Primordial Black Holes

Transcription

1 Primordial Black Holes In the reheating phase Juan Carlos Hidalgo. Instituto de Ciencias Físicas, UNAM

2 INFLATION I: Primordial Fluctuations

3 The Success of Inflation Explain the origin of our flatuniverse (Ω tot = 1) Solves the horizon problem of the Hot Big Bang H const. a t exp(ht) Proposes field fluctuations as the origin of Large Scale Structure. δ = δρ ρ

4 Inflation (structure formation) Assume a Perturbed FLRW spacetime. Sachs-Wolfe effect on large scales (superhorizon) ΔT = 1 T S,G 3 Φ 10 5, l 100 Curvature perturbation Powerspectrum

5 Inflation (Powerspectrum) Two Point correlation in Fourier space Red spectrum n s < 1 Parametrization of amplitude and scale dependence (n s, n sk, ) For single field Slow-Roll inflation.

6 Structure at small scales? Consider a running of the spectral index: Small scales could present large amplitudes Large amplitude fluctuations in a radiation era. Fomation of stars forbidden Very large fluctuations collapse into Primordial Black Holes J. A. Vazquez, et al. 2015, arxiv: END OF INFLATION LSS

7 PRIMORDIAL BLACK HOLES

8 Formation of PBHs with expanding background Misner-Sharp mass:, Future trapped region: r BH = 2MG/c 2

9 Formation of PBHs. Physics Primoridal Black Holes = Collapse of large overdensities in the early universe. B.J. Carr, 1975 Jeans Radius. (barotropic ) Collapse Criterion Formation Threshold. Harada, et al. 2015

10 Abundance of PBHs: Press-Schechter Formalism Formation Threshold Mass of the BH Initial Mass fraction (abundance)

11 Abundance of PBHs: Effects

12 Fate of PBHs: Evaporation. Accretion (later) dm dt = g a 2π 2 0 v σ ω f E p 3 dp *with the distribution function f E = 1 e E/T 1, for Bosons Evaporation (Hawking Radiation)

13 Abundance of PBHs: Effects Entropy of the Universe. Spallation of Lithium. Relative abundance of BBN elements. CMB distortions. Gamma Ray Background. 21 CM background. Gravitational waves from mergers. Dark matter in the form of MACHOs. Dark matter from Planck Relics.

14 Abundance of PBHs: Effects

15 INFLATION II: Reheating

16 End of Inflation: Reheating Scalar field Oscillating about its minimum. Necessary transfer of energy to relativistic matter. UNOBSERVED STAGE

17 End of Inflation: (p)reheating Reheating Preheating

18 End of Inflation: (p)reheating Preheating perturbations: Mathieu Equation Instability band

19 End of Inflation: (p)reheating Preheating perturbations: Mathieu Equation Instability band C. Jedamzik, et al. 10

20 Density peaks during preheating Torres-Lomas et al. 2014, arxiv: (????)

21 PRIMORDIAL BLACK HOLES II: collapse in preheating

22 Formation of PBHs. Physics Primoridal Black Holes = Collapse of large overdensities in the early universe. B.J. Carr, 1975 Jeans Radius. (barotropic ) Collapse Criterion Formation Threshold. Harada, et al. 2015

23 Formation of PBHs. (Scalar field) Primoridal Black Holes = Top-Hat collapse above the instability scale. Instability Radius Collapse Criterion Formation Threshold. N. Barbosa-Cendejas, et al. In prep.

24 Formation of PBHs. Simulations Musco, Miller & Rezzolla, 04 GR simulations of gravitational collapse Necessary for accurate estimation of δ c Precise determination of the mass of final BH.

25 Formation of PBHs. Radiation Results Shibata & Sasaki, 99 The criterion is put in terms of the curvature with

26 Formation of Structure. Scalar field. J M Torres et al Disipation of initial fluctuation Structure formation above λ C = 1 m Type equation here.

27 Formation of Structure. Scalar field. C Vergara 2015 Disipation of initial fluctuation Structure formation above λ C = 1 m

28 Scalar field collapse C Vergara et al. In prep. Gravitational collapse of configuration δφ = , φ = H collapse = 148 H entry analytical value ( )

29 SUMMARY & PROSPECTS. PBHs are probes of hidden eras in the universe after inflation. Preheating mechanisms could produce an excess of PBHs A criterion for the collapse of inhomogeneities in those eras is still missing ( but we re closing in!) Small PBHs could turn to be the first tool to probe physics at the end of inflation.

30 Formation of PBHs. Simulations GR simulations of gravitational collapse Matter contents encoded in the Stress-Energy Tensor.

31 Formation of PBHs. Simulations Gauge conditions β = 0. And a lapse function such that, f=0 is synchronous and f=1 is harmonic With the extrinsic curvature K ij and a traceless tensor given by And a form of the spatial metric

32 Formation of PBHs. Initial Conditions The Hamiltonian constraint is an equation for ψ = exp χ(x i ) such that for given initial data δρ 0 x i With the boundary conditions After evolving the equations with the initial profile for curvature Shibata & Sasaki, 09

33 MISSING