Consistency relation for the Lorentz invariant single-field inflation
  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.
