Primordial black holes in non-minimal Gauss–Bonnet inflation in light of the PTA data

Abstract Here, we investigate the formation of primordial black holes (PBHs) in non-minimal coupling Gauss–Bonnet inflationary model in the presence of power-law potentials. We employ a two part coupling function to enhance primordial curvatures at small scales as well as satisfy Planck measurements at the CMB scale. Moreover, our model satisfies the swampland criteria. We find PBHs with different mass scales and demonstrate that PBHs with masses around $$\mathcal {O}(10^{-14})M_{\odot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>14</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> can account for almost all of the dark matter in the universe. In addition, we investigate the implications of the reheating stage and show that the PBHs in our model are generated during the radiation-dominated era. Furthermore, we investigate the production of scalar-induced gravitational waves (GWs). More interestingly enough is that, for the specific cases $$D_\textrm{n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>D</mml:mi> <mml:mtext>n</mml:mtext> </mml:msub> </mml:math> in our model, the GWs can be considered as a source of PTA signal. Also, we conclude that the GWs energy density parameter at the nano-Hz regime can be parameterized as $$\Omega _\mathrm{GW_0} (f) \sim f^{5-\gamma }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ω</mml:mi> <mml:msub> <mml:mi>GW</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mrow> <mml:mn>5</mml:mn> <mml:mo>-</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , where the obtained $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> is consistent with the PTA Observations.