Relations Between Standard Model Parameters from $T^{'}$ Flavor Symmetry
Spontaneously broken flavor symmetry involving the binary tetrahedral group $T^{'}$ relates parameters in the standard model. In one example the CP violating Pontecorvo-Maki-Nakagawa-Sakata phase $\delta_{PMNS}$ and atmospheric mixing angle $\theta_{23}$ of neutrinos are related to the Cabibbo mixing angle $\Theta_C$ for quarks. A second formula relates a ratio of neutrino mass eigenvalues to the Cabibbo angle.
CYCLIC UNIVERSE AND INFINITE PAST
We address two questions about the past for infinitely cyclic cosmology. The first is whether it can contain an infinite length null geodesic into the past in view of the Borde–Guth–Vilenkin (BGV) "no-go" theorem, The second is whether, given that a small fraction of spawned universes fail to cycle, there is an adequate probability for a successful universe after an infinite time. We give positive answers to both questions and then show that in infinite cyclicity the total number of universes has been infinite for an arbitrarily long time.
The unfolded universe of elementary particles. A geometric explanation of the standard model structure
We propose a geometric explanation of the standard model of Glashow, Weinberg and Salam for the known elementary particles. Our model is a generic Quantum Field Theory in dimension four, obtained by developing along a Lorentz sub-manifold the lagrangian of Einstein and Dirac in dimension twelve. The main mechanism which gives birth to the standard model is a certain gauge fixing of triality, which permits to identify the multiplicity of fermions, as seen from the four dimensional world, with the eight unseen dimensions of the generating universe. In this way we get the known tables of particles, explaining the series of fermions and the gauge bosons. We suggest that the Higgs field dynamics could appear through a bosonization of the right handed neutrino and correspond to a displacement in the unseen dimensions. We also propose hypotheses for dark matter, and perhaps dark energy. Then we suggest predictions to go beyond the standard model.