A Clifford algebra gauge invariant Lagrangian for gravity. Part 2 : compatibility with General Relativity tests

TL;DR

This paper develops a gauge-invariant gravitational Lagrangian using Clifford algebra, extending General Relativity with additional quadratic, cosmological, and torsion terms, and shows compatibility with classical tests in weak fields.

Contribution

It introduces a Clifford algebra-based gauge invariant Lagrangian for gravity that extends Einstein's theory and demonstrates its consistency with known tests of General Relativity.

Findings

No contradiction with GR in weak fields

Extended Lagrangian includes quadratic, cosmological, and torsion terms

Compatibility shown for various gravitational scenarios

Abstract

Gauge fields associated to the Dirac matrix algebra used with the standard quadratic gauge field Lagrangian lead to an extended gravitational Lagrangian which includes the Einstein-Hilbert one, plus quadratic, cosmological constant and torsion terms. This note looks at three cases : the static central symmetric field, the isotropic expanding universe, and the asymptotic field of a rotating body, and show that, in weak gravitational fields, there is no contradiction with General Relativity results.