Local Non-Gaussianity Generated at a Bounce: The Sharpness Bound Imposed by the Planck fNL Measurement

Primordial non-Gaussianity of the local type is a sensitive probe of how many degrees of freedom were active when the perturbations were made. This paper computes the local non-Gaussianity parameter generated when perturbations pass through a bounce whose duration is finite, and converts the Planck constraint into a bound on that duration. The model gives fNL = 0.015 + 0.62 s squared, where s measures the sharpness of the bounce and the constant term is the squeezed-limit consistency contribution. At a fiducial sharpness s = 1.7 the prediction is fNL = 1.81, which deviates from the Planck 2018 value of -0.9 plus or minus 5.1 by 0.53 standard deviations. Requiring agreement within two standard deviations bounds the sharpness above at s = 3.9; a sharper bounce with s = 3 would already produce fNL = 5.6. An instantaneous bounce, often used as a modelling convenience, is therefore not innocuous: in this framework it would overproduce local non-Gaussianity beyond what the data allow. The study is computed from stated assumptions, not measured.