2006/07/31 by Antonio Troisi, A. TROISI, Emmanuel Sérié +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Generalization #Gravitation #Higgs boson #Higgs field #Inflation (cosmology) #Lagrangian #Noncommutative and Quantum Gravity Theories #Scalar (mathematics) #Scalar field #Scalar potential #gr-qc #hep-th
paper · pdf · doi:10.1142/s0219887807001989
published as ECONF C0602061:13,2006; Int.J.Geom.Meth.Mod.Phys.4:249,2007 · 27 pages
arxiv created 2006/09/24 · openalex publication_date 2007/03/01 · openalex created_date 2016/06/24 · arxiv updated 2016/08/16 · openalex updated_date 2026/08/05
The non-abelian generalization of the Born–Infeld non-linear lagrangian is extended to the non-commutative geometry of matrices on a manifold. In this case, not only do the usual SU(n) gauge fields appear, but also a natural generalization of the multiplet of scalar Higgs fields, with the double-well potential as a first approximation. The matrix realization of non-commutative geometry provides a natural framework in which the notion of a determinant can be easily generalized and used as the lowest-order term in a gravitational lagrangian of a new kind. As a result, we obtain a Born–Infeld-like lagrangian as a root of sufficiently high order of a combination of metric, gauge potentials and the scalar field interactions. We then analyze the behavior of cosmological models based on this lagrangian. It leads to primordial inflation with varying speed, with possibility of early deceleration ruled by the relative strength of the Higgs field.