Pre-gravitation [ SU(2)_R x U(1)_grav ] as the right-handed counterpart of the electroweak interaction.

There is a long history of researchers suspecting a connection between the weak force and gravitation. For several reasons; the foremost being that the weak force violates parity - only left-handed particles take part in it. Parity is a space-time symmetry, and if the weak force is exclusively an internal symmetry, how does it know about space-time, which is related to gravity? Also, unlike the strong force (only for quarks) and electrodynamics (only charged particles) the weak force is universal, just as gravity is. Moreover, the coupling constants for the weak force and for gravitation - both are dimensionful, whereas those for QCD and for electromagnetism are both dimensionless. Thus in many ways weak force is more like gravity and less like QCD and ED; maybe the weak force is the `gravity' of extra dimensions which are much smaller in scale than our 4D universe?

Many models have been put forth to unify weak force and gravity, but the going is not easy. Gravity is a spin-2 attractive force; whereas the weak interaction is a spin-one vector interaction unified in the electroweak theory. Trying to quantise gravi-weak will face the difficulties faced by quantum gravity theories.

The octonionic description of interactions provides promising evidence that pre-gravitation is the right-handed counterpart of electroweak. The octonions define the coordinate geometry of a physical space, the geometry of which is related to the four fundamental forces, generalising Einstein's vision of gravitation as geometry of 4D spacetime. The symmetry groups of the octonions [the exceptional Lie groups; particularly E_6 and E_8] exhibit subgroup structures coinciding with the symmetry groups of the standard model.

In particular, one sees subgroups SU(2) x U(1) x SU(2) x U(1) and it's possible to identify the first pair as SU(2)_L x U(1)_Y of the electroweak theory. The second SU(2)xU(1) arises in the description of the Left-Right symmetric extension of the standard model using E_6. Typically the associated vector bosons are interpreted as right-handed ultra-heavy W bosons.

We forego this interpretation, and instead associate the second pair SU(2)xU(1) with pre-gravitation: right handed counterpart SU(2)_R x U(1)_grav of EW. Analogous to how electric charge is defined from a U(1) operator in octonionic physics [U(1)_em --> U(1)_Y] we associate the quantum number sqrt {m} [square-root of mass] with fermions: plus sqrt{m} for matter, and -sqrt{m} for anti-matter. The motivation comes from noting that the mass ratios of electron, up quark and down quark are 1:4:9 whereas their charge ratios are 3:2:1 Invoking square-root of mass as quantum number introduces a L-R symmetry, also a gauge-gravity duality. Square-root of mass is the pre-gravitational charge which mediates pre-gravitation: attractive for matter-matter and for antimatter-antimatter, but repulsive for matter-antimatter.

Whatever was the early universe process that separated matter from antimatter, it leaves behind only attractive pre-gravity in our observed universe. It is known that SU(2)_R chiral gravity [Ashtekar connection gravity] can be mapped to Einstein's general relativity. The Chamseddine-Connes spectral action principle [eigenvalues of the squared Dirac operator as observables for gravity (Landi and Rovelli)] enables the same conclusion. Thus by removing antimatter from the scene, the pre-gravitational vector interaction is FAPP mapped to the attractive gravitational force we are familiar with.

What separated matter and antimatter in the early universe? Possibly a freeze-out accompanied by an effective CP violation, which disallowed further back-conversion of matter-antimatter to radiation. The matter became our universe; the antimatter perhaps went inside primordial black holes - the role of such antimatter PBH in our universe remains to be understood, including whether they are even allowed.

This apart, the octonionic theory gives rise to a decent possibility of convincingly relating the weak force to gravity, once plus-minus square-root mass is introduced as a quantum number mediating pre-gravitation. Weak interaction violates parity because the RH fermions take part in the RH counterpart of the weak force: pre-gravitation. There is evidence that the weak force is the gravity of two of the additional dimensions in octonionic space [ie 6D spacetime]. From the octonionic Lagrangian it is immediately evident that the ED and QCD coupling constants are dimensionless, whereas the other two are not.

It makes a whole lot of sense that all the four forces are vector interactions - unification becomes easier: spin 1/2 fermions and spin one gauge bosons.

The Higgs boson: the Higgs gives mass to the LH bosons, `transferring' it from the RH ones. It appears to be the case that additional Higgs ought to exist, giving electric charge to the RH bosons. This suggests that the Higgs is a triplet; something proposed by other researchers earlier. A triplet Higgs has also been suggested as a possible explanation for the recently claimed W boson mass anomaly [assuming it stands up to further scrutiny].