MG11 
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Inflationary Cosmological Model inspired by Non-Commutative Geometry

We propose to extend the non-abelian generalization of Born-Infeld non-linear Lagrangian to the non-commutative geometry of matrices on a manifold. In this model not only the usual SU(n) gauge fields appear, but also a natural generalization of the multiplet of scalar Higgs fields, with the double-well potential.The matrix realization of non-commutative geometry provides a natural framework for obtaining a Born-Infeld-like Lagrangian as a root of sufficiently high order of a combination of metric and gauge and scalar field interactions. We then analyze the behavior of cosmological models with this Lagrangian, It leads to primordial inflation with varying speed, with possibility of early deceleration ruled by the relative strength of the Higgs field.