An E₈ ⊗ E₈ Unification of the Standard Model with Pre-Gravitation, on an Exceptional Lie algebra - Valued Space

We propose an E₈ ⊗ E₈ unification of the standard model with pre-gravitation, on an exceptional Lie algebra-valued space . Each of the E₈ has in its branching an $SU(3)$ for space-time and an $SU(3)$ for three fermion generations. The first E₈ further branches to the standard model SU(3)c ⊗ SU(2)L ⊗ U(1)Y and describes the gauge bosons, Higgs and the left chiral fermions of the standard model. The second E₈ further branches into a right-handed counterpart (pre-gravitation) SU(3)grav⊗ SU(2)R ⊗ U(1)g of the standard model, and describes right chiral fermions, a Higgs, and twelve gauge bosons associated with pre-gravitation, from which general relativity is emergent. We account for 208 out of the 496 degrees of freedom of E₈ ⊗ E₈ and propose an interpretation for the remaining 288, motivated by the trace dynamics Lagrangian of our theory. We explain how the two copies of SU(3)spacetime together give rise to a 6D spacetime with signature $(3,3)$ which upon symmetry breaking gives rise to our 4D spacetime and to a second 4D anti-spacetime with flipped signature.