Black hole formation in a contracting universe

Transcription

1 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: ]

2 ΛCDM parameters Planck18 [ ] 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 [ ] Many inflation models can give you those numbers Jerome Quintin (McGill U.) Black hole formation in a contracting universe ( ) 2 / 13

3 But inflation is not the only possibility! Ekpyrotic cosmology (contraction with p = wρ, w 1) Khoury et al. [hep-th/ ], Ijjas et al. [ ], Lehners & Wilson-Ewing [ ], Fertig et al. [ ] 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. [ ], Brandenberger et al. [ ], Brandenberger [ ] n s < 1, r 1, f NL 1, n t 1 n s > 0 And other scenarios See review: Brandenberger & Peter [ ] Jerome Quintin (McGill U.) Black hole formation in a contracting universe ( ) 3 / 13

4 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 ( ) 4 / 13

5 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 ( ) 5 / 13

6 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 ( ) 6 / 13

7 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 ( ) 7 / 13

8 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 ( ) 8 / 13

9 Black hole formation probability Starting with a quantum vacuum JQ & Brandenberger [ ] α RBH / H log10 ( H /MPl ) log10 (α) 0.5 cs = 10 3 log10 (probability) log10 (α) 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 ( ) 0 9 / log10 (probability) cs = 10 4

10 Black hole formation probability Starting with a thermal state at Hini = MPl JQ & Brandenberger [ ] α RBH / H log10 ( H /MPl ) Jerome Quintin (McGill U.) cs = log10 (α) log10 ( H /MPl ) Black hole formation in a contracting universe ( ) 10 / log10 (probability) cs = 10 4 log10 (probability) log10 (α)

11 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 [ ] E.g. (quantum initial conditions): c s = = R BH l Pl m, M BH g M primordial black hole? E.g. 2: c s = 10 5 = R BH l Pl 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 ( ) 11 / 13

12 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. [ , , , ] If so, one can use observations to constrain bouncing cosmological models Chen et al. [ ] Could there be specific gravitational wave signals? Barrau et al. [ ] Also, could black holes play a role in the bounce itself? E.g., black holes at the string scale Mathur [ ], Masoumi [ ], JQ et al. [ ] Jerome Quintin (McGill U.) Black hole formation in a contracting universe ( ) 12 / 13

13 Thank you for your attention! I acknowledge support from the following agencies: Jerome Quintin (McGill U.) Black hole formation in a contracting universe ( ) 13 / 13