Author
Kenji Hayashi
Other affiliations: Max Planck Society, University of Tokyo
Bio: Kenji Hayashi is an academic researcher from Kitasato University. The author has contributed to research in topics: Introduction to gauge theory & General relativity. The author has an hindex of 13, co-authored 25 publications receiving 1994 citations. Previous affiliations of Kenji Hayashi include Max Planck Society & University of Tokyo.
Papers
More filters
••
TL;DR: In this article, it was shown that a static, spherically symmetric gravitational field is given by the Schwarzschild metric, and that in the weak-field approximation an antisymmetric field of zero mass and zero spin exists, besides gravitons.
Abstract: A gravitational theory is formulated on the Weitzenb\"ock space-time, characterized by the vanishing curvature tensor (absolute parallelism) and by the torsion tensor formed of four parallel vector fields. This theory is called new general relativity, since Einstein in 1928 first gave its original form. New general relativity has three parameters ${c}_{1}$, ${c}_{2}$, and $\ensuremath{\lambda}$, besides the Einstein constant $\ensuremath{\kappa}$. In this paper we choose ${c}_{1}=0={c}_{2}$, leaving open $\ensuremath{\lambda}$. We prove, among other things, that (i) a static, spherically symmetric gravitational field is given by the Schwarzschild metric, that (ii) in the weak-field approximation an antisymmetric field of zero mass and zero spin exists, besides gravitons, and that (iii) new general relativity agrees with all the experiments so far carried out.
1,075 citations
••
269 citations
••
TL;DR: In this paper, a new general relativity formulated on the Weitzenbock space-time has been proposed, which is invariant under a class of local Lorentz transformations.
Abstract: We make a short comment on our new general relativity formulated on the Weitzenb\"ock space-time. The new general relativity considered here has one free parameter besides the Einstein constant $\ensuremath{\kappa}$. The total action is invariant under a class of local Lorentz transformations, besides being invariant under general coordinate and global Lorentz transformations. The consequences of this "restricted local Lorentz invariance" are studied.
196 citations
••
103 citations
••
TL;DR: In this paper, the authors apply the weak field approximation to the most general general gravitational field equations in Poincare gauge theory and show that there are two routes to arrive at the Newtonian potential.
Abstract: We apply the weak field approximation to the most general gravitational field equations in Poincare gauge theory. The weak gravitational field h., is a multimass field obeying a fourth-order field equation. In the Newtonian approximation we show that there are two routes to arrive at the Newtonian potential. The torsion field is decomposed into six irre ducibe building blocks with spinparlty, 2+, z-, 1+, 1-, o+ and o-, each of which obeys the Klein-Gordon equation. Finally, we construct a possible candidate for the massless graviton field which obeys the linearized Einstein equation.
92 citations
Cited by
More filters
••
TL;DR: In this paper, the authors systematically review some standard issues and also the latest developments of modified gravity in cosmology, emphasizing on inflation, bouncing cosmology and late-time acceleration era.
1,950 citations
••
[...]
TL;DR: In this article, the authors considered a modified theory of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and of the trace of the stress-energy tensor.
Abstract: We consider $f(R,T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the trace of the stress-energy tensor $T$. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the stress-energy tensor. Generally, the gravitational field equations depend on the nature of the matter source. The field equations of several particular models, corresponding to some explicit forms of the function $f(R,T)$, are also presented. An important case, which is analyzed in detail, is represented by scalar field models. We write down the action and briefly consider the cosmological implications of the $f(R,{T}^{\ensuremath{\phi}})$ models, where ${T}^{\ensuremath{\phi}}$ is the trace of the stress-energy tensor of a self-interacting scalar field. The equations of motion of the test particles are also obtained from a variational principle. The motion of massive test particles is nongeodesic, and takes place in the presence of an extra-force orthogonal to the four velocity. The Newtonian limit of the equation of motion is further analyzed. Finally, we provide a constraint on the magnitude of the extra acceleration by analyzing the perihelion precession of the planet Mercury in the framework of the present model.
1,833 citations
••
TL;DR: In this paper, a review of different dark energy cosmologies for different fluids is presented, and their properties are also explored, and special attention is paid to the equivalence of different models.
Abstract: We review different dark energy cosmologies. In particular, we present the ΛCDM 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 ΛCDM 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 ΛCDM 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) Hořava-Lifshitz gravity and the teleparallel f(T) gravity. The cosmology of such models representing the ΛCDM-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.
1,552 citations
••
TL;DR: In this article, the authors present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the SL(4, R), or the GL(4-R) covering subgroup.
1,474 citations
••
TL;DR: In this article, a review of different dark energy cosmologies is presented, including the Lambda$CDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmology with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes.
Abstract: 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, 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 $F(R)$ Hořava-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.
1,467 citations