Cosmological long-wavelength solutions and primordial black hole formation

By T. Harada, Chul-Moon Yoo, T. Nakama, Yasutaka Koga. 2015

157 citations recorded by the source corpus.

We construct cosmological long-wavelength solutions without symmetry in general gauge conditions compatible with the long-wavelength scheme. We then specify the relationship among the solutions in different time slicings. Applying this general framework to spherical symmetry, we derive the correspondence relation between long-wavelength solutions in the constant mean curvature slicing with conformally flat spatial coordinates and asymptotic quasihomogeneous solutions in the comoving gauge and compare the numerical results of PBH formation in these two different approaches. To discuss the PBH formation, it is convenient and conventional to use $\tilde{\delta}_{c}$, the value which the averaged density perturbation at threshold in the comoving slicing would take at horizon entry in the lowest-order long-wavelength expansion. We numerically find that within compensated models, the sharper the transition from the overdense region to the FRW universe is, the larger the $\tilde{\delta}_{c}$ becomes. We suggest that, for the equation of state $p=(\Gamma-1)\rho$, we can apply the analytic formulas for the minimum $\tilde{\delta}_{c, {\rm min}}\simeq [3\Gamma/(3\Gamma+2)]\sin^{2}\left[\pi\sqrt{\Gamma-1}/(3\Gamma-2)\right]$ and the maximum $\tilde{\delta}_{c, {\rm max}}\simeq 3\Gamma/(3\Gamma+2)$. As for the threshold peak value of the curvature variable $\psi_{0,c}$, we find that the sharper the transition is, the smaller the $\psi_{0,c}$ becomes. We analytically explain this feature. Using simplified models, we also analytically deduce an environmental effect that $\psi_{0,c}$ can be significantly larger (smaller) if the underlying density perturbation of much longer wavelength is positive (negative).

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ee4bfd92bc267c788c62b55a006f8f578b4aa1af

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In Astronomy and Astrophysics

1. C. Byrnes
2. K. Kohri
3. A. Riotto
4. I. Musco
5. S. Young
6. G. Franciolini
7. T. Terada
8. A. Kehagias

In Nuclear and High Energy Physics

1. C. Byrnes
2. K. Kohri
3. I. Musco
4. S. Young
5. A. Riotto
6. G. Franciolini
7. T. Terada
8. A. Kehagias

Citations in the corpus

• 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)”
• The initial spin probability distribution of primordial black holes (2019, methodology): “J C A P 0 5 ( 2 0 1 9 ) 0 1 8 In the threading where the pertubed 0i component of the metric vanishes, the velocity in the long wavelength regime is given by [33]”
• Primordial black hole formation and abundance: contribution from the non-linear relation between the density and curvature perturbation (2019, methodology): “J C A P 1 1 ( 2 0 1 9 ) 0 1 2 In the superhorizon regime, applying the gradient expansion approximation, the compaction function is conserved and is related to ζ(r) as [23, 25, 29] C(r) = −f(w)rζ ′(r) [ 2 + rζ ′(r) ] , f(ω) = 3(1 + ω)”
• The ineludible non-Gaussianity of the primordial black hole abundance (2019, methodology): “In the comoving slicing, the overdensity turns out to be [33]”
• 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≔ ( ).”