# C. Castro: Clifford Space Gravitational Field Equations and Dark Energy

by Carlos Castro
Center for Theoretical Studies of Physical Systems
Clark Atlanta University, Atlanta, Georgia. 30314, perelmanc@hotmail.com
August 2012, Submitted to: J. Phys. A.

Abstract: We continue with the study of Clifford-space Gravity and analyze further the Clifford space ($C$-space) generalized gravitational field equations which are obtained from a variational principle based on the generalization of the Einstein-Hilbert-Cartan action. One of the main features is that the $C$-space connection requires $torsion$ in order to have consistency with the Clifford algebraic structure associated with the curved $C$-space basis generators. Hence no spin matter is required to induce torsion since it already exists in the vacuum. The field equations in $C$-spaces associated to a Clifford algebra in $D$-dimensions are $not$ equivalent to the ordinary gravitational equations with torsion in higher $2^D$-dimensions. The most physically relevant conclusion, besides the presence of torsion in the vacuum, is the contribution of the $higher$ grade metric components $g^{\mu_1 \mu_2 ~\nu_1 \nu_2}, g^{\mu_1 \mu_2 \mu_3~\nu_1 \nu_2 \nu_3 }, …$ of the $C$-space metric to dark energy/dark matter.