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We investigate the explicit role of negative local non-Gaussianity, $f_{\rmNL}$, in suppressing the abundance of primordial black holes (PBHs) in thesingle-field model of Galileon inflation. PBH formation requires significantlyenhancing the scalar power spectrum, which greatly affects their abundance. Theassociated frequencies in the nHz regime are also sensitive to the generationof scalar-induced gravitational waves (SIGWs) which may explain the currentdata from the pulsar timing arrays (PTAs). Our analysis using the thresholdstatistics on the compaction function demonstrates that Galileon theory notonly avoids PBH overproduction using the curvature perturbation enhancementsthat give $f_{\rm NL} \sim {\cal O}(-6)$, but also generates SIGWs that conformwell with the PTA data.

Primordial non-Gaussianity as a saviour for PBH overproduction in SIGWs generated by Pulsar Timing Arrays for Galileon inflation