Consistency relation for the Lorentz invariant single-field inflation

TL;DR

This paper derives a consistency relation between bispectrum shapes in Lorentz invariant single-field inflation and tests it against WMAP data, constraining models like DBI inflation.

Contribution

It provides a new theoretical consistency relation linking orthogonal and equilateral bispectra in Lorentz invariant inflation models, including mixed scenarios.

Findings

Derived a specific relation: $f_{NL}^{orth.}\, extless\, -0.054 f_{NL}^{equil.}$

Found that DBI inflation is disfavored by WMAP 7-year data at over 68% CL

Showed the validity of these relations in mixed inflation scenarios.

Abstract

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.