Consistency relation for the Lorentz invariant single-field inflation

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 $f_{NL}^{orth.}\lesssim -0.054f_{NL}^{equil.}$. In particular, for the single-field Dirac-Born-Infeld (DBI) inflation, the consistency relation becomes $f_{NL}^{orth.}\simeq 0.070f_{NL}^{equil.}\lesssim 0$. 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 ${\tau }_{NL}^{loc.}>(\frac{6}{5}{f}_{NL}^{loc.}{)}^2$. 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.

4 pages, 2 figures; v2: title changed, some mistakes corrected; v3: refs added, version accepted for publication in JCAP

References in corpus (6)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Angular Trispectrum of CMB Temperature Anisotropy from Primordial Non-Gaussianity with the Full Radiation Transfer Function
• Multi-brid inflation and non-Gaussianity
• Phenomenology of D-Brane Inflation with General Speed of Sound
• Comparing Infrared Dirac-Born-Infeld Brane Inflation to Observations
• Gravitational Wave Constraints on DBI Inflation

Cited by in corpus (4)

• Non-Gaussianity in single field models without slow-roll
• The trispectrum in ghost inflation
• An update on single field models of inflation in light of WMAP7
• Constraints on the primordial gravitational waves with variable sound speed from current CMB data