Threshold of primordial black hole formation

By T. Harada, Chul-Moon Yoo, K. Kohri. 2013

342 citations recorded by the source corpus.

Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the universe dominated by a perfect fluid with the equation of state $p=w\rho c^{2}$ for $w\ge 0$. The formula gives $\delta^{\rm UH}_{H c}=\sin^{2}[\pi \sqrt{w}/(1+3w)]$ and $\tilde{\delta}_{c}=[3(1+w)/(5+3w)]\sin^{2}[\pi\sqrt{w}/(1+3w)]$, where $\delta^{\rm UH}_{H c}$ and $\tilde{\delta}_{c}$ are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives $\delta^{\rm UH}_{H c}=w$ and $\tilde{\delta}_{c}=3w(1+w)/(5+3w)$. Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives $\delta^{\rm UH}_{H c}=\sin^{2}(\sqrt{3}\pi/6)\simeq 0.6203$ and $\tilde{\delta}_{c}=(2/3)\sin^{2}(\sqrt{3}\pi/6)\simeq 0.4135$. We also discuss the maximum amplitude and the cosmological implications of the present result.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b191491165c72545485eb07afa2daadf93b2a20a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. B. Carr
2. Florian Kuhnel
3. C. Byrnes
4. K. Kohri
5. V. Vennin
6. T. Terada
7. S. Young
8. I. Musco

In Nuclear and High Energy Physics

1. B. Carr
2. Florian Kuhnel
3. C. Byrnes
4. K. Kohri
5. S. Young
6. T. Terada
7. V. Vennin
8. I. Musco

Citations in the corpus

• Quantum diffusion during inflation and primordial black holes (2017, background): “In practice, PBHs form when the mean curvature perturbation in a given Hubble patch exceeds a threshold denoted ζc ' 1 [18, 19] (see ref.”
• Solar-mass primordial black holes explain NANOGrav hint of gravitational waves (2020, background): “42 [74, 75] (4), Erfc is the complementary error function, and the variance σ(2) 2 of the coarse-grained density perturbations is defined as σ(2) 2(k) = 16 81 ∫ ∞ −∞ d lnxw(2)(x)x(4)Pζ(xk), (6)”
• Single field double inflation and primordial black holes (2017, background): “In more detail, the fractional contribution of a PBH population of mass MPBH to the energy content of the Universe at the formation time tM is quantified by [90] β0(MPBH(N)) ≡ ρPBH(M) ρtot ∣∣∣∣ t=tM ≈ √ 2Pζ πζ2 c exp ( − ζ 2 c 2Pζ ) , (4.”
• Primordial Black Holes as Dark Matter: Recent Developments (2020, background): “In a radiation-dominated era, a simple analytic argument [64] suggests δc ≈ 1/3, but more precise numerical [52] and analytical [65] investigations suggest δc = 0.”
• On primordial black holes from an inflection point (2017, result): “[7] used the rescaled range of δc found in [19] instead of the bare ranges that are compatible with earlier works, e.”
• PRIMORDIAL BLACK HOLE FORMATION IN THE MATTER-DOMINATED PHASE OF THE UNIVERSE (2016, methodology): “Following Harada et al. (2013, 2015), let us describe the criterion by using the density perturbation d̃ at horizon entry in the comoving slicing in the long-wavelength limit, where d̃ is defined as d d -lim 49 0 2˜ ≔ ( ) and ck aH≔ ( ).”