Mass spectrum ofMass spectrum of PBH PBHssfrom inflationary perturbationfrom inflationary perturbation

in the RS braneworldin the RS braneworld

Yuuiti Sendouda(University of Tokyo)

Brane-world meeting@Portsmouth19 Sep 2006

Based on Sendouda, Nagataki, Sato, JCAP 0606 (2006) 003

1.Introduction2.PBHs in RS Braneworld3.Constraints on Brane Inflation4.Conclusion

Plan of TalkPlan of Talk

Primordial Black HoleA “visible” component of density perturbation

by virtue of Hawking radiation

Method to Probe Early Universe

PBHDensity

Perturbation

Mass Wave length

Abundance Amplitude

Correspondence:

1. Introduction1. Introduction

Obs. of cosmic-raysAbundance of PBHs?Density perturbationCurvature perturbationInflation

Higher dimensionalit

y

Back to the beginning

~1Mpc (Ly)

ScalesScales

Upper limits of PBH abundance (in 4D)Green & Liddle (1997)

CR

~1Gpc

?~km (M¯)

~fmPlanck

has particular importance

Large Scale Structure(from Tegmark’s webpage)

Constraints

2. PBHs in RS Braneworld2. PBHs in RS Braneworld

RS2 CosmologyRS2 Cosmology

log t

log a

Matter

Radiation

Slower

Brane expansion = Modified Friedmann Eq.

Tension

+Matter T

Curvature radius l . 0.1mm

l

Evolution of density perturbation (Note: Bulk effects omitted)

Treatment of density Treatment of density perturbationperturbation

Characterize (second) inflation bypower-law curvature perturbation

log t5D

4D

Spectrum of density perturbation

and reheating temperature Trh

HorizonComoving scale

Perturbations above some threshold form PBHs

Radiation-dominated phaseJeans length～ Hubble radius～ Schwarzschild radius of horizon mass

Formation of PBHFormation of PBH

Smoothed

Carr (1975)

Distribution: Gaussian

Threshold~O(0.1)

Variance at horizon entry

~10-5@Mpcfrom WMAP+SDSS+Ly

Seljak et al. (2005)

n~1:

AbundanceAbundance

Fraction ofcollapsing region

10-60

10-40

10-20

100

1020

1040

1010 1015 1020 1025 1030 1035 1040 1045

dnbh

/dM

bh,p

[ar

bitr

ary]

Mbh,p [g]

4Dl=0.1mm F=0

F=1

10-60

10-40

10-20

100

1020

1040

1010 1015 1020 1025 1030 1035 1040 1045

dnbh

/dM

bh,p

[g-1

pc-3

]

Mbh,p [g]

4Dl=0.1mm F=0

F=1

n=1.00 n=1.60

Reheating temp. = Minimum mass

Mass FunctionMass Function

Dominates in number

Not formed

l

4D

5D

l

4D

5D

3. Constraints on Brane Inflation3. Constraints on Brane Inflation

d-dim. BH’s Hawking radiation

Photons coming to eatrh

PBH Evaporation in BraneworldPBH Evaporation in Braneworld

KK modes

Matter

Stefan-Boltzmann law

(1) Large extra dim. = Low temp. (2) Life / Mbh2 in 5D

Page (1976), Harris et al. (2003), Cardoso et al. (2006), Creek et al. (2006)

10-60

10-40

10-20

100

1020

1040

1010 1015 1020 1025 1030 1035 1040 1045

dnbh

/dM

bh,p

[g-1

pc-3

]

Mbh,p [g]

4Dl=0.1mm F=0

F=1

Reconsidering Mass Reconsidering Mass FunctionFunction

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 Trh= High TH

visible

10-60

10-40

10-20

100

1020

1040

1010 1015 1020 1025 1030 1035 1040 1045

dnbh

/dM

bh,p

[g-1

pc-3

]

Mbh,p [g]

4Dl=0.1mm F=0

F=1AbsentLow Trh = Low TH

difficult to see

Trh has a threshold below which PBH signals cannot observed

10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

4D n=1.40 Trh=5.0x108 GeVTrh=7.9x108 GeV

n=1.42 Trh=1.3x108 GeVTrh=2.0x108 GeV

10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

l=0.1mm F=1 n=1.29 Trh=2.5x106 GeVTrh=3.2x105 GeV

n=1.33 Trh=4.0x105 GeVTrh=5.0x105 GeV

10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

l=0.1mm F=0 n=1.35 Trh=2.5x105 GeVTrh=2.8x105 GeV

n=1.38 Trh=9.0x104 GeVTrh=1.0x105 GeV

COMPTEL (Weidenspointner et al. 2000)EGRET (Strong et al. 2004)

EGRET (Sreekumar et al. 1998)

10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

HEAO (Gruber et al. 1999)10-10

10-8

10-6

10-4

10-2

100

102

104

100 101 102 103 104 105 106 107 108

Sur

face

Brig

htne

ss I

[ke

V c

m-2

s-1

sr-1

keV

-1]

Energy E0 [keV]

NG

OK

Comparison with Diffuse Comparison with Diffuse Photon BackgroundPhoton Background

OK

OK

NG

NG

105

106

1.260 1.280 1.300 1.320 1.340 1.360 1.380

Reh

eatin

g T

empe

ratu

re T

rh [

GeV

]

Spectral Index n

l=0.1mm F=1

105

106

1.260 1.280 1.300 1.320 1.340 1.360 1.380

Reh

eatin

g T

empe

ratu

re T

rh [

GeV

]

Spectral Index n

l=0.1mm F=0

107

108

109

1.380 1.400 1.420

4D

Excluded

Allowed

Allowed RegionAllowed Region

Excluded

Allowed

EA

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 106 GeV: severer than 4D (1.3 ! 1.4 、 106 ! 108 GeV)

Constraints on brane inflation from PBH

PBHs have importance in higher-dimensional cosmologyeven they haven’t been detected