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, $f_{\mathrm{N}\mathrm{L}}=(-39.95,-35\mathrm{/}8)$, found within the ekpyrotic contraction and the matter bounce scenarios, respectively, and show that a negatively large amount of $f_{\mathrm{N}\mathrm{L}}$ can provide sizeable abundance, ${10}^{-3}\le f_{\mathrm{P}\mathrm{B}\mathrm{H}}\le 1$, and completely mitigates the PBH overproduction issue. We also highlight that the case with the effective sound speed $c_s=1$, coupled with $f_{\mathrm{N}\mathrm{L}}=-39.95$, 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, $f_{\mathrm{N}\mathrm{L}}\sim -60$, below which we show breaching of the underlying perturbativity constraints on the power spectrum amplitude.