de Sitter group and Einstein-Hilbert Lagrangian

TL;DR

This paper explores the role of axial vector torsion in Einstein-Cartan space, linking Einstein-Hilbert parameters to topological densities through a modified Pontryagin term.

Contribution

It introduces a novel Lagrangian density derived from a modified SO(4,1) Pontryagin density, connecting Einstein-Hilbert constants with topological invariants.

Findings

$$ and $$ appear as integration constants

$$ linked with Nieh-Yan density

Modified Pontryagin density yields new insights into torsion and gravity

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.