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(NLorth.) <= -0.054f(NL)(equil.). In particular, for the single-field Dirac-Born-Infeld (DBI) inflation, the consistency relation becomes f(NL)(orth.) = 0.070f(NL)(equil.) <= 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(loc.)(NL) > (6/5 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.