Cosmological solutions in F(R) Horava-Lifshitz gravity

At the present work, it is studied the extension of F (R) gravities to the new recently proposed theory of gravity, the so-called Horava-Lifshitz gravity, which provides a way to make the theory power counting renormalizable by breaking Lorentz invariance. It is showed that dark energy can be well explained in the frame of this extension, just in terms of gravity. It is also explored the possibility to unify inflation and late-time acceleration under the same mechanism, providing a natural explanation the accelerated expansion.Comment: 4 pages. Contribution to the Proceedings of the Spanish Relativity Meeting (ERE) 2010, Granada, Spai

New Models of f(R) Theories of Gravity

We introduce new models of f(R) theories of gravity that are generalization of Horava-Lifshitz gravity.Comment: 16 pages, typos corrected, v2:minor changes, references adde

Note About Equivalence of F(R) and Scalar Tensor Horava-Lifshitz Gravities

In this note we study the relation between F(R) and scalar tensor Horava-Lifshitz gravity. We find that due to the broken diffeomorphism invariance corresponding scalar tensor theory has more complicated form than in case of the full diffeomorphism invariant F(R) theory of gravity. We also show that in the low energy limit this theory flows to the relativistic scalar tensor theory of gravity.Comment: 12 pages,v2: references adde

Hamiltonian Analysis of Lagrange Multiplier Modified Gravity

We develop Hamiltonian formalism for Lagrange Multiplier Modified Gravity. We further calculate the Poisson brackets between constraints and we show that they coincide with the algebra of constraints in Hamiltonian formulation of General Relativity.Comment: 15 pages, references adde

Modified F(R) Horava-Lifshitz gravity: a way to accelerating FRW cosmology

We propose a general approach for the construction of modified gravity which is invariant under foliation-preserving diffeomorphisms. Special attention is paid to the formulation of modified $F(R)$ Ho\v{r}ava-Lifshitz gravity (FRHL), whose Hamiltonian structure is studied. It is demonstrated that the spatially-flat FRW equations of FRHL are consistent with the constraint equations. The analysis of de Sitter solutions for several versions of FRHL indicates that the unification of the early-time inflation with the late-time acceleration is possible. It is shown that a special choice of parameters for FRHL leads to the same spatially-flat FRW equations as in the case of traditional $F(R)$-gravity. Finally, an essentially most general modified Ho\v{r}ava-Lifshitz gravity is proposed, motivated by its fully diffeomorphism-invariant counterpart, with the restriction that the action does not contain derivatives higher than the second order with respect to the time coordinate.Comment: LaTeX 11 pages. v4: Some errors have been correcte

T-Duality For String in Horava-Lifshitz Gravity

We continue our study of the Lorentz breaking string theories. These theories are defined as string theory with modified Hamiltonian constraint which breaks the Lorentz symmetry of target space-time. We analyze properties of this theory in the target space-time that possesses isometry along one direction. We also derive the T-duality rules for Lorentz breaking string theories and show that they are the same as that of Buscher's T-duality for the relativistic strings.Comment: 17 pages, references adde

Horava-Lifshitz f(R) Gravity

This paper is devoted to the construction of new type of f(R) theories of gravity that are based on the principle of detailed balance. We discuss two versions of these theories with and without the projectability condition.Comment: 22 pages, references adde

U(1) Invariant F(R) Horava-Lifshitz Gravity

This paper is devoted to the study of various aspects of projectable F(R) Horava-Lifshitz (HL) gravity. We show that some versions of F(R) HL gravity may have stable de Sitter solution and instable 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 arXiv:1007.2410, we formulate U(1) extension of scalar theory and of F(R) Horava-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 flat background indicates towards the consistency of the theory because it contains graviton with only transverse polarization. Finally, we analyze the spatially-flat FRW equations for U(1) invariant F(R) Horava-Lifshitz gravity.Comment: 26 pages, several mysprints correcte

Interacting Ricci Dark Energy with Logarithmic Correction

Motivated by the holographic principle, it has been suggested that the dark energy density may be inversely proportional to the area $A$ of the event horizon of the universe. However, such a model would have a causality problem. In this work, we consider the entropy-corrected version of the holographic dark energy model in the non-flat FRW universe and we propose to replace the future event horizon area with the inverse of the Ricci scalar curvature. We obtain the equation of state (EoS) parameter $\omega_{\Lambda}$, the deceleration parameter $q$ and $\Omega_D'$ in the presence of interaction between Dark Energy (DE) and Dark Matter (DM). Moreover, we reconstruct the potential and the dynamics of the tachyon, K-essence, dilaton and quintessence scalar field models according to the evolutionary behavior of the interacting entropy-corrected holographic dark energy model.Comment: 24 pages, accepted for publication in 'Astrophysics and Space Science, DOI:10.1007/s10509-012-1031-8