  In scalar-tensor theories the scalar fields generically couple nontrivially
to gravity. We study the observable properties of inflationary models with
non-minimally coupled inflaton and Dirac-Born-Infeld (DBI) kinetic term. Within
the assumptions of the priors of our Monte-Carlo simulations we find these
models can generate new interesting observable signatures. Our discussion
focuses on string theory inspired phenomenological models of relativistic
D-brane inflation. While successful string theory constructions of ultra-violet
DBI brane inflation remain elusive, we show that in suitable regions of the
parameter space it is possible to use cosmological observables to probe the
non-minimial coupling. Fortunately, the most observationally promising range of
parameters include models yielding intermediate levels of non-gaussianity in
the range consistent with WMAP 5-year data, and to be constrained further by
the Planck satellite.
