Spinning Primordial Black Holes and Scalar Induced Gravitational Waves from Single Field Inflation

Abstract We investigate the formation of primordial black holes (PBHs), their spin and abundance, in a single-field inflationary model based on a mutated hilltop potential inserted with a small step-like feature. This step induces a brief phase of ultra-slow-roll inflation, producing large enhancement of the scalar power spectrum required for an appreciable amount of PBH abundance. Instead of an analytical power spectra, we compute the power spectrum accurately by numerically solving the Mukhanov–Sasaki equation. Then, we apply peak theory with ∇ 2 ζ treated as a Gaussian random field and parameterize the curvature profile by its amplitude μ and width K . Confining the study to Type-I PBH, the threshold value is calculated using two robust methods: the average of the compaction function and the q-function method. Using the result, the dimensionless spin parameter of the PBHs is calculated at linear order and found to be <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msqrt> <mml:mrow> <mml:mo stretchy="false">〈</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⋆</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">〉</mml:mo> </mml:mrow> </mml:msqrt> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> ; however, it can be higher for smaller masses. We present detailed predictions for two representative parameter sets, calculate the PBH mass function and the associated scalar-induced gravitational waves (SIGWs). The first produces PBHs of mass M ≃ 10 −13 M ⊙ that can account for 100% of dark matter, while the second yields M ≃ 10 −2 M ⊙ PBHs contributing approximately 2.3% of the dark matter. The predicted signals of SIGWs lie within the sensitivity bands of future experiments such as LISA, DECIGO, BBO, and SKA. In particular, the second parameter set produces a SIGW compatible with the recent NANOGrav evidence for a low-frequency gravitational-wave signal.