Kazuharu Bamba

Publications of Kazuharu Bamba

• 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.

• Periodic generalizations of Chaplygin gas type models for dark energy

  Authors: Kazuharu Bamba, Ujjal Debnath, Kuralay Yesmakhanova, Petr Tsyba, Gulgasyl Nugmanova, Ratbay Myrzakulov

  03/2012;

  We demonstrate two periodic generalizations of the Chaplygin gas type models to explain the origins of dark energy as well as dark matter by using the Weierstrass $\wp(t)$, $\sigma(t)$ and $\zeta(t)$We demonstrate two periodic generalizations of the Chaplygin gas type models to explain the origins of dark energy as well as dark matter by using the Weierstrass $\wp(t)$, $\sigma(t)$ and $\zeta(t)$ functions. In particular, we examine the cosmological evolution of the equation of state of dark energy in the homogeneous and isotropic Friedmann-Lema\^{i}tre-Robertson-Walker cosmology. Other periodic and quasi-periodic gas models are also explored. Furthermore, we explicitly illustrate that there exist three type models in which the universe always stays in the non-phantom (quintessence) phase, whereas it always evolves in the phantom phase, or the crossing of the phantom divide can be realized.

• Reconstruction of the equation of state for the cyclic universes in homogeneous and isotropic cosmology

  Authors: Kazuharu Bamba, Kuralay Yesmakhanova, Koblandy Yerzhanov, Ratbay Myrzakulov

  03/2012;

  We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time. In particular,We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time. In particular, we reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic functions. It is explicitly illustrated that in several models the universe always stays in the non-phantom (quintessence) phase, whereas there also exist models in which the crossing of the phantom divide can be realized in the reconstructed cyclic universes.

• Cosmological evolution of equation of state for dark energy in G-essence models

  Authors: Kazuharu Bamba, Olga Razina, Koblandy Yerzhanov, Ratbay Myrzakulov

  03/2012;

  We explore the cosmological evolution of equation of state (EoS) for dark energy in g-essence models, the action of which is described by a function of both the canonical kinetic term of both theWe explore the cosmological evolution of equation of state (EoS) for dark energy in g-essence models, the action of which is described by a function of both the canonical kinetic term of both the scalar and fermionic fields. We examine g-essence models with realizing the crossing of the phantom divide line of $w_{\mathrm{DE}}=-1$ as well as the models in which the universe always stays in the non-phantom (quintessence) phase ($w_{\mathrm{DE}}>-1$). In particular, we find an explicit g-essence model with the crossing from the non-phantom phase to the phantom one ($w_{\mathrm{DE}}<-1$). This transition behavior is consistent with the recent observational data analyses.

• 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.

• Equation of State for Dark Energy in Modified Gravity Theories

  Authors: Kazuharu Bamba

  02/2012;

  We explore the equation of state (EoS) for dark energy $w_{\mathrm{DE}}$ in modified gravitational theories to explain the current accelerated expansion of the universe. We explicitly demonstrateWe explore the equation of state (EoS) for dark energy $w_{\mathrm{DE}}$ in modified gravitational theories to explain the current accelerated expansion of the universe. We explicitly demonstrate that the future crossings of the phantom divide line of $w_{\mathrm{DE}}=-1$ are the generic feature in the existing viable $f(R)$ gravity models. Furthermore, we show that the crossing of the phantom divide can be realized in the combined $f(T)$ theory constructed with the exponential and logarithmic terms. In addition, we investigate the effective EoS for the universe when the finite-time future singularities occur in non-local gravity.

• 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.

• Thermodynamics of cosmological horizons in $f(T)$ gravity

  Authors: Kazuharu Bamba, Chao-Qiang Geng

  09/2011;

  We explore thermodynamics of the apparent horizon in $f(T)$ gravity with both equilibrium and non-equilibrium descriptions. We find the same dual equilibrium/non-equilibrium formulation for $f(T)$ asWe explore thermodynamics of the apparent horizon in $f(T)$ gravity with both equilibrium and non-equilibrium descriptions. We find the same dual equilibrium/non-equilibrium formulation for $f(T)$ as for $f(R)$ gravity. In particular, we show that the second law of thermodynamics can be satisfied for the universe with the same temperature of the outside and inside 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.

• Phantom crossing in viable $f(R)$ theories

  Authors: Kazuharu Bamba, Chao-Qiang Geng, Chung-Chi Lee

  08/2011;

  We review the equation of state for dark energy in modified gravity theories. In particular, we summarize the generic feature of the phantom divide crossing in the past and future in viable $f(R)$We review the equation of state for dark energy in modified gravity theories. In particular, we summarize the generic feature of the phantom divide crossing in the past and future in viable $f(R)$ gravity models.

• Large-scale magnetic fields from inflation due to a $CPT$-even Chern-Simons-like term with Kalb-Ramond and scalar fields

  Authors: Kazuharu Bamba, C. Q. Geng, S. H. Ho, W. F. Kao

  07/2011;

  We investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the $CPT$-even dimension-six Chern-Simons-likeWe investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the $CPT$-even dimension-six Chern-Simons-like effective interaction with a fermion current by taking account of the dynamical Kalb-Ramond and scalar fields in inflationary cosmology. It is explicitly demonstrated that the magnetic fields on 1Mpc scale with the field strength of $\sim 10^{-9}$G at the present time can be induced.

• 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.

• Thermodynamics in Modified Gravity Theories

  Authors: Kazuharu Bamba, Chao-Qiang Geng, Shinji Tsujikawa

  01/2011;

  We demonstrate that there does exist an equilibrium description of thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories withWe demonstrate that there does exist an equilibrium description of thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density $f(R, \phi, X)$, where $R$ is the Ricci scalar and $X$ is the kinetic energy of a scalar field $\phi$. This comes from a suitable definition of an energy momentum tensor of the "dark" component obeying the local energy conservation law in the Jordan frame. It is shown that the equilibrium description in terms of the horizon entropy $S$ is convenient because it takes into account the contribution of the horizon entropy $\hat{S}$ in non-equilibrium thermodynamics as well as an entropy production term.

• 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.

• Equation of state for dark energy in $f(T)$ gravity

  Authors: Kazuharu Bamba, Chao-Qiang Geng, Chung-Chi Lee, Ling-Wei Luo

  11/2010;

  We study the cosmological evolutions of the equation of state for dark energy $w_{\mathrm{DE}}$ in the exponential and logarithmic as well as their combination $f(T)$ theories. We show that theWe study the cosmological evolutions of the equation of state for dark energy $w_{\mathrm{DE}}$ in the exponential and logarithmic as well as their combination $f(T)$ theories. We show that the crossing of the phantom divide line of $w_{\mathrm{DE}} = -1$ can be realized in the combined $f(T)$ theory even though it cannot be in the exponential or logarithmic $f(T)$ theory. In particular, the crossing is from $w_{\mathrm{DE}} > -1$ to $w_{\mathrm{DE}} < -1$, in the opposite manner from $f(R)$ gravity models. We also demonstrate that this feature is favored by the recent observational data.

• Comment on "Einstein's Other Gravity and the Acceleration of the Universe''

  Authors: Kazuharu Bamba, Chao-Qiang Geng, Chung-Chi Lee

  08/2010;

  We show that in the exponential $f(T)$ model studied by E. Linder [arXiv:1005.3039, Phys.Rev.D 81, 127301 (2010)], it is impossible to have the crossing of the phantom divide lineWe show that in the exponential $f(T)$ model studied by E. Linder [arXiv:1005.3039, Phys.Rev.D 81, 127301 (2010)], it is impossible to have the crossing of the phantom divide line $w_{\mathrm{DE}}=-1$. Comment: 2 pages, 1 figure

• Cosmological birefringence due to CPT-even Chern-Simons-like term with Kalb-Ramond and scalar fields

  Authors: Shih-Hao Ho, W. F. Kao, Kazuharu Bamba, C. Q. Geng

  08/2010;

  We study the CPT-even dimension-six Chern-Simons-like term by including dynamical Kalb-Ramond and scalar fields to examine the cosmological birefringence. We show that the combined effect of neutrinoWe study the CPT-even dimension-six Chern-Simons-like term by including dynamical Kalb-Ramond and scalar fields to examine the cosmological birefringence. We show that the combined effect of neutrino current and Kalb-Ramond field could induce a sizable rotation polarization angle in the cosmic microwave background radiation polarization. Comment: 9 pages

• Generic feature of future crossing of phantom divide in viable $f(R)$ gravity models

  Authors: Kazuharu Bamba, Chao-Qiang Geng, Chung-Chi Lee

  07/2010;

  We study the equation of state for dark energy and explicitly demonstrate that the future crossings of the phantom divide line $w_{\mathrm{DE}}=-1$ are the generic feature in the existing viableWe study the equation of state for dark energy and explicitly demonstrate that the future crossings of the phantom divide line $w_{\mathrm{DE}}=-1$ are the generic feature in the existing viable $f(R)$ gravity models. We also explore the future evolution of the cosmological horizon entropy and illustrate that the cosmological horizon entropy oscillates with time due to the oscillatory behavior of the Hubble parameter. The important cosmological consequence is that in the future, the sign of the time derivative of the Hubble parameter changes from negative to positive in these viable $f(R)$ gravity models. Comment: 12 pages, 3 figures, accepted for publication in JCAP