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 $κ$ and $λ$ of Einstein-Hilbert Lagrangian, appear as integration constants in such a way that $κ$ has been found to be linked with the topological Nieh-Yan density of $U_{4}$ space.