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Mass spectrum of PBH s from inflationary perturbation in the RS braneworld

Mass spectrum of PBH s from inflationary perturbation in the RS braneworld. Yuuiti Sendouda (University of Tokyo) Brane-world meeting@Portsmouth 19 Sep 2006. Based on Sendouda, Nagataki, Sato, JCAP 0606 (2006) 003. Plan of Talk. Introduction PBHs in RS Braneworld

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Mass spectrum of PBH s from inflationary perturbation in the RS braneworld

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  1. Mass spectrum of PBHsfrom inflationary perturbationin the RS braneworld Yuuiti Sendouda (University of Tokyo) Brane-world meeting@Portsmouth 19 Sep 2006 Based on Sendouda, Nagataki, Sato, JCAP0606 (2006) 003

  2. Plan of Talk • Introduction • PBHs in RS Braneworld • Constraints on Brane Inflation • Conclusion

  3. 1. Introduction Primordial Black Hole A “visible” component of density perturbation by virtue of Hawking radiation Correspondence: Method to Probe Early Universe • Obs. of cosmic-rays • Abundance of PBHs? • Density perturbation • Curvature perturbation • Inflation Higher dimensionality Back to the beginning

  4. Scales Planck ~fm ~km (M¯) ~1Mpc (Ly) ~1Gpc ? Constraints CR Large Scale Structure (from Tegmark’s webpage)  has particular importance Upper limits of PBH abundance (in 4D) Green & Liddle (1997)

  5. 2. PBHs in RS Braneworld

  6. RS2 Cosmology Brane expansion = Modified Friedmann Eq.  < 0 Curvature radius l . 0.1mm log a Tension  > 0 +Matter T Matter Slower log t Radiation l

  7. Treatment of density perturbation Comoving scale Horizon Characterize (second) inflation by power-law curvature perturbation 4D Trh 5D log t and reheating temperature Evolution of density perturbation (Note: Bulk effects omitted) Spectrum of density perturbation

  8. Formation of PBH Carr (1975) Radiation-dominated phase Jeans length～Hubble radius～Schwarzschild radius of horizon mass Smoothed Perturbations above some threshold form PBHs

  9. Abundance Variance at horizon entry ~10-5@Mpc from WMAP+SDSS+Ly Seljak et al. (2005) Distribution: Gaussian Fraction of collapsing region Threshold~O(0.1) n~1:

  10. Mass Function n=1.00 n=1.60 5D 5D 4D 4D l l Not formed Reheating temp. = Minimum mass Dominates in number

  11. 3. Constraints on Brane Inflation

  12. PBH Evaporation in Braneworld d-dim. BH’s Hawking radiation Stefan-Boltzmann law (1) Large extra dim. = Low temp. (2) Life /Mbh2 in 5D KK modes Matter Photons coming to eatrh Page (1976), Harris et al. (2003), Cardoso et al. (2006), Creek et al. (2006)

  13. Reconsidering Mass Function PBHs have lifetime. The most “visible” ones are those evaporated very recently. If the reheating temp low, only heavy, cold ones exist which cannot be seen. Absent High Trh= High TH visible Low Trh = Low TH difficult to see Trh has a threshold below which PBH signals cannot observed

  14. Comparison with Diffuse Photon Background NG NG OK OK NG OK

  15. Allowed Region E Excluded A Allowed Excluded Allowed

  16. 4. Conclusion Constraints on brane inflation from PBH • Derived braneworld PBH mass function emerging from inflationary • perturbation normalised at Ly scale • Calculated diffuse photon spectrum from PBH and obtained constraints • on perturbation and reheating by comparing with obs. • Spectrum index larger than 1.3 requires reheating temperature • lower than 106 GeV: severer than 4D (1.3 ! 1.4、106! 108 GeV) PBHs have importance in higher-dimensional cosmology even they haven’t been detected

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