## 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.

**Download:** **PDF**

### Submission history

[v1] 11 Sep 2010

**Unique-IP document downloads:** 194 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*