Cosmological model with Born-Infeld type scalar field

Antonio Troisi (1) , Emmanuel Sérié (2, 3) , Richard Kerner (3)

1 Dipartimento di Scienze Fisiche [Naples]
2 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
3 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

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.

Mots clés: Born-Infeld Lagrangian; Primordial cosmology; Scalar field

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Antonio Troisi, Emmanuel Sérié, Richard Kerner. Cosmological model with Born-Infeld type scalar field. 2006. ⟨hal-00087300v2⟩