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 $f_{ \rm NL}$ and one of the local-form { \it trispectrum} amplitudes, $\tau_{ \rm NL}$, such that $\tau_{ \rm NL}>\frac12(\frac65f_{ \rm NL})^2$ 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.
Categories: gr-qc astro-ph.CO hep-th