A topic review on probing primordial black hole dark matter with scalar induced gravitational waves

Primordial black holes (PBHs) might form from the collapse of over-densed regions generated by large scalar curvature perturbations in radiation dominated era. Despite decades various independent observations, nature dark matter (DM) remains highly puzzling. Recently, PBH DM have aroused interest since they provide an attracting explanation to merger events binary discovered LIGO/VIRGO and may play important role on DM. During formation PBH, gravitational waves will be sourced linear at second-order, known as induced (SIGWs), which provides a new way hunt for This topic review mainly focuses physics about SIGWs accompanying recently, not only because can represent our Universe but also explain hole mergers Sasaki et al., 2016M. Sasaki, T. Suyama, Tanaka, S. Yokoyama, Phys. Rev. Lett. 117, 061101 (2016), [erratum: 121,no.5,059901 (2018)], arXiv:1603.08338 [astro-ph.CO] .Google Scholar; Chen Huang, 2018Chen Z.-C. Huang Q.-G. Merger rate distribution primordial binaries.Astrophys. 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In section Formation give brief introduction reviewed Scalar then discuss how use probe Searching using SIGWs. Finally, summary outlook Summary outlook. section, introduce take calculating function β. inside Hubble volume. exists one-to-one correspondence between frequency f∗, namely Scholar.mpbh∗≈2.3×1018M⊙(3.91g∗form)1/6(H0f∗)2,(Equation 1) g∗form corresponding degrees freedom H0 constant transferred another useful form, namelympbh∗≈2×105M⊙(t1s).(Equation 2) fpbh≡ΩPBH/ΩDM estimated Scholar.fpbh≃2.5×108β(g∗form10.75)−14(mpbhM⊙)−12.(Equation 3) On slices, relation perturbation, ζ(k), contrast, Δ(k), linear-order byΔ(k)=2(1+w)5+3w(kaH)2ζ(k),(Equation 4) w equation state H parameter. perturbation ζ related metric byζ≡ψ−H(v+B),(Equation 5) notations ψ, v, B introduced Equation (3) below. Bardeen potential (see (23) below) byζ=Ψ−23(1+w)(H−1Ψ'+Φ)(Equation 6) For adiabatic perturbations, stays superhorizon scales. Then Φ=−3(1+w)/(5+3w)ζ assuming absence anisotropies Φ=−2/3ζ RD. contrast smoothed over scale, R, asΔ(x,R)=∫d3x′W(|x−x′|,R)Δ(x′),Δ(k,R)=W(k,R)Δ(k),(Equation 7) with W chosen smooth contrast. variance Δ(k,R) by⟨Δ2⟩=∫0∞dkkW2(k,R)4(1+w)2(5+3w)2(kR)4Pζ(k),(Equation 8) define dimensionless ⟨ζ(k)ζ(k′)⟩≡2π2k3δ(k+k′)Pζ(k). Usually, amplitude assumed obey Gaussian distribution. satisfies criterion, generated. regarded statistics peaks three-dimensional random field, peak 1986Bardeen J.M. Bond Kaiser Szalay A.S. fields.Astrophys. 1986; 304: 15Crossref very amplitudes O(0.01−0.1) constitute most As result, “bump” smaller Ivanov 1994Ivanov Naselsky Novikov Inflation 50: 7173Crossref (173) 1996Garcia-Bellido Linde 1996; 54: 6040arXiv:astro-ph/9605094 (391) Ivanov, 1998Ivanov Nonlinear production holes.Phys. 57: 7145arXiv:astro-ph/9708224 1997Yokoyama 1997; 318: 673arXiv:astro-ph/9509027 2006Kawasaki Takayama Yamaguchi 2006; 74: 043525arXiv:hep-ph/0605271 Hertzberg Yamada, 2018Hertzberg M.P. Yamada 083509arXiv:1712.09750 2018Inomata 043514arXiv:1711.06129 (67) 2017bInomata 96: 043504arXiv:1701.02544 2018bKohri inflation running spectral indices: matter- and/or radiation-dominated universe.Class. 235017arXiv:1802.06785 benchmark example, assume “spicky” particular k∗, calculate case, almost monochromatic. Otherwise, broad spectrum, one has taken into account so-called “cloud-in-cloud” problem swallowed bigger PBH. different blur calculation. spicky theory, number approximated e.g., (4.14) Scholar)npk(νc)≃(⟨k2⟩/3)3/2(2π)2(νc2−1)e−νc2/2,(Equation 9) defined νc≡Δc/⟨Δ2⟩. ⟨k2⟩ as⟨k2⟩=1Δ2∫0∞dkkk2W2(k,R)Pζ(k)(Equation 10) β npk β=npk(νc)(2π)3/2R3. Another commonly used method Press-Schechter formalism, evaluated simply integrating probability (PDF) beyond valueβ=∫νc+∞dν2πe−ν2/2=12erfc(νc2).(Equation 11) formalism considers neglecting higher derivatives. comparison Young 2014Young Calculating 2014; 2014: 045arXiv:1405.7023 (97) result showed close agreement differing factor 10 νc. depends many aspects, problems We aspects next. takes place tail PDF perturbations. Hence any non-Gaussianities significantly change impacts been discussed long ago Bullock Primack, 1997Bullock J.S. Primack Non-Gaussian fluctuations inflation.Phys. 55: 7423arXiv:astro-ph/9611106 Pina Avelino, 2005Pina Avelino 124004arXiv:astro-ph/0510052Crossref Hidalgo, 2007Hidalgo J.C. arXiv:0708.3875 [astro-ph]Date: 2007Google Bugaev, 2012Klimai 17th International Seminar High Energy Physics. 2. INR, 2012: 163-174arXiv:1210.3262 Besides considering model, non-Gaussian model local-type non-Gaussianities, expanded part (up cubic order)ζ=f(ζg)=ζg+FNL(ζg2−⟨ζg2⟩)+GNLζg3.(Equation 12) Here ζg whose Gaussian. parameter FNL skew GNL kurtosis PDF. above convenient estimating presence non-Gaussianities. Let PNG PG part, ζg. obtained changing variables, ζg=f−1(ζ), thatβ=∫ζc∞PNG(ζ)dζ=∫fi−1(ζ)>ζc∑i=1ndfi−1(ζ)dζPG[fi−1(ζ)]dζ.(Equation 13) equivalent integrate region, fi−1(ζ)>ζc. Here, lower index i indicates i-th solution total n real solutions. 2012Byrnes Copeland E.J. 86: 043512arXiv:1206.4188 (79) al. up order. that, was studied fifth-order Byrnes, 2013Young 08: 052arXiv:1307.4995 (69) their results sensitive parameters (FNL, GNL, etc.). Except variables (13), 2018Franciolini 03: 016arXiv:1801.09415 adopted method, path-integral formulation, regions. authors expressed sum N-point correlation function. Readers interested formulation refer work references therein. However, impractical Riccardi argued affect cumulants 2021Riccardi Taoso Urbano arXiv:2102.04084 get impractical. semi-analytical expression estimate see standard procedure based (4). just perturbation. slicing, non-linear long-wavelength approximation Harada 2015Harada Yoo C.-M. Koga 084057arXiv:1503.03934 (55) 2018Yoo Garriga PTEP. : 123E01arXiv:1805.03946 Musco, 2019Musco 100: 123524arXiv:1809.02127 Scholar.Δ(r,t)=−4(1+w)5+3w(1aH)2e−5ζ(r)/2∇2eζ(r)/2.(Equation 14) Owing relation, longer even unavoidably make these “intrinsic non-Gaussianities” effects K