On the Slow Roll Expansion for Brane Inflation

TL;DR

This paper examines the slow roll approximation in string theory-based brane inflation models with non-canonical kinetic terms, deriving modified conditions for inflation when using the Dirac-Born-Infeld action.

Contribution

It derives the slow roll expansion for DBI brane inflation models, extending standard conditions to non-canonical kinetic energy frameworks.

Findings

Slow roll conditions are modified for DBI models.

Inflation can occur without potential energy dominance in DBI scenarios.

The standard slow roll approximation is extended to non-canonical kinetic terms.

Abstract

One possibility for identifying the inflaton in the framework of string theory is that it is a $D$-brane modulus. This option involves a specific, non-canonical form of the kinetic energy -- the Dirac-Born-Infeld action. This note investigates the applicability of the slow roll approximation in inflationary models of this type. To this end the slow roll expansion of Liddle, Parsons and Barrow is derived for the case of the DBI action. The resulting slow roll conditions augment the standard ones valid in the case of canonical kinetic terms. It is also shown that in DBI models inflation does not require that the potential dominate the energy density.