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Orthogonal black di-ring solution
Keisuke Izumi
Physics , 2007, DOI: 10.1143/PTP.119.757
Abstract: We construct a five dimensional exact solution of the orthogonal black di-ring which has two black rings whose $S^1$-rotating planes are orthogonal. This solution has four free parameters which represent radii of and speeds of $S^1$-rotation of the black rings. We use the inverse scattering method. This method needs the seed metric. We also present a systematic method how to construct a seed metric. Using this method, we can probably construct other solutions having many black rings on the two orthogonal planes with or without a black hole at the center.
Stellar center is dynamical in Horava-Lifshitz gravity
Keisuke Izumi,Shinji Mukohyama
Physics , 2009, DOI: 10.1103/PhysRevD.81.044008
Abstract: In Horava-Lifshitz gravity, regularity of a solution requires smoothness of not only the spacetime geometry but also the foliation. As a result, the regularity condition at the center of a star is more restrictive than in general relativity. Assuming that the energy density is a piecewise-continuous, non-negative function of the pressure and that the pressure at the center is positive, we prove that the momentum conservation law is incompatible with the regularity at the center for any spherically-symmetric, static configurations. The proof is totally insensitive to the structure of higher spatial curvature terms and, thus, holds for any values of the dynamical critical exponent $z$. Therefore, we conclude that a spherically-symmetric star should include a time-dependent region near the center. We also comment on the condition under which linear instability of the scalar graviton does not show up.
Trispectrum from Ghost Inflation
Keisuke Izumi,Shinji Mukohyama
Physics , 2010, DOI: 10.1088/1475-7516/2010/06/016
Abstract: Ghost inflation predicts almost scale-invariant primordial cosmological perturbations with relatively large non-Gaussianity. The bispectrum is known to have a large contribution at the wavenumbers forming an equilateral triangle and the corresponding nonlinear parameter $f_{NL}^{equil}$ is typically of order $O(10^2)$. In this paper we calculate trispectrum from ghost inflation and show that the corresponding nonlinear parameter $\tau_{NL}$ is typically of order $O(10^4)$. We investigate the shape dependence of the trispectrum and see that it has some features different from DBI inflation. Therefore, our result may be useful as a template to distinguish ghost inflation from other models of inflation by future experiments.
No de Sitter invariant vacuum in massive gravity theory with ghost
Keisuke Izumi,Takahiro Tanaka
Physics , 2007, DOI: 10.1143/PTP.121.419
Abstract: In this letter we point out that the massive gravity theory with a graviton ghost mode in de Sitter background cannot possess a de Sitter invariant vacuum state. In order to avoid a negative norm state, we must associate the creation operator of the ghost mode with a negative-energy mode function instead of a positive-energy one as the mode function. Namely, we have to adopt a different procedure of quantization for a ghost. When a theory has a symmetry mixing a ghost mode with ordinary non-ghost modes, the choice of a ghost mode is not unique. However, quantization of a ghost is impossible without specifying a choice of ghost mode, which breaks the symmetry. For this reason, the vacuum state cannot respect the symmetry. In the massive gravity theory with a graviton ghost mode in de Sitter background, the ghost is the helicity-0 mode of the graviton. This ghost mode is mixed with the other helicity graviton modes under the action of de Sitter symmetry. Therefore, there is no de Sitter invariant vacuum in such models. This leads to an interesting possibility that non-covariant cutoff of the low energy effective theory may naturally arise. As a result, the instability due to the pair production of a ghost and normal non-ghost particles gets much milder and that the model may escape from being rejected.
Nonlinear superhorizon perturbations in Horava-Lifshitz gravity
Keisuke Izumi,Shinji Mukohyama
Physics , 2011, DOI: 10.1103/PhysRevD.84.064025
Abstract: We perform a fully nonlinear analysis of superhorizon perturbation in Ho\v{r}ava-Lifshitz gravity, based on the gradient expansion method. We present a concrete expression for the solution of gravity equations up to the second order in the gradient expansion, and prove that the solution can be extended to any order. The result provides yet another example for analogue of the Vainshtein effect: the nonlinear solution is regular in the limit $\lambda\to 1$ and recovers general relativity coupled to dark matter at low energy. Finally, we propose a definition of nonlinear curvature perturbation ${\cal R}$ in Ho\v{r}ava-Lifshitz gravity and show that it is conserved up to the first order in the gradient expansion.
Renormalized Newtonian Cosmic Evolution with Primordial Non-Gaussianity
Keisuke Izumi,Jiro Soda
Physics , 2007, DOI: 10.1103/PhysRevD.76.083517
Abstract: We study Newtonian cosmological perturbation theory from a field theoretical point of view. We derive a path integral representation for the cosmological evolution of stochastic fluctuations. Our main result is the closed form of the generating functional valid for any initial statistics. Moreover, we extend the renormalization group method proposed by Mataresse and Pietroni to the case of primordial non-Gaussian density and velocity fluctuations. As an application, we calculate the nonlinear propagator and examine how the non-Gaussianity affects the memory of cosmic fields to their initial conditions. It turns out that the non-Gaussianity affect the nonlinear propagator. In the case of positive skewness, the onset of the nonlinearity is advanced with a given comoving wavenumber. On the other hand, the negative skewness gives the opposite result.
Cosmological Perturbation in f(T) Gravity Revisited
Keisuke Izumi,Yen Chin Ong
Physics , 2012, DOI: 10.1088/1475-7516/2013/06/029
Abstract: We perform detailed investigation of cosmological perturbations in f(T) theory of gravity coupled with scalar field. Our work emphasizes on the way to gauge fix the theory and we examine all possible modes of perturbations up to second order. The analysis includes pseudoscalar and pseudovector modes in addition to the usual scalar, vector, and tensor modes. We find no gravitational propagating degree of freedom in the scalar, pseudoscalar, vector, as well as pseudovector modes. In addition, we find that the scalar and tensor perturbations have exactly the same form as their counterparts in usual general relativity with scalar field, except that the factor of reduced Planck mass squared $M_{\text{pl}}^2 \equiv 1/(8\pi G)$ that occurs in the latter has now been replaced by an effective time-dependentgravitational coupling $-2 (df/dT)|_{T=T_0}$, with $T_0$ being the background torsion scalar. The absence of extra degrees of freedom of f(T) gravity at second order linear perturbation indicates that f(T) gravity is highly nonlinear. Consequently one cannot conclusively analyze stability of the theory without performing nonlinear analysis that can reveal the propagation of the extra degrees of freedom.
An Analysis of Characteristics in Non-Linear Massive Gravity
Keisuke Izumi,Yen Chin Ong
Physics , 2013, DOI: 10.1088/0264-9381/30/18/184008
Abstract: We study the Cauchy problem in a special case of non-linear massive gravity: the two-tensor "f-g" theory. Despite being ghost-free, it has recently been argued that the theory is inherently problematic due to the existence of superluminal shock waves. Furthermore it is claimed that acausal characteristic can arise for any choice of background. In order to further understand the causal structure of the theory, we carefully perform a detailed analysis of the characteristic equations and show that the theory does admit a well-posed Cauchy problem, i.e., there exist hypersurfaces that are not characteristic hypersurface. Puzzles remain regarding the existence of a superluminal propagating mode in both the f-g theory, as well as in the full non-linear massive gravity. That is, our result should not be taken as any indication of the healthiness of the theory. We also give a detailed review of Cauchy-Kovalevskaya theorem and its application in the Appendix, which should be useful for investigating causal structures of other theories of gravity.
Non-Gaussianity from Lifshitz Scalar
Keisuke Izumi,Takeshi Kobayashi,Shinji Mukohyama
Physics , 2010, DOI: 10.1088/1475-7516/2010/10/031
Abstract: A Lifshitz scalar with the dynamical critical exponent z = 3 obtains scale-invariant, super-horizon field fluctuations without the need of an inflationary era. Since this mechanism is due to the special scaling of the Lifshitz scalar and persists in the presence of unsuppressed self-couplings, the resulting fluctuation spectrum can deviate from a Gaussian distribution. We study the non-Gaussian nature of the Lifshitz scalar's intrinsic field fluctuations, and show that primordial curvature perturbations sourced from such field fluctuations can have large non-Gaussianity of order f_NL = O(100), which will be detected by upcoming CMB observations. We compute the bispectrum and trispectrum of the fluctuations, and discuss their configurations in momentum space. In particular, the bispectrum is found to take various shapes, including the local, equilateral, and orthogonal shapes. Intriguingly, all integrals in the in-in formalism can be performed analytically.
Systematic solution-generation of five-dimensional black holes
Hideo Iguchi,Keisuke Izumi,Takashi Mishima
Physics , 2011, DOI: 10.1143/PTPS.189.93
Abstract: Solitonic solution-generating methods are powerful tools to construct nontrivial black hole solutions of the higher-dimensional Einstein equations systematically. In five dimensions particularly, the solitonic methods can be successfully applied to the construction of asymptotically Minkowski spacetimes with multiple horizons. We review the solitonic methods applicable to higher-dimensional vacuum spacetimes and present some five-dimensional examples derived from the methods.
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