1. Mass spectrum of PBHs 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

2. 1.Introduction 2.PBHs in RS Braneworld 3.Constraints on Brane Inflation 4.Conclusion Plan of Talk

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

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

5. 2. PBHs in RS Braneworld

6. RS2 Cosmology log t log a Matter Radiation Slower Brane expansion = Modified Friedmann Eq.  Tension  +Matter T  Curvature radius l. 0.1mm l

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

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

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

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

11. 3. Constraints on Brane Inflation

12. d- dim. BH ’ s Hawking radiation Photons coming to eatrh PBH Evaporation in Braneworld KK modes Matter Stefan-Boltzmann law (1) Large extra dim. = Low temp. (2) Life / M bh 2 in 5D 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. High T rh = High T H visible Absent Low T rh = Low T H difficult to see T rh has a threshold below which PBH signals cannot observed

14. NG OK Comparison with Diffuse Photon Background OK NG

15. Excluded Allowed Allowed Region Excluded Allowed E A

16. 4. Conclusion 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 10 6 GeV: severer than 4D (1.3 ! 1.4、10 6 ! 10 8 GeV) Constraints on brane inflation from PBH PBHs have importance in higher-dimensional cosmology even they haven ’ t been detected