Cosmological model with Born-Infeld type scalar field

TL;DR

This paper develops a novel cosmological model using a Born-Infeld type scalar field within non-commutative geometry, leading to inflationary scenarios with variable speed and potential early deceleration.

Contribution

It introduces a new Born-Infeld-like gravitational Lagrangian incorporating non-commutative geometry and scalar fields, extending previous models with a matrix-based approach.

Findings

Predicts primordial inflation with varying speed

Allows for early deceleration depending on Higgs field strength

Provides a framework for integrating gauge fields and scalar fields in cosmology

Abstract

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.