Orthogonal non-Gaussianities from Dirac-Born-Infeld Galileon inflation

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 nonlinear 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.