On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity (II)

Abstract

It is shown that all torsion-free vacuum solutions of the model of de Sitter (dS) gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories with more general quadratic gravitational Lagrangian (F 2 + T 2 ), the torsion-free vacuum solutions are also the vacuum solutions of Einstein field equations.Keywords torsion-free vacuum solutions, model of de sitter gauge theory, gravity PACS numbers 04.20.Jb The astronomical observations show that our universe is probably an asymptotically de Sitter(dS) one [1][2][3][4][5][6]. This raises the interest on dS gauge theories of gravity. There is a model of dS gravity † , which was first proposed in the 1970s [7][8][9][10][11][12][13][14]. The dS gravity can be stimulated from dS invariant special relativity [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] and the principle of localization -the full symmetry of the special relativity as well as the laws of dynamics are both localized [32-37] -and realized in terms of the dS connection on a kind of totally umbilical submanifolds (under the dS-Lorentz gauge) and Yang-Mills type action [7][8][9][10][11][12][32][33][34][35][36]. It has been shown [35,36] that the dS gravity may explain the accelerating expansion and supply a natural transit from decelerating expansion to accelerating expansion without the help of the introduction of matter fields in addition to dust. The different de Sitter spacetimes with nonzero torsion in the dS gravity have been presented in Ref.[38]. It has also been shown that all vacuum solutions of Einstein field equations with a cosmological constant are the vacuum solutions of the set of field equations without torsion [32][33][34]37]. In particular, Schwarzschild-dS and Kerr-dS metrics are two solutions. The purpose of the present letter is to show that all vacuum, torsion-free solutions in the dS gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Therefore, one may expect that the dS gravity may pass all solar-system-scale observations and experimental tests for general relativity (GR).The dS gauge theory of gravity is established based on the following consideration. The non-gravitational theory is de Sitter invariant special relativity. The theory of gravity should follow the principle of localization, which says that the full symmetry as well as the laws of dynamics are both localized, and the gravitational action takes Yang-Mills-type.A model of dS gauge theory of gravity has been constructed [7][8][9][10][11][12][13][14][32][33][34][35][36][37] in terms of the de Sitter connection in the dS-Lorentz frame, which reads † †where B AB μ = η BC B A Cμ . Its curvature is thenwhere e a bμν = e a μ e bν − e a ν e bμ , e aμ = η ab e b μ , F ab μν and T a μν are the curvature and torsion of the Lorentz connection † Hereafter, the model of dS gauge theory of gravity is called the dS gravity for short in this paper. † † The...

Weak field approximation in a model of de Sitter gravity: Schwarzschild solutions and galactic rotation curves

“…Actually it has been shown [9,10] that the model with a small cosmological constant may explain the accelerating expansion of the universe and supply a natural transit from decelerating expansion to accelerating expansion without the help of introducing matter fields in addition to dust. It has also been shown [11,12] that all torsion-free vacuum solutions of this model are the vacuum solutions of Einstein's field equation with the same cosmological constant, and vise versa. Therefore, one may expect that the model with a small cosmological constant may pass all solar-system-scale experimental tests for general relativity (GR).…”

“…In the torsion-free case, the scalar curvature would be a constant from Eq. (12), and, therefore, Σ = const from Eq. (10).…”

Kaluza–Klein-type models of de Sitter and Poincaré gauge theories of gravity

“…where C abcd is the Weyl curvature tensor. It has been shown that all the torsion-free vacuum solutions of the dS gravity model are the vacuum solutions of GR with the same cosmological constant, and vice versa [18,19].…”

Weak Field Approximation in a Model of De Sitter Gravity: Schwarzschild–de Sitter Solutions

“…In this viewpoint, the metric field of the base spacetime contains not only the zeroth-order term but also the higher-order terms, as was shown in Eq. (9).…”

“…The model under this case, hereafter referred to as the dS gravity model or simply as the model, might be very different from GR. But fortunately, it has been shown [8,9] that all torsion-free vacuum solutions of the model are the vacuum solutions of GR with the same cosmological constant, and vise versa. Moreover, it has been shown [10,11] that the model may explain the accelerating expansion of the universe and supply a natural transit from decelerating expansion to accelerating expansion without the help of dark energy.…”