De Sitter gauge theory of gravitation, 2

De Sitter gauge theory of gravitation formulated in a previous paper is developed further. Covariant field strengths and their decompositions into the irreducible components are given, and with them the most general form of quadratic Lagrangian density of the gauge field is constructed. In the infinite limit of the radius Ω of the de Sitter universe, the Lagrangian density is reduced to Poincare gauge invariant one if the parameters in it satisfy certain conditions. The affine connection of the space-time is related to the gauge field on the basis of a postulate from which the metricity of the space-time follows. The space-time is torsionless if and only if a field-field strength identity is satisfied. The Einstein and Kibble type Lagrangian densities are special cases of our Lagrangian density. (author)