Primordial black holes and slow-roll violation

By H. Motohashi, Wayne Hu. 2017

270 citations recorded by the source corpus.

For primordial black holes (PBH) to be the dark matter in single-field inflation, the slow-roll approximation must be violated by at least $\mathcal{O}(1)$ in order to enhance the curvature power spectrum within the required number of $e$-folds between cosmic microwave background scales and PBH mass scales. Power spectrum predictions which rely on the inflaton remaining on the slow-roll attractor can fail dramatically leading to qualitatively incorrect conclusions in models like an inflection potential and misestimate the mass scale in a running mass model. We show that an optimized temporal evaluation of the Hubble slow-roll parameters to second order remains a good description for a wide range of PBH formation models where up to a $1{0}^{7}$ amplification of power occurs in 10 $e$-folds or more.

View Paper: https://www.semanticscholar.org/paper/aec7aeaeafda35c8a91f5ed023f7a784a94f88b5

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1. C. Byrnes
2. S. Young
3. B. Carr
4. M. Braglia
5. S. S. Mishra
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7. V. Sahni
8. G. Franciolini

Citations in the corpus

• Mechanisms for primordial black hole production in string theory (2018, background): “hort range of e-folds that is associated with CMB scales (e.g. between N= 20 and N= 30 in both cases we considered), the slow-roll parameters can be small and smoothly varying [17]. 10See for example [43] for a general discussion. 12 0 20 40 60 80 0 2 4 6 8 10 12 N M pl 0 20 40 60 80 0 1 2 3 4 5 N H”
• Primordial Black Holes from Polynomial Potentials in Single Field Inflation (2017, unknown): “Thus we need to consider the non-slow-roll inflation to generate a large amplitude of power spectrum at small scales [39].”
• Primordial black holes from a tiny bump/dip in the inflaton potential (2019, methodology): “following expressions for the mass of a newly formed PBH (see appendix B, [25, 38, 48, 49])”
• Generating PBHs and small-scale GWs in two-field models of inflation (2020, background): “This can be achieved in single-field inflation scenarios by using a local feature in the inflaton potential like a rapid change of its amplitude or a break in its first derivative [7–9], an inflection point [10–18] or a tiny bump superimposed on it [19, 20], non-trivial inflaton sound speed [21–23]1”
• Primordial black holes from α-attractors (2018, background): “It is during that phase that at least O(1) changes in the slow-roll parameters happen and the power spectrum amplitude gets amplified [62].”
• Primordial black holes from inflation and quantum diffusion (2018, background): “It corresponds to a present dark matter abundance made of PBH of masses M given by (neglecting accretion) [28] ( ΩDM(M)h 2”
• Primordial black holes from inflation and non-Gaussianity (2018, methodology): “where we have normalised σ2 RH to the value necessary to get the right abundance of dark matter from PBHs [32] (neglecting accretion), we see that the Gaussian estimate on the PBH mass fraction is hardly trustable.”
• Primordial black holes and second order gravitational waves from ultra-slow-roll inflation (2017, background): “If changes too quickly at the near inflection point, then the slow-roll condition will be violated [23] because ∣∣∣∣ d dφ ∣∣∣∣ = 2 |η − 2 |, (2.”
• Primordial black holes as generators of cosmic structures (2018, background): “Indeed, many people have argued for a spike or non-Gaussianity in the intermediate mass range (10− 103M ) in order to explain the dark matter with PBHs (Frampton et al. 2010; Byrnes, Copeland & Green 2010; Motohashi & Hu 2017; Garcia-Bellido & Ruiz Morales 2017, 2018).”
• Primordial black holes with an accurate QCD equation of state (2018, background): “The scale associated to the PBHs detected by LIGO with M ∼ 30M⊙ is k ∼ 106Mpc (see (22)) and such a rapid growth of the power spectrum requires a break down in slow-roll somewhere in between these scales [59].”
• Primordial black hole dark matter from single field inflation (2017, methodology): “19) for describing PBH formation from a very flat inflationary potential has also been recently pointed out in [58] and [54].”