In this paper we compute the sizes of equilateral and orthogonal shape bispectrum for the general Lorentz invariant single-field inflation. The stability of field theory implies a non-negative square of sound speed which leads to a consistency relation between the sizes of orthogonal and equilateral shape bispectrum, namely $f_{ NL}^{ orth.}\lesssim -0.054 f_{ NL}^{ equil.}$. In particular, for the single-field Dirac-Born-Infeld (DBI) inflation, the consistency relation becomes $f_{ NL}^{ orth.}\simeq 0.070 f_{ NL}^{ equil.}\lesssim 0$. These consistency relations are also valid in the mixed scenario where the quantum fluctuations of some other light scalar fields contribute to a part of total curvature perturbation on the super-horizon scale and may generate a local form bispectrum. A distinguishing prediction of the mixed scenario is $\tau_{ NL}^{ loc.}>({ 6\over 5}f_{ NL}^{ loc.})^2$. Comparing these consistency relations to WMAP 7yr data, there is still a big room for the Lorentz invariant inflation, but DBI inflation has been disfavored at more than 68% CL.
Categories: astro-ph.CO gr-qc hep-ph hep-th