Gravi-Weak Unification and Multiple Point Principle

Abstract

We construct a model unifying gravity with weak $SU(2)$ gauge and "Higgs" scalar fields. We assume the existence of a visible and an invisible (hidden) sector of the Universe. We used the extension of Plebanski's 4-dimensional gravitational theory, in which the fundamental fields are two-forms containing tetrads, spin connections and additional auxiliary fields. Considering a $Spin(4,4)$ invariant extended Plebanski action, we recover the actions in both (visible and invisible) sectors of the Universe. After symmetry breaking of the graviweak (GW) unification, its physical constants (Newton's constants, cosmological constants, YM-couplings, etc.), are determined by a parameter $g_{uni}$ of the GW unification. It is discussed that if this "Higgs" field coming in the GW unification could be the Higgs of the Standard Model, then the idea that its vacuum value could be, according to the Multiple Point Principle, a second minimum of the Higgs field effective potential, turns out not to be viable. Then other scalar "Higgs" field, giving the inflation and axion fields, has a Planck scale expectation value, and could have a better chance of being the scalar field unified with gravity.