Inflation in DBI models with constant γ

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 cs<1 for which the spectrum of scalar perturbations can be found analytically without resorting to the slow-roll approximation