Certain aspects of regularity in scalar field cosmological dynamics

We consider dynamics of the FRW Universe with a scalar field. Using Maupertuis principle we find a curvature of geodesics flow and show that zones of positive curvature exist for all considered types of scalar field potential. Usually, phase space of systems with the positive curvature contains islands of regular motion. We find these islands numerically for shallow scalar field potentials. It is shown also that beyond the physical domain the islands of regularity exist for quadratic potentials as well.Comment: 15 pages with 4 figures; typos corrected, final version to appear in Regular and Chaotic Dynamic

Induced cosmological constant and other features of asymmetric brane embedding

We investigate the cosmological properties of an "induced gravity" brane scenario in the absence of mirror symmetry with respect to the brane. We find that brane evolution can proceed along one of four distinct branches. By contrast, when mirror symmetry is imposed, only two branches exist, one of which represents the self-accelerating brane, while the other is the so-called normal branch. This model incorporates many of the well-known possibilities of brane cosmology including phantom acceleration (w < -1), self-acceleration, transient acceleration, quiescent singularities, and cosmic mimicry. Significantly, the absence of mirror symmetry also provides an interesting way of inducing a sufficiently small cosmological constant on the brane. A small (positive) Lambda-term in this case is induced by a small asymmetry in the values of bulk fundamental constants on the two sides of the brane.Comment: 17 pages, 4 figures. New results and two figures discussing transient acceleration are included. Version accepted for publication in JCA

Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities

We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom-like phases. In particular, it is found that there is a case in which a crossing of the phantom divide from the non-phantom (quintessence) phase to the phantom one can be realized when a finite-time future singularity occurs. Moreover, it is demonstrated that the addition of an $R^2$ term can cure the finite-time future singularities in non-local gravity. It is also suggested that in the framework of non-local gravity, adding an $R^2$ term leads to possible unification of the early-time inflation with the late-time cosmic acceleration.Comment: 42 pages, no figure, version accepted for publication in General Relativity and Gravitatio

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