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

Abstract

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.

On the difference between Poincaré and Lorentz gravity

“…is the curvature 2-form of Ω A Ba . It can be verified that F α βab = R α βab is the Lorentz curvature (11), and in the Lorentz gauge F α 4ab = S α ab · l −1 is the torsion 2-form. Finally, the gravitational field equations are given by V A Ba ≡ δS/δΩ A Ba = 0 and V A ≡ δS/δξ A = 0, where S = S M + S G .…”

R+S2 theories of gravity without big-bang singularity

“…[9] is used, L G is the gravitational Lagrangian, R is the scalar curvature, Λ is the positive cosmological constant, S cab = g cd S d ab , S d ab is the torsion tensor, g cd is the metric tensor, S a = S c ac , a, b, c, etc., are abstract indices [21,22], and a 1 , a 2 , a 3 are three dimensionless parameters. The Lagrangian (1) is gauge invariant because each of the metric, torsion and curvature can be expressed in a gauge-invariant way [2][3][4][8][9][10]. Moreover, the Lagrangian is complete in the sense that it contains all components of the gravitational field strength F ab , i.e., it contains both curvature and torsion.…”

“…in a special gauge [8,9], where R α βab is the curvature 2-form with respect to an orthonormal frame field {e α a }, S α ab is the torsion 2-form with respect to {e α a }, {e α a } is the dual of {e α a }, e βb = η αβ e α b , S βab = η αβ S α ab , α, β = 0, 1, 2, 3, and l > 0 is related to the cosmological constant by Λ = 3/l 2 . Also, the Lagrangian (1) is simple in the sense that it is comprised of the simplest curvature and torsion scalars.…”

“…The spacetime torsion is introduced in the gauge theory of gravity [1][2][3][4][5][6][7][8][9][10] to realize the local Poincaré, de Sitter (dS) or Anti-de Sitter (AdS) symmetry. It is shown that the torsion effect in the Einstein-Cartan (EC) theory, which is the simplest model of the gauge theory of gravity, may avert the initial singularity of the homogeneous but anisotropic universe [11], where the matter fields are described by a spin fluid [12].…”

Cosmological meaning of the gravitational gauge group

“…It has been pointed out that there are three kinds of special relativity (SR) [1][2][3][4] and gravity should be based on the localization of a SR with full symmetry [5][6][7]. It is a motivation for the study of the Poincaré, de Sitter (dS) or Anti-de Sitter (AdS) gauge theory of gravity [8][9][10][11][12], where the Riemann-Cartan (RC) geometry with nontrivial metric and torsion is introduced to realize the corresponding gauge symmetry.…”