Shin'ichi Nojiri

Publications of Shin'ichi Nojiri

• 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.

• Generalized Galileon Model -- cosmological reconstruction and the Vainshtein mechanism --

  Authors: Norihito Shirai, Kazuharu Bamba, Shota Kumekawa, Jiro Matsumoto, Shin'ichi Nojiri

  03/2012;

  Explicit formulae of the equations in the generalized Galileon models are given. We also develop the formulation of the reconstruction. By using the formulation, we can explicitly construct an actionExplicit formulae of the equations in the generalized Galileon models are given. We also develop the formulation of the reconstruction. By using the formulation, we can explicitly construct an action which reproduces an arbitrary development of the expansion of the universe. The conditions how the reconstructed solution becomes stable and therefore it becomes an attractor solution are also given. Working in the static and spherically symmetric space-time, we investigate how the Vainshtein mechanism works in the generalized Galileon model and the correction to the Newton law becomes small. It is also shown that any spherically symmetric and static geometry can be realized by properly choosing the form of the action, which may tell that the solution could have fourth hair corresponding to the scalar field.

• Scalar Domain Wall as the Universe

  Authors: Yuta Toyozato, Kazuharu Bamba, Shin'ichi Nojiri

  02/2012;

  By using the formulation of the reconstruction, we construct models which have an exact solution describing the domain wall. The shape of the domain wall can be flat, de Sitter space-time, or anti-deBy using the formulation of the reconstruction, we construct models which have an exact solution describing the domain wall. The shape of the domain wall can be flat, de Sitter space-time, or anti-de Sitter space-time. In the constructed domain wall solutions, there often appears ghost with negative kinetic energy. We give, however, an example of the de Sitter domain wall solution without ghost, which could be a toy model of the inflation. We also investigate the localization of the gravity as in the Randall-Sundrum model. It is shown that the four dimensional Newton law could be reproduced even in the de Sitter space-time domain wall solution.

• 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.

• Cosmological perturbations in $k$-essence model

  Authors: Kazuharu Bamba, Jiro Matsumoto, Shin'ichi Nojiri

  09/2011;

  Subhorizon approximation is often used in cosmological perturbation theory. In this paper, however, it is shown that the subhorizon approximation is not always a good approximation at least in caseSubhorizon approximation is often used in cosmological perturbation theory. In this paper, however, it is shown that the subhorizon approximation is not always a good approximation at least in case of $k$-essence model. We also show that the sound speed given by $k$-essence model exerts a huge influence on the time evolution of the matter density perturbation, and the future observations could clarify the differences between the $\Lambda$CDM model and $k$-essence model.

• Cyclic, ekpyrotic and little rip universe in modified gravity

  Authors: Shin'ichi Nojiri, Sergei D. Odintsov, Diego Saez-Gomez

  08/2011;

  We propose the reconstruction of $F(R)$ gravity in such a way that corresponding theory admits cyclic and ekpyrotic universe solutions. The number of explicit examples of such $F(R)$ model is found.We propose the reconstruction of $F(R)$ gravity in such a way that corresponding theory admits cyclic and ekpyrotic universe solutions. The number of explicit examples of such $F(R)$ model is found. The comparison with the reconstructed scalar-tensor theory is made. We also present $F(R)$ gravity which provides the little rip evolution and gives the realistic gravitational alternative for $\Lambda$CDM cosmology. The time for little rip dissolution of bound structures in such theory is estimated. We demonstrate that transformed little rip $F(R)$ solution becomes qualitatively different cosmological solution with Big Bang type singularity in Einstein frame.

• 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.

• Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors

  Authors: Josef Kluson, Shin'ichi Nojiri, Sergei D. Odintsov

  04/2011;

  We formulate higher derivative gravity with Lagrange multiplier constraint and scalar projectors. Its gauge-fixed formulation as well as vector fields formulation is developed and correspondingWe formulate higher derivative gravity with Lagrange multiplier constraint and scalar projectors. Its gauge-fixed formulation as well as vector fields formulation is developed and corresponding spontaneous Lorentz symmetry breaking is investigated. We show that the only propagating mode is higher derivative graviton while scalar and vector modes do not propagate. Despite to higher derivatives structure of the action, its first FRW equation is the first order differential equation which admits the inflationary universe solution.

• 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.

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

  Authors: Josef Kluson, Shin'ichi Nojiri, Sergei D. Odintsov, Diego Saez-Gomez

  12/2010;

  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 instableThis 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.

• 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

• Modified first-order Horava-Lifshitz gravity: Hamiltonian analysis of the general theory and accelerating FRW cosmology in power-law F(R) model

  Authors: Sante Carloni, Masud Chaichian, Shin'ichi Nojiri, Sergei D. Odintsov, Markku Oksanen, Anca Tureanu

  03/2010;

  We propose the most general modified first-order Ho\v{r}ava-Lifshitz (HL) gravity, whose action does not contain time derivatives higher than the second order. The Hamiltonian structure of thisWe propose the most general modified first-order Ho\v{r}ava-Lifshitz (HL) gravity, whose action does not contain time derivatives higher than the second order. The Hamiltonian structure of this theory is studied in all the details in the case of the spatially-flat FRW space-time, demonstrating many of the features of the general theory. It is shown that, with some plausible assumptions, including the projectability of the lapse function, this model is consistent. As a large class of such theories, the modified HL $F(R)$ gravity is introduced. The study of its ultraviolet properties shows that its $z=3$ version seems to be renormalizable in the same way as the original HL proposal. The Hamiltonian analysis of the modified HL $F(R)$ gravity shows that it is in general a consistent theory. The $F(R)$ gravity action is also studied in the fixed-gauge form, where the appearance of a scalar field is particularly illustrative. Then the spatially-flat FRW cosmology for this $F(R)$ gravity is investigated. It is shown that a special choice of parameters for this theory leads to the same equations of motion as in the case of traditional $F(R)$ gravity. Nevertheless, the cosmological structure of the modified HL $F(R)$ gravity turns out to be much richer than for its traditional counterpart. The emergence of multiple de Sitter solutions indicates to the possibility of unification of early-time inflation with late-time acceleration within the same model. Power-law $F(R)$ theories are investigated in detail. It is analytically shown that they have a quite rich cosmological structure: early/late-time cosmic acceleration of quintessence, as well as of phantom types. Also it is demonstrated that all the four known types of finite-time future singularities may occur in the power-law HL $F(R)$ gravity. Finally, a covariant proposal for (renormalizable) $F(R)$ gravity within the HL spirit is presented. Comment: LATEX, 32 pages, 3 figures. v3: added subsection VI.C, "Explicit model for the unification of inflation with dark energy"

• 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.

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

  Authors: Masud Chaichian, Shin'ichi Nojiri, Sergei D. Odintsov, Markku Oksanen, Anca Tureanu

  01/2010;

  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 $F(R)$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 12 pages. v2: discussion is expanded, Hamiltonian analysis is extended, references are added. v3: arguments improved, wording corrected