Mass spectrum of pbh s from inflationary perturbation in the rs braneworld
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Mass spectrum of PBH s from inflationary perturbation in the RS braneworld. Yuuiti Sendouda (University of Tokyo) Brane-world [email protected] 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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Mass spectrum of pbh s from inflationary perturbation in the rs braneworld

Mass spectrum of PBHsfrom inflationary perturbationin the RS braneworld

Yuuiti Sendouda

(University of Tokyo)

Brane-world [email protected]

19 Sep 2006

Based on Sendouda, Nagataki, Sato, JCAP0606 (2006) 003


Plan of talk

Plan of Talk

  • Introduction

  • PBHs in RS Braneworld

  • Constraints on Brane Inflation

  • Conclusion


1 introduction

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


Mass spectrum of pbh s from inflationary perturbation in the rs braneworld

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)


2 pbhs in rs braneworld

2. PBHs in RS Braneworld


Rs2 cosmology

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


Treatment of density perturbation

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


Formation of pbh

Formation of PBH

Carr (1975)

Radiation-dominated phase

Jeans length~Hubble radius~Schwarzschild radius of horizon mass

Smoothed

Perturbations above some threshold form PBHs


Abundance

Abundance

Variance at horizon entry

[email protected]

from WMAP+SDSS+Ly

Seljak et al. (2005)

Distribution: Gaussian

Fraction of

collapsing region

Threshold~O(0.1)

n~1:


Mass function

Mass Function

n=1.00

n=1.60

5D

5D

4D

4D

l

l

Not formed

Reheating temp. = Minimum mass

Dominates in number


3 constraints on brane inflation

3. Constraints on Brane Inflation


Pbh evaporation in braneworld

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)


Reconsidering mass function

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


Comparison with diffuse photon background

Comparison with Diffuse Photon Background

NG

NG

OK

OK

NG

OK


Allowed region

Allowed Region

E

Excluded

A

Allowed

Excluded

Allowed


4 conclusion

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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