Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce

Non-Gaussianity in the primordial curvature perturbation is a crucial element of the early universe due to its significant impact on the primordial black hole (PBH) production. In this work, we focus on the effects of negative non-Gaussianity on PBH abundance through the lens of the compaction function criterion for PBH formation. Our setup utilizes an effective field theory of non-singular bounce, including the standard slow-roll inflation with an ultra-slow roll phase for amplifying the curvature perturbations to form PBHs. We investigate with two separate values of the non-Gaussianity parameter, \(f_{\rm NL}=(-39.95,-35/8)\), found within the ekpyrotic contraction and the matter bounce scenarios, respectively, and show that a negatively large amount of \(f_{\rm NL}\) can provide sizeable abundance, \(10^{-3}\leq f_{\rm PBH}\leq 1\), and completely mitigates the PBH overproduction issue. We also highlight that the case with the effective sound speed \(c_{s}=1\), coupled with \(f_{\rm NL}=-39.95\), provides an agreement under \(1\sigma\) for the scalar-induced gravitational wave explanation of the latest PTA (NANOGrav15 and EPTA) signal. Lastly, we extract an upper bound on the most negative value of, \(f_{\rm NL}\sim -60\), below which we show breaching of the underlying perturbativity constraints on the power spectrum amplitude.