We review the paradigm of quintom cosmology. This scenario is motivated by the observational indications that the equation of state of dark energy across the cosmological constant boundary is mildly favored, although the data are still far from being conclusive. As a theoretical setup we introduce a no-go theorem existing in quintom cosmology, and based on it we discuss the conditions for the equation of state of dark energy realizing the quintom scenario. The simplest quintom model can be achieved by introducing two scalar fields with one being quintessence and the other phantom. Based on the double-field quintom model we perform a detailed analysis of dark energy perturbations and we discuss their effects on current observations. This type of scenarios usually suffer from a manifest problem due to the existence of a ghost degree of freedom, and thus we review various alternative realizations of the quintom paradigm. The developments in particle physics and string theory provide potential clues indicating that a quintom scenario may be obtained from scalar systems with higher derivative terms, as well as from nonscalar systems. Additionally, we construct a quintom realization in the framework of braneworld cosmology, where the cosmic acceleration and the phantom divide crossing result from the combined effects of the field evolution on the brane and the competition between four and five dimensional gravity. Finally, we study the outsets and fates of a universe in quintom cosmology. In a scenario with null energy condition violation one may obtain a bouncing solution at early times and therefore avoid the Big Bang singularity. Furthermore, if this occurs periodically, we obtain a realization of an oscillating universe. Lastly, we comment on several open issues in quintom cosmology and their connection to future investigations.

We investigate the validity of the generalized second law of thermodynamics, in the cosmological scenario where dark energy interacts with both dark matter and radiation. Calculating separately the entropy variation for each fluid component and for the apparent horizon itself, we show that the generalized second law is always and generally valid, independently of the specific interaction form, of the fluids equation-of-state parameters and of the background geometry.Comment: 7 pages, version published in Phys.Rev.

In this paper we study cosmological application of holographic dark energy density in the Brans-Dicke framework. We employ the holographic model of dark energy to obtain the equation of state for the holographic energy density in non-flat (closed) universe enclosed by the event horizon measured from the sphere of horizon named L. Our calculation show, taking Ω Λ = 0.73 for the present time, the lower bound of w Λ is −0.9. Therefore it is impossible to have w Λ crossing −1. This implies that one can not generate phantom-like equation of state from a holographic dark energy model in non-flat universe in the Brans-Dicke cosmology framework. In the other hand, we suggest a correspondence between the holographic dark energy scenario in flat universe and the phantom dark energy model in framework of Brans-Dicke theory with potential. *

In this paper we consider a correspondence between the holographic dark energy density and Chaplygin gas energy density in FRW universe. Then we reconstruct the potential and the dynamics of the scalar field which describe the Chaplygin cosmology.Comment: 9 pages, no figure

In this paper we study the Generalized Minimal Massive Gravity (GMMG) in asymptotically AdS 3 background. The generalized minimal massive gravity theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. We study the linearized excitations around the AdS 3 background and find that at special point (tricritical) in parameter space the two massive graviton solutions become massless and they are replaced by two solutions with logarithmic and logarithmic-squared boundary behavior. So it is natural to proposed that GMMG model could also provide a holographic description for a 3−rank Logarithmic Conformal Field Theory (LCFT). We calculate the energy of the linearized gravitons in AdS 3 background, and show that the theory is free of negative-energy bulk modes. Then we obtain the central charges of the CFT dual explicitly and show GMMG also avoids the aforementioned "bulk-boundary unitarity clash". After that we show that General Zwei-Dreibein Gravity (GZDG) model can reduce to GMMG model. Finally by a Hamiltonian analysis we show that the GMMG model has no Boulware-Deser ghosts and this model propagate only two physical modes.

In this paper we consider the holographic model of interacting dark energy in non-flat universe. With the choice of c ≤ 0.84, the interacting holographic dark energy can be described by a phantom scalar field. Then we show this phantomic description of the holographic dark energy with c ≤ 0.84 and reconstruct the potential of the phantom scalar field. *

The holographic Λ(t)CDM model in a non-flat universe is studied in this paper. In this model, to keep the form of the stress-energy of the vacuum required by general covariance, the holographic vacuum is enforced to exchange energy with dark matter. It is demonstrated that for the holographic model the best choice for the IR cutoff of the effective quantum field theory is the event horizon size of the universe. We derive the evolution equations of the holographic Λ(t)CDM model in a non-flat universe. We constrain the model by using the current observational data, including the 557 Union2 type Ia supernovae data, the cosmic microwave background anisotropy data from the 7-yr WMAP, and the baryon acoustic oscillation data from the SDSS. Our fit results show that the holographic Λ(t)CDM model tends to favor a spatially closed universe (the best-fit value of Ω k0 is −0.042), and the 95% confidence level range for the spatial curvature is −0.101 < Ω k0 < 0.040. We show that the interaction between the holographic vacuum and dark matter induces an energy flow of which the direction is first from vacuum to dark matter and then from dark matter to vacuum. Thus, the holographic Λ(t)CDM model is just a time-varying vacuum energy scenario in which the interaction between vacuum and dark matter changes sign during the expansion of the universe. PACS numbers: 95.36.+x, 98.80.Es, 98.80.-k

We investigate canonical, phantom and quintom models, with the various fields being nonminimally coupled to gravity, in the framework of holographic dark energy. We classify them and we discuss their cosmological implications. In particular, we examine the present value of the dark energy equation-of-state parameter and the crossing through the phantom divide, and we extract the conditions for a future cosmological singularity. The combined scenarios are in agreement with observations and reveal interesting cosmological behaviors.PACS numbers: 04.50. Kd, 95.36.+x,04.60.Bc