de Sitter group and Einstein-Hilbert Lagrangian

Abstract

Axial vector torsion in the Einstein-Cartan space $U_4$ is considered here. By picking a particular term from the SO(4,1) Pontryagin density and then modifying it in a SO(3,1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then considering torsion and torsion-less connection as independent fields, it has been found that $\kappa$ and $\lambda$ of Einstein-Hilbert Lagrangian, appear as integration constants in such a way that $\kappa$ has been found to be linked with the topological Nieh-Yan density of $U_4$ space.

14 pages

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Cited by in corpus (10)

• de Sitter gauge theories and induced gravities
• Cosmological Solutions with Torsion in a Model of de Sitter Gauge Theory of Gravity
• Torsion, Dirac Field, Dark Matter and Dark Radiation
• De Sitter spacetimes with torsion in the model of dS gauge theory of gravity
• Gauge theories and gravity
• On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity (II)
• Induced gravity from gauge theories
• Torsion, Chern-Simons Term and Diffeomorphism Invariance
• From Special Relativity to embedded generators in Cartan subalgebras of rank-4 spin algebras
• Axial Current and Noether Charge