Octonions, scale invariance, and a CPT symmetric universe

In the octonionic theory, prior to the so-called left-right symmetry breaking, the symmetry group is E8 and the Lagrangian of the theory is scale invariant. There is only one parameter, a length scale, which appears as an overall multiplier of the trace Lagrangian.

Something dramatic happens after the symmetry breaking. Three new parameters emerge, to characterise the fermions:

Electric charge, has two signs, sign change operation C is complex conjugation. Ratios (0, 1/3, 2/3, 1)

Chirality / spin, has two signs, sign change operation P is octonionic conjugation. Ratios (1/2, -1/2)

Square-root of mass, has two signs, sign change operation T is time reversal t --> -t . Ratios (0, 1/3, 2/3, 1)

Thus there are 2x2x2 = 8 types of fermions, based on sign of charge, sqrt mass, spin.

This offers an attractive explanation for the origin of matter-antimatter asymmetry. A CPT symmetric universe. The four types of fermions which have positive sqrt mass become matter, our universe, moving forward in time. The other four types of fermions, which have negative sqrt mass, become anti-matter, a mirror universe moving backward in time ! The forward moving universe and the backward moving universe together restore CPT symmetry. Our universe by itself violates T, and hence also CP. Matter and anti-matter repel each other gravitationally, thus explaining their separation.

Prior to the symmetry breaking, an octonionic inflation [scale invariant, time-dependent in Connes time] precedes the `big bang' creation event, which is the symmetry breaking itself. Freeze out happens when radiation --> matter-antimatter is no longer favorable. Segregation takes place; our matter universe has a one in a billion excess of matter over anti-matter. The backward in time mirror universe has a one in a billion excess of anti-matter over matter.

The maths of complex octonions naturally accounts for the C, P, T operations. Scale invariance is transformed into CPT invariance in the emergent universe.

In an elegant proposal, Turok and Boyle have also recently proposed a CPT symmetric universe [mirror universes]. They, however, did not use the octonions.