Black hole formation in a contracting universe Jerome Quintin McGill University Montréal, Québec, Canada ITC Luncheon, Harvard CfA, Cambridge September 13, 2018 Based on work with Robert Brandenberger (McGill U.) JCAP 1611, 029 (2016) [arxiv:1609.02556]
ΛCDM parameters Planck18 [1807.06209] α s dn s /d ln k = 04 ± 13, r < 65 (95 %) f local NL equil = 0.8 ± 5.0, fnl = 4 ± 43, fnl ortho = 26 ± 21 Planck15 [1502.01592] Many inflation models can give you those numbers Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 2 / 13
But inflation is not the only possibility! Ekpyrotic cosmology (contraction with p = wρ, w 1) Khoury et al. [hep-th/0103239], Ijjas et al. [1404.1265], Lehners & Wilson-Ewing [1507.08112], Fertig et al. [1607.05663] n s 0.97, α s O( 10 3 ), r 0, f NL O(1) O(10) String gas cosmology (quasi-static, thermal) Brandenberger & Vafa [ 89], Chen et al. [0712.2477], Brandenberger et al. [1403.4927], Brandenberger [1505.02381] n s < 1, r 1, f NL 1, n t 1 n s > 0 And other scenarios See review: Brandenberger & Peter [1603.05834] Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 3 / 13
Bouncing Cosmology a(t) t Many alternatives are bouncing scenarios: the Big Bang is replaced by a bounce, before which the Universe was contracting Can we find generic predictions or imprints of a contracting Universe before the Big Bang/bounce? Take a minimal assumption: consider a contracting universe with matter as we know it today (i.e., dust, radiation, etc.) Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 4 / 13
Hydrodynamical fluid in a contracting universe Energy density and pressure: ρ(t, x) = ρ(t) + δρ(t, x), p(t, x) = p(t) + δp(t, x) p = w ρ, δp = c s δρ (constant entropy), c = 1 Dust: w = c 2 s 1; radiation w = c 2 s = 1/3 Density contrast in Fourier space: δ k δρ k / ρ Jeans scale: k J 4πG N ρ/c s, λ J 1/k J Sub-Jeans scales (λ < λ J ) = oscillations (δ k (t) e ±icskt ) Super-Jeans scales (λ > λ J ) = gravitational instability (δ k (t) ) Can this lead to black holes? Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 5 / 13
Jeans and Hubble scales Jeans radius: λ J = c s (a H ) 1 ; Hubble radius: λ H = (a H ) 1 Radiation = c 2 s = 1/3 = λ J λ H time k 1 length scale super-hubble (outside horizon) λ H λ J sub-jeans (oscillations) Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 6 / 13
Jeans and Hubble scales Jeans radius: λ J = c s (a H ) 1 ; Hubble radius: λ H = (a H ) 1 Dust = c 2 s 1 = λ J λ H time k 1 length scale super-hubble (outside horizon) super-jeans/ sub-hubble (instability) λ H sub-jeans (oscillations) λ J Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 7 / 13
Black hole formation probability Specify initial conditions (e.g., quantum vacuum, thermal state, etc.) get full solution for δ k (t) by solving the linearized Einstein equations Probability of black hole formation (Press-Schechter formalism): 2 1 δ2 /2σ2 Prob(R, t) = dδ e, π σ δ c σ 2 (R, t) = 1 2π 2 0 dk k 2 W 2 (kr) δ k (t) 2, W (kr) = Window function High probability when σ δ c Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 8 / 13
Black hole formation probability Starting with a quantum vacuum JQ & Brandenberger [1609.02556] α RBH / H 1 1.0 4.5 2.0 6.0 2.5 7.5 9.0 3.5 4.0 10 10.5 8 6 4 log10 ( H /MPl ) 2 0 12.0 0.5 log10 (α) 0.5 cs = 10 3 log10 (probability) log10 (α) 1.0 4.5 6.0 7.5 2.0 9.0 2.5 10 10.5 8 6 4 log10 ( H /MPl ) 2 2 dust, super-jeans/sub-hubble: δk (t) 2 k 3 c 5 s H(t) Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 0 9 / 13 12.0 log10 (probability) cs = 10 4
Black hole formation probability Starting with a thermal state at Hini = 10 16 MPl JQ & Brandenberger [1609.02556] α RBH / H 1 1.0 4.5 2.0 6.0 2.5 7.5 9.0 3.5 4.0 10.5 12 10 8 6 4 2 log10 ( H /MPl ) Jerome Quintin (McGill U.) 0 12.0 cs = 10 3 0.5 log10 (α) 0.5 1.0 4.5 6.0 7.5 2.0 9.0 2.5 10.5 12 10 8 6 4 2 0 log10 ( H /MPl ) Black hole formation in a contracting universe (1609.02556) 10 / 13 12.0 log10 (probability) cs = 10 4 log10 (probability) log10 (α)
Implications and discussion If a long-enough phase of dust-dominated contraction lasts, Hubble-size black holes form well before Planckian densities: R BH cs 5/2 l Pl (quantum); R BH c 18/5 s l Pl (thermal) JQ & Brandenberger [1609.02556] E.g. (quantum initial conditions): c s = 10 10 = R BH 10 25 l Pl 10 10 m, M BH 10 20 g 10 13 M primordial black hole? E.g. 2: c s = 10 5 = R BH 10 12 l Pl 10 23 m, M BH 10 7 g evaporated black hole remnant? Harder to form black holes if c s increases (e.g., no radiation black holes before Planckian densities) But easier to form black holes if there are structures already in the Universe (rather than just a quantum vacuum) Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 11 / 13
Outlook First estimate of black hole formation in a contracting universe analysis could be refined Can black holes pass through a bounce? Carr et al. [1104.3796, 1402.1437, 1701.05750, 1704.02919] If so, one can use observations to constrain bouncing cosmological models Chen et al. [1609.02571] Could there be specific gravitational wave signals? Barrau et al. [1711.05301] Also, could black holes play a role in the bounce itself? E.g., black holes at the string scale Mathur [0803.3727], Masoumi [1505.06787], JQ et al. [1809.01658] Jerome Quintin (McGill U.) Black hole formation in a contracting universe (1609.02556) 12 / 13
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