Sergei D. Odintsov

Publications of Sergei D. Odintsov

• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

  Authors: Kazuharu Bamba, Salvatore Capozziello, Shin'ichi Nojiri, Sergei D. Odintsov

  05/2012;

  We review different dark energy cosmologies. In particular, we present the $\Lambda$CDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, IIIWe review different dark energy cosmologies. In particular, we present the $\Lambda$CDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the $\Lambda$CDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the $\Lambda$CDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes $F(R)$ gravity as well as $F(R)$ Ho\v{r}ava-Lifshitz gravity and the teleparallel $f(T)$ gravity. The cosmology of such models representing the $\Lambda$CDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.

• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics

  Authors: Kazuharu Bamba, Ratbay Myrzakulov, Shin'ichi Nojiri, Sergei D. Odintsov

  02/2012;

  We demonstrate that there appear finite-time future singularities in $f(T)$ gravity with $T$ being the torsion scalar. We reconstruct a model of $f(T)$ gravity with realizing the finite-time futureWe demonstrate that there appear finite-time future singularities in $f(T)$ gravity with $T$ being the torsion scalar. We reconstruct a model of $f(T)$ gravity with realizing the finite-time future singularities. In addition, it is explicitly shown that a power-low type correction term $T^\beta$ ($\beta>1$) such as a $T^2$ term can remove the finite-time future singularities in $f(T)$ gravity. Moreover, we study $f(T)$ models with realizing inflation in the early universe, the $\Lambda$CDM model, Little Rip cosmology and Pseudo-Rip cosmology. It is demonstrated that the disintegration of bound structures for Little Rip and Pseudo-Rip cosmologies occurs in the same way as in gravity with corresponding dark energy fluid. We also discuss that the time-dependent matter instability in the star collapse can occur in $f(T)$ gravity. Furthermore, we explore thermodynamics in $f(T)$ gravity and illustrate that the second law of thermodynamics can be satisfied around the finite-time future singularities for the universe with the temperature inside the horizon being the same as that of the apparent horizon.

• Domain wall solution in $F(R)$ gravity and variation of the fine structure constant

  Authors: Kazuharu Bamba, Shin'ichi Nojiri, Sergei D. Odintsov

  07/2011;

  We construct a domain wall solution in $F(R)$ gravity. We reconstruct a static domain wall solution in a scalar field theory. We also reconstruct an explicit $F(R)$ gravity model in which a staticWe construct a domain wall solution in $F(R)$ gravity. We reconstruct a static domain wall solution in a scalar field theory. We also reconstruct an explicit $F(R)$ gravity model in which a static domain wall solution can be realized. Moreover, we show that there could exist an effective (gravitational) domain wall in the framework of $F(R)$ gravity. In addition, it is demonstrated that a logarithmic non-minimal gravitational coupling of the electromagnetic theory in $F(R)$ gravity may produce time-variation of the fine structure constant which may increase with decrease of the curvature, and that this model would be ruled out by the constraints on the time variation of the fine structure constant from quasar absorption lines. We also present cosmological consequences of the coupling of the electromagnetic field to a scalar field as well as the scalar curvature and discuss the relation between variation of the fine structure constant and the breaking of the conformal invariance of the electromagnetic field.

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

  Authors: Kazuharu Bamba, Shin'ichi Nojiri, Sergei D. Odintsov, Misao Sasaki

  04/2011;

  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 scenarioWe 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.

• Time-dependent matter instability and star singularity in $F(R)$ gravity

  Authors: Kazuharu Bamba, Shin'ichi Nojiri, Sergei D. Odintsov

  01/2011;

  We investigate a curvature singularity appearing in the star collapse process in $F(R)$ gravity. In particular, we propose an understanding of the mechanism to produce the curvature singularity.We investigate a curvature singularity appearing in the star collapse process in $F(R)$ gravity. In particular, we propose an understanding of the mechanism to produce the curvature singularity. Moreover, we explicitly demonstrate that $R^\alpha$ ($1 < \alpha \leq 2$) term addition could cure the curvature singularity and viable $F(R)$ gravity models could become free of such a singularity. Furthermore, we discuss the realization process of the curvature singularity and estimate the time scale of its appearance. For exponential gravity, it is shown that in case of the star collapse, the time scale is much shorter than the age of the universe, whereas in cosmological circumstances, it is as long as the cosmological time.

• On Isotropic Turbulence in the Dark Fluid Universe

  Authors: Iver Brevik, Olesya Gorbunova, Shin'ichi Nojiri, Sergei D. Odintsov

  11/2010;

  As first part of this work, experimental information about the decay of isotropic turbulence in ordinary hydrodynamics, u^2(t) proportional to t^{-6/5}, is used as input in FRW equations in order toAs first part of this work, experimental information about the decay of isotropic turbulence in ordinary hydrodynamics, u^2(t) proportional to t^{-6/5}, is used as input in FRW equations in order to investigate how an initial fraction f of turbulent kinetic energy in the cosmic fluid influences the cosmological development in the late, quintessence/phantom, universe. First order perturbative theory to the first order in f is employed. It turns out that both in the Hubble factor, and in the energy density, the influence from the turbulence fades away at late times. The divergences in these quantities near the Big Rip behave essentially as in a non-turbulent fluid. However, for the scale factor, the turbulence modification turns out to diverge logarithmically. As second part of our work, we consider the full FRW equation in which the turbulent part of the dark energy is accounted for by a separate term. It is demonstrated that turbulence occurrence may change the future universe evolution due to dissipation of dark energy. For instance, phantom-dominated universe becomes asymptotically a de Sitter one in the future, thus avoiding the Big Rip singularity.

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov

  11/2010;

  Classical generalization of general relativity is considered as gravitational alternative for unified description of the early-time inflation with late-time cosmic acceleration. The structure andClassical generalization of general relativity is considered as gravitational alternative for unified description of the early-time inflation with late-time cosmic acceleration. The structure and cosmological properties of number of modified theories, including traditional $F(R)$ and Ho\v{r}ava-Lifshitz $F(R)$ gravity, scalar-tensor theory, string-inspired and Gauss-Bonnet theory, non-local gravity, non-minimally coupled models, and power-counting renormalizable covariant gravity are discussed. Different representations and relations between such theories are investigated. It is shown that some versions of above theories may be consistent with local tests and may provide qualitatively reasonable unified description of inflation with dark energy epoch. The cosmological reconstruction of different modified gravities is made in great detail. It is demonstrated that eventually any given universe evolution may be reconstructed for the theories under consideration: the explicit reconstruction is applied to accelerating spatially-flat FRW universe. Special attention is paid to Lagrange multiplier constrained and conventional $F(R)$ gravities, for last theory the effective $\Lambda$CDM era and phantom-divide crossing acceleration are obtained. The occurrence of Big Rip and other finite-time future singularities in modified gravity is reviewed as well as its curing via the addition of higher-derivative gravitational invariants.

• Screening of cosmological constant in non-local gravity

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov, Misao Sasaki, Ying-li Zhang

  10/2010;

  We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of of non-local gravity with the Lagrangian of the form,We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of of non-local gravity with the Lagrangian of the form, $R+f(\Box^{-1}R)-2\Lambda$ where $f(X)$ is a quadratic function of $X$, there is a flat spacetime solution despite the presence of the cosmological constant $\Lambda$. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of `time'. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.

• Non-singular modified gravity unifying inflation with late-time acceleration and universality of viscous ratio bound in F(R) theory

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov

  08/2010;

  The review of basic cosmological properties of four-dimensional F(R)-gravity, including FRW equations of motion and its accelerating solutions, generalized fluid and scalar-tensor representation ofThe review of basic cosmological properties of four-dimensional F(R)-gravity, including FRW equations of motion and its accelerating solutions, generalized fluid and scalar-tensor representation of the theory is done. Cosmological reconstruction equation is written and conditions for stability of cosmological solution are discussed. The overview of realistic F(R)-models unifying inflation with dark energy epoch is made. The avoidance of finite-time future singularities in such theories via the introduction of R^2-term is studied. New realistic non-singular F(R)-gravity unifying early-time inflation with late-time acceleration is presented. The exit from inflationary era in such model may be caused by the gravitational scenario. It is demonstrated that five-dimensional F(R)-gravity considered as non-perturbative stringy effective action leads to universal relation for viscous bound ratio. Comment: LaTeX 18 pages, based on the talks given at the international conferences: YKIS 2010, Gravitation and Cosmology (YITP, Kyoto) and QFTG-10 (Tomsk)

• A proposal for covariant renormalizable field theory of gravity

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov

  04/2010;

  The class of covariant gravity theories which have nice ultraviolet behavior and seem to be (super)-renormalizable is proposed. The apparent breaking of Lorentz invariance occurs due to the couplingThe class of covariant gravity theories which have nice ultraviolet behavior and seem to be (super)-renormalizable is proposed. The apparent breaking of Lorentz invariance occurs due to the coupling with the effective fluid which is induced by Lagrange multiplier constrained scalar field. Spatially-flat FRW cosmology for such covariant field gravity may have accelerating solutions. Renormalizable versions of more complicated modified gravity which depends on Riemann and Ricci tensor squared may be constructed in the same way. Comment: LaTeX, 6 pages, published version, mistypes are corrected, refs. are added

• Crossing of Phantom Divide in $F(R)$ Gravity

  Authors: Kazuharu Bamba, Chao-Qiang Geng, Shin'ichi Nojiri, Sergei D. Odintsov

  03/2010;

  An explicit model of $F(R)$ gravity with realizing a crossing of the phantom divide is reconstructed. In particular, it is shown that the Big Rip singularity may appear in the reconstructed model ofAn explicit model of $F(R)$ gravity with realizing a crossing of the phantom divide is reconstructed. In particular, it is shown that the Big Rip singularity may appear in the reconstructed model of $F(R)$ gravity. Such a Big Rip singularity could be avoided by adding $R^2$ term or non-singular viable $F(R)$ theory to the model because phantom behavior becomes transient. Comment: 9 pages, 1 figure, to be published in the proceedings of the International Workshop on Dark Matter, Dark Energy and Matter-antimatter Asymmetry in Special Issue of Modern Physics Letters A, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, 20th - 21st November, 2009

• Cardy-Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity

  Authors: Iver Brevik, Shin'ichi Nojiri, Sergei D. Odintsov, Diego Sáez-Gómez

  02/2010;

  We derive a Cardy-Verlinde-like formula which relates the entropy of the closed FRW universe to its energy, and Casimir energy, for a multicomponent coupled fluid. The generalized fluid obeys anWe derive a Cardy-Verlinde-like formula which relates the entropy of the closed FRW universe to its energy, and Casimir energy, for a multicomponent coupled fluid. The generalized fluid obeys an inhomogeneous equation of state. A viscous dark fluid is included, and we include also modified gravity using its fluid representation. It is demonstrated how such an expression reduces to the standard Cardy-Verlinde formula corresponding to the 2d CFT entropy only in some special cases. The dynamical entropy bound for a closed FRW universe with dark components is obtained. The universality of the dynamical entropy bound near a future singularity (of all four types), as well as near the Big Bang singularity, is investigated. It is demonstrated that except from some special cases of Type II and Type IV singularities the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account. The dynamical entropy bound seems to be universal for the case of a regular universe, including the asymptotic de Sitter one.

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

  Authors: Kazuharu Bamba, Sergei D. Odintsov, Lorenzo Sebastiani, Sergio Zerbini

  11/2009;

  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 RicciWe 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 added

• Is the future universe singular: Dark Matter versus modified gravity?

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov

  11/2009;

  The fundamental problem of the occurrence/removal of finite-time future singularity in the universe evolution for coupled dark energy (DE) is addressed. It is demonstrated the existence of theThe fundamental problem of the occurrence/removal of finite-time future singularity in the universe evolution for coupled dark energy (DE) is addressed. It is demonstrated the existence of the (instable or local minimum) de Sitter space solution which may cure the Type II or Type IV future singularity for DE coupled with DM as the result of tuning the initial conditions. In case of phantom DE, the corresponding coupling may help to resolve the coincidence problem but not the Big Rip (Type I) singularity issue. We show that modified gravity of special form or inhomogeneous DE fluid may offer the universal scenario to cure the Type I,II,III or IV future singularity of coupled (fluid or scalar) DE evolution. Comment: LaTeX 9 pages

• Non-singular modified gravity: the unification of the inflation, dark energy and dark mater

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov

  10/2009;

  Using the fluid representation, we formulate the conditions for the appearance of all four types finite-time future singularity in modified gravity in accelerating FRW universe. It stressed thatUsing the fluid representation, we formulate the conditions for the appearance of all four types finite-time future singularity in modified gravity in accelerating FRW universe. It stressed that number of standard quintessence/phantom DE theories (including scalar, fluid, DBI ones, etc) brings the accelerating cosmology to future singularity precisely in the same way as singular modified gravity DE. The viable non-singular modified gravity unifying the early-time inflation with late-time acceleration is considered. It is shown that adding such non-singular theory to another realistic singular modified gravity which has the accelerating solution with future singularity may cure the singularity of resulting combined model. This universal scenario may be naturally applied to standard singular DE models as well as to inflationary theories with initial singularity. This suggests the additional fundamental reasoning for modification of General Relativity. Comment: Conference Proceedings, LaTeX 6 pags

• Equivalence of modified gravity equation to the Clausius relation

  Authors: Kazuharu Bamba, Chao-Qiang Geng, Shin'ichi Nojiri, Sergei D. Odintsov

  09/2009;

  We explicitly show that the equations of motion for modified gravity theories of $F(R)$-gravity, the scalar-Gauss-Bonnet gravity, $F(\mathcal{G})$-gravity and the non-local gravity are equivalent toWe explicitly show that the equations of motion for modified gravity theories of $F(R)$-gravity, the scalar-Gauss-Bonnet gravity, $F(\mathcal{G})$-gravity and the non-local gravity are equivalent to the Clausius relation in thermodynamics. In addition, we discuss the relation between the expression of the entropy and the contribution from the modified gravity as well as the matter to the definition of the energy flux (heat). Comment: 6 pages, no figure, several statements clarified, references added

• Covariant renormalizable gravity and its FRW cosmology

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov

  05/2009;

  We consider the diffeomorphism invariant gravity coupled with the ideal fluid in the non-standard way. The Lorentz-invariance of the graviton propagator in such a theory considered as perturbationWe consider the diffeomorphism invariant gravity coupled with the ideal fluid in the non-standard way. The Lorentz-invariance of the graviton propagator in such a theory considered as perturbation over flat background turns out to be broken due to non-standard coupling with the ideal fluid. As a result the behavior of the propagator in the ultraviolet/infrared region indicates that some versions of such theory are (super-)renormalizable ones (with appearance of only physical transverse modes). The FRW cosmology in same cases may be different from the one in General Relativity with the possible quintessence/phantom-like inflationary stage. Comment: LaTeX 5 pages, no figure, Phys. Rev. D published version, title is changed, reference is corrected

• One-loop effective action for non-local modified Gauss-Bonnet gravity in de Sitter space

  Authors: Guido Cognola, Emilio Elizalde, Shin'ichi Nojiri, Sergei D. Odintsov, Sergio Zerbini

  05/2009;

  We discuss the classical and quantum properties of non-local modified Gauss-Bonnet gravity in de Sitter space, using its equivalent representation via string-inspired local scalar-Gauss-BonnetWe discuss the classical and quantum properties of non-local modified Gauss-Bonnet gravity in de Sitter space, using its equivalent representation via string-inspired local scalar-Gauss-Bonnet gravity with a scalar potential. A classical, multiply de Sitter universe solution is found where one of the de Sitter phases corresponds to the primordial inflationary epoch, while the other de Sitter space solution--the one with the smallest Hubble rate--describes the late-time acceleration of our universe. A Chameleon scenario for the theory under investigation is developed, and it is successfully used to show that the theory complies with gravitational tests. An explicit expression for the one-loop effective action for this non-local modified Gauss-Bonnet gravity in the de Sitter space is obtained. It is argued that this effective action might be an important step towards the solution of the cosmological constant problem. Comment: latex file, 17 pages, 4 figures. Published version. Significative improvement and new references

• Crossing of the phantom divide in modified gravity

  Authors: Kazuharu Bamba, Chao-Qiang Geng, Shin'ichi Nojiri, Sergei D. Odintsov

  10/2008;

  We reconstruct an explicit model of modified gravity in which a crossing of the phantom divide can be realized. It is shown that the (finite-time) Big Rip singularity appears in the model of modifiedWe reconstruct an explicit model of modified gravity in which a crossing of the phantom divide can be realized. It is shown that the (finite-time) Big Rip singularity appears in the model of modified gravity (i.e., in the so-called Jordan frame), whereas that in the corresponding scalar field theory obtained through the conformal transformation (i.e., in the so-called Einstein frame) the singularity becomes the infinite-time one. Furthermore, we investigate the relations between the scalar field theories with realizing a crossing of the phantom divide and the corresponding modified gravitational theories by using the inverse conformal transformation. It is demonstrated that the scalar field theories describing the non-phantom phase (phantom one with the Big Rip) can be represented as the theories of real (complex) $F(R)$ gravity through the inverse (complex) conformal transformation. We also study a viable model of modified gravity in which the transition from the de Sitter universe to the phantom phase can occur. In addition, we explore the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction coming from conformal anomaly. Comment: 34 pages, 4 figures, revised version, accepted in Phys. Rev. D

• Modified gravity as realistic candidate for dark energy, inflation and dark matter

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov

  10/2008;

  We review the unification of early-time inflation with late-time acceleration in several local modified gravity models which pass Solar System and cosmological tests. It is also demonstrated thatWe review the unification of early-time inflation with late-time acceleration in several local modified gravity models which pass Solar System and cosmological tests. It is also demonstrated that account of non-local gravitational corrections to the action does not destroy the possibility of such unification. Dark matter effect is caused by composite graviton degree of freedom in such models. Comment: LaTeX 6 pages, based on the talk given at DSU08 conference, June 2008