Primordial Black Hole Formation in Starobinsky's Linear Potential Model

Abstract

We study the power spectrum of the comoving curvature perturbation R in the model that glues two linear potentials of different slopes, originally proposed by Starobinsky. We find that the enhanced power spectrum reaches its maximum at the wavenumber which is π times the junction scale. The peak is ∼ 2.61 times larger than the ultraviolet plateau. We also show that its near-peak behavior can be well approximated by a constant-roll model, once we define the effective ultraslow-roll e-folding number appropriately by considering the contribution from nonsingle-clock phase only. Such an abrupt transition to non-attractor phase can leave some interesting characteristic features in the energy spectrum of the scalar-induced gravitational waves, which are detectable in the space-borne interferometers if the primordial black holes generated at such a high peak are all the dark matter.

Inflation and Primordial Black Holes

“…From a concrete model-building perspective, scalar potentials (V(φ)) that can induce this type of dynamics include a characteristic 'plateau' within a non-vanishing field range (∆φ = 0) [38,39,208]. This property gives rise to phases of transient non-attractor dynamics of ultra slow-roll (USR) [40,43,44] or constant-roll (CR) [45,209,210] evolution, depending on the shape profile of the potential around the aforementioned feature.…”

Hybrid α-attractors, primordial black holes and gravitational wave backgrounds

“…Many other interesting mechanisms were proposed to produce a bump in the PPS from inflation. Among them is the PBH production due to large isocurvature perturbations [4], amplification of perturbations during rapid turns of inflationary trajectory [5][6][7][8][9][10][11], a sudden slowing down of the inflaton evolution often referred to as Ultra Slow Roll [12][13][14][15][16][17][18][19][20][21][22] or other types of features [23][24][25][26][27][28][29] and creation of black holes and wormholes by colliding walls [30,31]. For a review of these and other mechanisms of PBH formation and their cosmological implications see e.g.…”

Sudden braking and turning with a two-field potential bump: primordial black hole formation

“…Throughout the past few decades, massive inflationary models have been used to study PBH production, with the goal of enhancing small-scale primordial curvature disturbances while maintaining the scale-invariant spectrum seen in the cosmic microwave background (CMB). To the best of our knowledge, PBH formation mechanisms fall under the following broad groups: extra contributions from other fields to curvature perturbations in multi-field models [5][6][7][8][9][10][11][12][13][14][15][16][17][18], the non-attractor evolutions lead to the amplification of perturbations (e.g., in the presence of ultra-slow-roll (USR) phases) [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], parametric resonance or tachyonic instability of curvature perturbations [37][38][39][40][41][42][43][44][45], the non-Gaussianity of distribution probability [46][47][48]…”