Embedding DBI inflation in scalar-tensor theory
  The Dirac-Born-Infeld (DBI) action has been widely studied as an interesting
example of a model of k-inflation in which the sound speed of the cosmological
perturbations differs from unity. In this article we consider a scalar-tensor
theory in which the matter component is a field with a DBI action. Transforming
to the Einstein frame, we explore the effect of the resulting coupling on the
background dynamics of the fields and the first-order perturbations. We find
that the coupling forces the scalar field into the minimum of its effective
potential. While the additional scalar field contributes significantly to the
energy density during inflation, the dynamics are determined by the DBI field,
which has the interesting effect of increasing the number of efolds of
inflation and decreasing the boost factor of the DBI field. Focusing on this
case, we show, with the benefit of numerical examples, that the power spectrum
of the primordial perturbations is determined by the behaviour of the
perturbations of the modified DBI field.
