C. Castro: On Clifford Space and Higher Curvature Gravity

Authors: Carlos Castro

Abstract: Clifford-space Gravity is revisited and new results are found. A derivation of the proper expressions for the connections (with $torsion$) in Clifford spaces ( $C$-spaces) is presented. The introduction of hyper-determinants of hyper-matrices are instrumental in the derivation of the C-space generalized gravitational field equations from a variational principle and based on the extension of the Einstein-Hilbert-Cartan action. We conclude by pointing out the relations of Clifford space gravity to Lanczos-Lovelock-Cartan higher curvature gravity with torsion and extended gravitational theories based on $f ( R ), f ( R_{\mu \nu} ), …$ actions, for polynomial-valued functions. Introducing nonmetricity furnishes higher curvature extensions of metric affine theories of gravity.

Comments: 16 Pages. Submitted to Foundations of Physics.