Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of sound

Abstract: Inflationary perturbations in multi-field theories can exhibit a transient tachyonic instability as a consequence of their non-trivial motion in the internal field space. When an effective single-field description is applicable, the resulting theory is characterized by fluctuations that propagate with an $imaginary$ speed of sound. We use the effective field theory of fluctuations to study such a set-up in a model-independent manner, highlighting the peculiarities and subtleties that make it different from the standard case. In particular, perturbations feature exponentially growing and decaying modes whose relative amplitude is undetermined within the effective field theory. Nevertheless, we prove that in an interesting limit the dimensionless bispectrum is in fact universal, depending only on the speed of sound and on the cutoff scale that limits the validity of the effective theory. Contrary to the power spectrum, we find that the bispectrum does not display an exponential enhancement. The amplitude of non-Gaussianities in the equilateral configuration is similar to the one of conventional models, but it is enhanced in flattened configurations in a way that is ultraviolet sensitive.