## R x C x H x O-valued Gravity as a Grand Unified Field Theory

**Authors:** Carlos Castro

We argue how {\bf R} $\otimes$ {\bf C} $\otimes$ {\bf H} $\otimes$ {\bf O}-valued Gravity (real-complex-quaterno-octonionic Gravity) naturally can describe a grand unified field theory of Einstein's gravity
with an $ U(8)$ Yang-Mills theory. In particular, it allows for an extension of the Standard Model by including a $3$-family $SU(3)_F$ symmetry group, a $SU(2)_R$ and an extra $ U(1)$ symmetry. A unification of left-right $SU(3)_L \times SU(3)_R$, color $SU(3)_C$ and family $SU(3)_F$ symmetries in a
maximal rank-$8$ subgroup of $E_8$ has been proposed by \cite{Molina} as a landmark for future explorations beyond the
Standard Model. It is warranted to explore further if this latter model also admits a similar gravitational interpretation based on the above
composition of normed division algebras. Furthermore, our construction leads also to a $bimetric$ theory of gravity which may have a role in dark energy. The crux of this approach is that we have $replaced$ the Kaluza-Klein prescription to generate gauge symmetries in lower dimensions from isometries of the internal manifold, by the $U (8)$ isometry transformations of the {\bf R} $\otimes$ {\bf C} $\otimes$ {\bf H} $\otimes$ {\bf O}-valued metric. We finalize with a discussion on $U(16)$ Matrix Gravity (Geometry), String Theory and Division algebras.

**Comments:** 18 Pages. Submitted to Advances in Applied Clifford Algebras

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### Submission history

[v1] 2018-08-14 08:40:38

[v2] 2018-08-19 03:22:19

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