Inflation in DBI models with constant gamma

TL;DR

This paper explores specific DBI inflation models with a constant speed of sound, allowing for exact solutions and analytical spectra of scalar perturbations without slow roll assumptions.

Contribution

It introduces a class of DBI models with constant sound speed, detailing the conditions on potential and tension for exact solutions.

Findings

Exact solutions for scalar perturbations with constant sound speed

Models with $c_s<1$ where spectra are analytically derived

Relations between potential and tension for constant $c_s$

Abstract

Dirac-Born-Infeld scalar field theories which appear in the context of inflation in string theory in general have a field dependent speed of sound. It is however possible to write down DBI models which possess exact solutions characterized by a constant speed of sound different from unity. This requires that the potential and the effective D-brane tension appearing in a DBI action have to be related in a specific way. This paper describes such models in general and presents some examples with a constant speed of sound $c_s<1$ for which the spectrum of scalar perturbations can be found analytically without resorting to the slow roll approximation.