## Generalized Gravity in Clifford Spaces, Vacuum Energy and Grand Unification

**Authors:** Carlos Castro

Polyvector-valued gauge field theories in Clifford spaces are used to
construct a novel Cl(3, 2) gauge theory of gravity that furnishes modified
curvature and torsion tensors leading to important modifications of the
standard gravitational action with a cosmological constant. Vacuum solutions
exist which allow a cancellation of the contributions of a very
large cosmological constant term and the extra terms present in the modified
field equations. Generalized gravitational actions in Clifford-spaces
are provided and some of their physical implications are discussed. It is
shown how the 16 fermions and their masses in each family can be accommodated
within a Cl(4) gauge field theory. In particular, the Higgs
fields admit a natural Clifford-space interpretation that differs from the
one in the Chamseddine-Connes spectral action model of Noncommutative
geometry. We finalize with a discussion on the relationship with the
Pati-Salam color-flavor model group SU(4)_{C} x SU(4)_{F} and its symmetry
breaking patterns. An Appendix is included with useful Clifford algebraic
relations.

**Comments:** 21 pages, submitted to the Int. J. Mod. Phys. A.

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### Submission history

[v1] 11 Sep 2010

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