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In this note, we study cosmic microwave background (CMB) constraints onprimordial non-Gaussianity in DBI galileon models in which an induced gravityterm is added to the Dirac-Born-Infeld (DBI) action. In this model, thenon-Gaussianity of orthogonal shape can be generated. We provide a relationbetween theoretical parameters and orthogonal/equilateral non-linear parametersusing the Fisher matrix approach for the CMB bispectrum. In doing so, weinclude the effect of the CMB transfer functions and experimental noiseproperties by employing the recently developed \textsf{SONG} code. The relationis also shown in the language of effective theory so that it can be applied togeneral single-field models. Using the bispectrum Fisher matrix and the centralvalues for equilateral and orthogonal non-Gaussianities found by the Plancktemperature survey, we provide forecasts on the theoretical parameters of theDBI galileon model. We consider the upcoming Planck polarisation data and theproposed post-Planck experiments COrE and PRISM. We find that Planckpolarisation measurements may provide a hint for a non-canonical sound speed atthe 68% confidence level. COrE and PRISM will not only confirm a non-canonicalsound speed but also exclude the conventional DBI inflation model at more thanthe 95% and 99% confidence level respectively, assuming that the central valueswill not change. This indicates that improving constraints on non-Gaussianityfurther by future CMB experiments is invaluable to constrain the physics of theearly universe.

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