Orthogonal non-Gaussianity in DBI Galileon: prospect for Planck polarisation and post-Planck experiments

In this note, we study cosmic microwave background (CMB) constraints on primordial non-Gaussianity in DBI galileon models in which an induced gravity term is added to the Dirac-Born-Infeld (DBI) action. In this model, the non-Gaussianity of orthogonal shape can be generated. We provide a relation between theoretical parameters and orthogonal/equilateral non-linear parameters using the Fisher matrix approach for the CMB bispectrum. In doing so, we include the effect of the CMB transfer functions and experimental noise properties by employing the recently developed \textsf{SONG} code. The relation is also shown in the language of effective theory so that it can be applied to general single-field models. Using the bispectrum Fisher matrix and the central values for equilateral and orthogonal non-Gaussianities found by the Planck temperature survey, we provide forecasts on the theoretical parameters of the DBI galileon model. We consider the upcoming Planck polarisation data and the proposed post-Planck experiments COrE and PRISM. We find that Planck polarisation measurements may provide a hint for a non-canonical sound speed at the 68% confidence level. COrE and PRISM will not only confirm a non-canonical sound speed but also exclude the conventional DBI inflation model at more than the 95% and 99% confidence level respectively, assuming that the central values will not change. This indicates that improving constraints on non-Gaussianity further by future CMB experiments is invaluable to constrain the physics of the early universe.