  We study the cosmology of the multifield relativistic Galileon model in which
an induced gravity term is added to the Dirac-Born-Infeld action. We highlight
the physical insight that is gained by employing a bimetric perspective in
which the induced gravity and Einstein-Hilbert action are treated on equal
footing. We derive the conditions under which a phase of quasi exponential
inflation can be sustained and demonstrate the existence of a critical
background energy density above which cosmological fluctuations become ghosts.
At the non-linear level, this scenario provides the first concrete early
Universe model in which the shape of the bispectrum can be predominantly of
orthogonal type. More generally, we show that the shape and sign of the
primordial non-Gaussianities act as powerful discriminants of the precise
strength of the induced gravity.
