Cosmological model with Born-Infeld type scalar field

Details Cosmological model with Born-Infeld type scalar field Cosmological model with Born-Infeld type scalar field

2006-07-24

arxiv.org/abs/gr-qc/0607105v2

ECONF C0602061:13,2006; Int.J.Geom.Meth.Mod.Phys.4:249,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages

Scientific paper

10.1142/S0219887807001989

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 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.

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