Non-Gaussianity Consistency Relation for Multi-field Inflation

Abstract

While detection of the "local form" bispectrum of primordial perturbations would rule out all single-field inflation models, multi-field models would still be allowed. We show that multi-field models described by the $\delta N$ formalism obey an inequality between $f_{\mathrm{NL}}$ and one of the local-form {\it trispectrum} amplitudes, ${\tau }_{\mathrm{NL}}$, such that ${\tau }_{\mathrm{NL}}>\frac{1}{2}(\frac{6}{5}{f}_{\mathrm{NL}}{)}^2$ with a possible logarithmic scale dependence, provided that 2-loop terms are small. Detection of a violation of this inequality would rule out most of multi-field models, challenging inflation as a mechanism for generating the primoridal perturbations.

5 pages. Accepted for publication in Physical Review Letters

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• Constraining $\mathcal{N}=1$ supergravity inflation with non-minimal Kähler operators using $\delta N$ formalism
• The different varieties of the Suyama-Yamaguchi consistency relation and its violation as a signal of statistical inhomogeneity
• Local non-Gaussianity from rapidly varying sound speeds
• An introduction to inflation after Planck: from theory to observations