## Progress in Clifford Space Gravity

**Authors:** Carlos Castro

Clifford-space Gravity is revisited and new results are found.
The Clifford space ($ C$-space) generalized gravitational field equations are obtained from a variational principle and which is based on an extension of the Einstein-Hilbert-Cartan action. One of the main results of this work is that the $C$-space connection requires torsion in order to have consistency between the Clifford algebraic structure and the zero nonmetricity condition $ \nabla_K g^{MN} = 0 $. A discussion on the cosmological constant and bi-metric theories of gravity follows. We continue by pointing out the relations of Clifford space gravity to Lanczos-Lovelock-Cartan (LLC) higher curvature gravity with torsion. We finalize by pointing out that $ C$-space gravity involves higher-spins beyond spin $ 2 $ and argue why one could view the LLC higher curvature actions, and
other extended gravitational theories based on $ f ( R ), f ( R_{\mu \nu} ), ... $ actions, for polynomial-valued functions, as mere $effective$ actions after integrating the $C$-space gravitational action with respect to all the poly-coordinates, except the vectorial ones $ x^\mu$.

**Comments:** 22 Pages. Submitted to Advances in Applied Clifford Algebras

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### Submission history

[v1] 2012-07-24 09:18:58

[v2] 2012-07-25 03:48:47

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