Inverse problem - reconstruction of dark energy models

We review how we can construct the gravity models which reproduces the arbitrary development of the universe. We consider the reconstruction in the Einstein gravity coupled with generalized perfect fluid, scalar-Einstein gravity, scalar-Einstein-Gauss-Bonnet gravity, Einstein-$F(G)$-gravity, and $F(R)$-gravity. Very explicit formulas are given to reconstruct the models, which could be used when we find the detailed data of the development of the universe by future observations. Especially we find the formulas using e-foldings, which has a direct relation with observed redshift. As long as we observe the time development of the Hubble rate $H$, there exists a variety of models describing the arbitrary development of universe.Comment: LaTeX 11 pages, references are added, to appear in Proceedings of International Workshop on Dark Matter, Dark Energy and Matter-Antimatter Asymmetry, National Tsing Hua University, Hsinchu, Taiwan, November 20-21, 200

Modified f(R) gravity from scalar-tensor theory and inhomogeneous EoS dark energy

The reconstruction of f(R)-gravity is showed by using an auxiliary scalar field in the context of cosmological evolution, this development provide a way of reconstruct the form of the function f (R) for a given evolution of the Hubble parameter. In analogy, f(R)-gravity may be expressed by a perfect fluid with an inhomogeneous equation of state that depends on the Hubble parameter and its derivatives. This mathematical equivalence that may confuse about the origin of the mechanism that produces the current acceleration, and possibly the whole evolution of the Hubble parameter, is shown here.Comment: 8 page

Tachyon fields with effects of quantum matter in an Anti-de Sitter Universe

We consider an Anti-de Sitter universe filled by quantum conformal matter with the contribution from the usual tachyon and a perfect fluid. The model represents the combination of a trace-anomaly annihilated and a tachyon driven Anti-de Sitter universe. The influence exerted by the quantum effects and by the tachyon on the AdS space is studied. The radius corresponding to this universe is calculated and the effect of the tachyon potential is discussed, in particular, concerning to the possibility to get an accelerated scale factor for the proposed model (implying an accelerated expansion of the AdS type of universe). Fulfillment of the cosmological energy conditions in the model is also investigatedComment: 14 Latex pages, no figure

Thermodynamics of Schwarzschild-(Anti-)de Sitter Black Holes with account of quantum corrections

We discuss the quantum corrections to thermodynamics (and geometry) of S(A)dS BHs using large $N$ one-loop anomaly induced effective action for dilaton coupled matter (scalars and spinors). It is found the temperature, mass and entropy with account of quantum effects for multiply horizon SdS BH and SAdS BH what also gives the corresponding expressions for their limits: Schwarzschild and de Sitter spaces. In the last case one can talk about quantum correction to entropy of expanding Universe. The anomaly induced action under discussion corresponds to 4d formulation (s-wave approximation, 4d quantum matter is minimal one) as well as 2d formulation (complete effective action, 2d quantum matter is dilaton coupled one). Hence, most of results are given for the same gravitational background with interpretation as 4d quantum corrected BH or 2d quantum corrected dilatonic BH. Quantum aspects of thermodynamics of 4d 't Hooft BH model are also considered.Comment: LaTeX file, 28 pages, some misprints are correcte

Dark Energy and Viscous Cosmology

Singularities in the dark energy universe are discussed, assuming that there is a bulk viscosity in the cosmic fluid. In particular, it is shown how the physically natural assumption of letting the bulk viscosity be proportional to the scalar expansion in a spatially flat FRW universe can drive the fluid into the phantom region (w -1) in the non-viscous case.Comment: 11 pages. Printing error in eq.(23) corrected. To appear in Gen. Rel. Gra

Viscous Fluids and Gauss-Bonnet Modified Gravity

We study effects of cosmic fluids on finite-time future singularities in modified $f(R,G)$-gravity, where $R$ and $G$ are the Ricci scalar and the Gauss-Bonnet invariant, respectively. We consider the fluid equation of state in the general form, $\omega=\omega(\rho)$, and we suppose the existence of a bulk viscosity. We investigate quintessence region ($\omega>-1$) and phantom region ($\omega<-1$) and the possibility to change or avoid the singularities in $f(R,G)$-gravity. Finally, we study the inclusion of quantum effects in large curvatures regime.Comment: 14 page

Wormholes and Off-Diagonal Solutions in f(R,T), Einstein and Finsler Gravity Theories

The aims of this work are 1) to sketch a proof that there are such parameterizations of the local frame and canonical connection structures when the gravitational field equations in f(R,T)-modified gravity, MG, can be integrated in generic off-diagonal forms with metrics depending on all spacetime coordinates and 2) to provide some examples of exact solutions.Comment: 4 pages, ERE2012-Proceedings macros, Contribution to the Spanish Relativity Meeting in Portugal, Guimaraes, September 3-7, 201

Conformal anomaly for dilaton coupled electromagnetic field

The derivation of the conformal anomaly for dilaton coupled electromagnetic field in curved space is presented. The models of this sort naturally appear in stringy gravity or after spherical reduction of multidimensional Einstein-Maxwell theory. It is shown that unlike the case of minimal vector in curved space or dilaton coupled scalar the anomaly induced effective action cannot be derived. The reason is the same why anomaly induced effective action cannot be constructed for interacting theories (like QED) in curved space.Comment: Latex file, 10 page

String versus Einstein frame in an AdS/CFT induced quantum dilatonic brane-world universe

AdS/CFT induced quantum dilatonic brane-world where 4d boundary is flat or de Sitter (inflationary) or Anti-de Sitter brane is considered. The classical brane tension is fixed but boundary QFT produces the effective brane tension via the account of corresponding conformal anomaly induced effective action. This results in inducing of brane-worlds in accordance with AdS/CFT set-up as warped compactification. The explicit, independent construction of quantum induced dilatonic brane-worlds in two frames: string and Einstein one is done. It is demonstrated their complete equivalency for all quantum cosmological brane-worlds under discussion, including several examples of classical brane-world black holes. This is different from quantum corrected 4d dilatonic gravity where de Sitter solution exists in Einstein but not in Jordan (string) frame. The role of quantum corrections on massive graviton perturbations around Anti-de Sitter brane is briefly discussed.Comment: LaTeX file, 24 pages, minor changes to match with published versio

Dark energy generated from a (super)string effective action with higher order curvature corrections and a dynamical dilaton

We investigate the possibility of a dark energy universe emerging from an action with higher-order string loop corrections to Einstein gravity in the presence of a massless dilaton. These curvature corrections (up to $R^4$ order) are different depending upon the type of (super)string model which is considered. We find in fact that Type II, heterotic, and bosonic strings respond differently to dark energy. A dark energy solution is shown to exist in the case of the bosonic string, while the other two theories do not lead to realistic dark energy universes. Detailed analysis of the dynamical stability of the de-Sitter solution is presented for the case of a bosonic string. A general prescription for the construction of a de-Sitter solution for the low-energy (super)string effective action is also indicated. Beyond the low-energy (super)string effective action, when the higher-curvature correction coefficients depend on the dilaton, the reconstruction of the theory from the universe expansion history is done with a corresponding prescription for the scalar potentials.Comment: 15 pages, 7 eps figures, minor corrections, published versio