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

Abstract 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, $$f_\textrm{NL}=(-\,39.95,-\,35/8)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mtext>NL</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mspace/> <mml:mn>39.95</mml:mn> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mspace/> <mml:mn>35</mml:mn> <mml:mo>/</mml:mo> <mml:mn>8</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , found within the ekpyrotic contraction and the matter bounce scenarios, respectively, and show that a negatively large amount of $$f_\textrm{NL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mtext>NL</mml:mtext> </mml:msub> </mml:math> can provide sizeable abundance, $$10^{-3}\leqslant f_\textrm{PBH}\leqslant 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mo>⩽</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mtext>PBH</mml:mtext> </mml:msub> <mml:mo>⩽</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , and completely mitigates the PBH overproduction issue. We also highlight that the case with the effective sound speed $$c_{s}=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , coupled with $$f_\textrm{NL}=-\,39.95$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mtext>NL</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mspace/> <mml:mn>39.95</mml:mn> </mml:mrow> </mml:math> , provides an agreement under $$1\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> 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, $$f_\textrm{NL}\sim -60$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mtext>NL</mml:mtext> </mml:msub> <mml:mo>∼</mml:mo> <mml:mo>-</mml:mo> <mml:mn>60</mml:mn> </mml:mrow> </mml:math> , below which we show breaching of the underlying perturbativity constraints on the power spectrum amplitude.