The most complete mass-dimension four topological gravity

Abstract

The usual Chern-Simons extension of Einstein gravity theory consists in adding a squared Riemann contribution to the Hilbert Lagrangian, which means that a square-curvature term is added to the linear-curvature leading term governing the dynamics of the gravitational field. However, in such a way the Lagrangian consists of two terms with a different number of curvatures, and therefore not homogeneous. To develop a homogeneous Chern-Simons correction to Einstein gravity we may, on the one hand, use the above-mentioned square-curvature contribution as the correction for the most general square-curvature Lagrangian, or on the other hand, find some linear-curvature correction to the Hilbert Lagrangian. In the first case, we will present the most general square-curvature leading term, which is in fact the already-known re-normalizable Stelle Lagrangian. In the second case, the topological current has to be an axial-vector built only in terms of gravitational degrees of freedom and with a unitary mass dimension, and we will display such an object. The comparison of the two theories will eventually be commented.

7 pages

References in corpus (5)

• Classification of Singular Spinor Fields and Other Mass Dimension One Fermions
• Bilinear Covariants and Spinor Fields Duality in Quantum Clifford Algebras
• Revealing how different spinors can be: the Lounesto spinor classification
• Spinors in Polar Form
• Polar solutions with tensorial connection of the spinor equation

Cited by in corpus (2)

• Revisiting Takahashi's inversion theorem in discrete symmetry-based dual frameworks
• Chern-Simons Extension of ESK Theory