitter epoch is revisited by expanding the modified equations of motion around the de Sitter solution. Then, during the matter epoch, the time dependence of the dark energy perturbations is discussed by using two different local expansions. For high values of the red shift, the matter epoch is a stable point of the theory, giving the possibility to expand the $F(R)$-functions in terms of the dark energy perturbations. In the late-time matter era, the realistic case is considered where dark energy tends to a constant. The results obtained are confirmed by precise numerical computation on a specific model of exponential gravity. A novel and very detailed discussion is provided on the critical points in the matter era and on the relation of the oscillations with possible singularities.Comment: 23 pages, 11 figures, version to appear in EPJ

On thermodynamics second law in the modified Gauss Bonnet gravity

The second law and the generalized second law of thermodynamics in cosmology in the framework of the modified Gauss-Bonnet theory of gravity are investigated. The conditions upon which these laws hold are derived and discussed.Comment: 9pages, typos corrected, references adde

Inflation and late-time cosmic acceleration in non-minimal Maxwell-F(R)F(R) gravity and the generation of large-scale magnetic fields

We study inflation and late-time acceleration in the expansion of the universe in non-minimal electromagnetism, in which the electromagnetic field couples to the scalar curvature function. It is shown that power-law inflation can be realized due to the non-minimal gravitational coupling of the electromagnetic field, and that large-scale magnetic fields can be generated due to the breaking of the conformal invariance of the electromagnetic field through its non-minimal gravitational coupling. Furthermore, it is demonstrated that both inflation and the late-time acceleration of the universe can be realized in a modified Maxwell-$F(R)$ gravity which is consistent with solar system tests and cosmological bounds and free of instabilities. At small curvature typical for current universe the standard Maxwell theory is recovered. We also consider classically equivalent form of non-minimal Maxwell-$F(R)$ gravity, and propose the origin of the non-minimal gravitational coupling function based on renormalization-group considerations.Comment: 20 pages, no figure, JCAP versio

Finite-time future singularities in modified Gauss-Bonnet and F(R,G)\mathcal{F}(R,G) gravity and singularity avoidance

We study all four types of finite-time future singularities emerging in late-time accelerating (effective quintessence/phantom) era from $\mathcal{F}(R,G)$-gravity, where $R$ and $G$ are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of $\mathcal{F}(R,G)$-gravity, we also investigate modified Gauss-Bonnet gravity, so-called $F(G)$-gravity. In particular, we reconstruct the $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss-Bonnet gravity is presented. It turns out that adding such non-singular modified gravity to singular Dark Energy makes the combined theory to be non-singular one as well.Comment: 35 pages, no figure, published version, references adde