We construct Kaluza-Klein-type models with a de Sitter or Minkowski bundle in the de Sitter or Poincaré gauge theory of gravity, respectively. A manifestly gaugeinvariant formalism has been given. The gravitational dynamics is constructed by the geometry of the de Sitter or Minkowski bundle and a global section which plays an important role in the gauge-invariant formalism. Unlike the old Kaluza-Kleintype models of gauge theory of gravity, a suitable cosmological term can be obtained in the Lagrangian of our models and the models in the spin-current-free and torsionfree limit will come back to general relativity with a corresponding cosmological term. We also generalize the results to the case with a variable cosmological term.
In de Sitter (dS) gravity, where gravity is a gauge field introduced to realize the local dS invariance of the matter field, two kinds of conservation laws are derived. The first kind is a differential equation for a dS-covariant current, which unites the canonical energy-momentum (EM) and angular momentum (AM) tensors. The second kind presents a dS-invariant current which is conserved in the sense that its torsion-free divergence vanishes. The dS-invariant current unites the total (matter plus gravity) EM and AM currents. It is well known that the AM current contains an inherent part, called the spin current. Here it is shown that the EM tensor also contains an inherent part, which might be observed by its contribution to the deviation of the dust particle's world line from a geodesic. All the results are compared to the ordinary Lorentz gravity. divergence vanishes [7,8]. The Lorentz-invariant currents can be used to define the total EMA currents in Lorentz gravity.Note that in Lorentz gravity, gravity is not a gauge field, in the sense that it is not an Ehresmann connection of some principal fiber bundle. On the other hand, there exists the de Sitter (dS) gravity [9-13], where gravity is described by an Ehresmann connection which is introduced to realize the local dS invariance of the matter field. The dS gravity is well motivated for some cosmological reasons. Firstly, the observed cosmological constant may be related to that of the internal dS space, which is a characteristic structure in dS gravity. Moreover, an interesting investigation shows that [13,14], the dS symmetry together with a Kaluza-Klein-type ansatz can pick out the only one model that is free of the big-bang singularity in the Robertson-Walker universe filled with a spin fluid [15], among the R + βS abc S abc models of gravity [16], where R is the scalar curvature, β is a parameter, and S abc denotes the torsion tensor.In this paper, the EMA conservation laws are generalized to dS gravity. The result consists of two kinds of conservation laws. Firstly, it is shown that the diffeomoriphism and dS symmetries lead to a differential equation for a dS-covariant current, which unites the EM and spin tensors. Secondly, provided the gravitational field equation is satisfied, each one-parameter group of dS rotations result in a dS-invariant current, which is conserved in the sense that its torsion-free divergence vanishes. The dS-invariant current can be used to define the total (matter plus gravity) EMA currents in dS gravity. In the analysis of the first kind conservation law, it is found that the EM tensor contains an inherent part, just like the fact that the angular momentum (AM) current contains an inherent part (the spin current). Also, the dust particle's world line is studied, which deviates from a geodesic for two reasons. The first is the existence of the spin tensor, while the second is the existence of the inherent EM tensor discovered here.The paper is arranged as follows. In section 2, the dS gravity is briefly introduced. In sections 3...
Weak field approximate solutions in the Λ → 0 limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotation curves without invoking dark matter.
It is shown that among the R+beta S^{abc}S_{abc} models, only the one with beta=1/2 has nonvanishing torsion effect in the Robertson--Walker universe filled with a spin fluid, where S_{abc} denotes torsion. Moreover, the torsion effect in that model is found to be able to replace the big-bang singularity by a big bounce. Furthermore, we find that the model can be obtained under a Kaluza--Klein-like ansatz, by assuming that the gravitational gauge group is the de Sitter group.Comment: 9 pages. arXiv admin note: substantial text overlap with arXiv:1402.365
In de Sitter (dS) special relativity (SR), two kinds of conserved currents are derived. The first kind is a 5-dimensional (5d) dS-covariant angular momentum (AM) current, which unites the energy-momentum (EM) and 4d AM current in an inertial-type coordinate system. The second kind is a dS-invariant AM current, which can be generalized to a conserved current for the coupling system of the matter field and gravitational field in dS gravity. Moreover, an inherent EM tensor is predicted, which comes from the spin part of the dS-covariant current. All the above results are compared to the ordinary SR with Lorentz invariance.
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