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Grand symmetry models in noncommutative geometry have been introduced toexplain how to generate minimally (i.e. without adding new fermions) an extrascalar field beyond the standard model, which both stabilizes the electroweakvacuum and makes the computation of the mass of the Higgs compatible with itsexperimental value. In this paper, we use Connes-Moscovici twisted spectraltriples to cure a technical problem of the grand symmetry, that is theappearance together with the extra scalar field of unbounded vectorial terms.The twist makes these terms bounded and - thanks to a twisted version of thefirst-order condition that we introduce here - also permits to understand thebreaking to the standard model as a dynamical process induced by the spectralaction. This is a spontaneous breaking from a pre-geometric Pati-Salam model tothe almost-commutative geometry of the standard model, with two Higgs-likefields: scalar and vector.

Twisted spectral triple for the Standard Model and spontaneous breaking of the Grand Symmetry