Primordial black holes and scalar-induced gravitational waves in radiative hybrid inflation

Abstract We study the possibility that primordial black holes (PBHs) can be formed from large curvature perturbations generated during the waterfall phase transition due to the effects of one-loop radiative corrections of Yukawa couplings between the inflaton and a dark fermion in a non-supersymmetric hybrid inflationary model. We obtain a spectral index $$n_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> , and a tensor-to-scalar ratio r , consistent with the current Planck data. Our findings show that the abundance of PBHs is correlated to the dark fermion mass $$m_N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> and peak in the GW spectrum. We identify parameter space where PBHs can be the entire dark matter (DM) candidate of the universe or a fraction of it. Our predictions are consistent with any existing constraints of PBH from microlensing, BBN, CMB, etc. Moreover, the scenario is also testable via induced gravitational waves (GWs) from first-order scalar perturbations detectable in future observatories such as LISA and ET. For instance, with inflaton mass $$m \sim 2\times 10^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>12</mml:mn> </mml:msup> </mml:mrow> </mml:math> GeV, $$m_N \sim 5.4\times 10^{15}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>N</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>5.4</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>15</mml:mn> </mml:msup> </mml:mrow> </mml:math> GeV, we obtain PBHs of around $$10^{-13}\, M_\odot $$ <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>13</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> mass that can explain the entire abundance of DM and predict GWs with amplitude $$\Omega _\textrm{GW}h^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mtext>GW</mml:mtext> </mml:msub> <mml:msup> <mml:mi>h</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> $$\sim 10^{-9}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>9</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> with peak frequency f $$\sim $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∼</mml:mo> </mml:math> 0.1 Hz in LISA. By explicitly estimating fine-tuning we show that the model has very mild tuning. We discuss successful reheating at the end of the inflationary phase via the conversion of the waterfall field into standard model (SM) particles. We also briefly speculate a scenario where the dark fermion can be a possible heavy right-handed neutrino (RHN) which is responsible for generating the SM neutrino masses via the seesaw mechanism. The RHN can be produced due to waterfall field decay and its subsequent decay may also explain the observed baryon asymmetry in the universe via leptogenesis. We find the reheat temperature $$T_R\lesssim 5\times 10^9$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>R</mml:mi> </mml:msub> <mml:mo>≲</mml:mo> <mml:mn>5</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>9</mml:mn> </mml:msup> </mml:mrow> </mml:math> GeV that explains the matter-anti-matter asymmetry of the universe.