TAUP Conference @ SendaiSep 11 2007

Cosmic rays emitted by PBHsin a 5D RS braneworld

Yuuiti Sendouda(Yukawa Inst., Kyoto)

with

S. Nagataki (YITP), K. Kohri (Lancaster),K. Sato (Tokyo, RESCEU)

Overview

Strategy

Cosmic-ray observations

Exotic models for Universe

Modified theories offormation and evaporationof PBHs

Now, Braneworld

What to do

Gamma-ray

10-4

10-3

10-2

10-1

0.1 1.0 10.0

Ant

ipro

ton

flux

[m-2

s-1sr

-1G

eV-1

]

Kinetic energy [GeV]

BESS 1995BESS 1997BESS 1998

CAPRICE1994CAPRICE 1998

totalsecondary

primaryprimary (4D)

I[k

eV c

m

s

sr

keV

]

E [keV]

l=l, F=, i=. l=l, F=, i=. l=l, F=, i=. l=l, F=, i=. l=l, F=, i=. l=l, F=, i=.

Too many PBHs would disturb standard cosmologyCosmic-ray spectra differently dependent on extra dimensionImplications to braneworld and PBHs

Antiproton

Braneworld and PBHs

RS2 Braneworld

ℓ . 0.1mm

[Randall & Sundrum (1999a,b)]

Bulk: Anti-de Sitter (<0)

Warped 5D metric

4D onlarge scales

5D gravitybelow ℓ

Tensio

n >

+Matter T

Scales

Cosmology

Inflation

t

a(t)

ℓ

5D RD

Matter

2 distinctive epochs in RD

/ a-4

V ~ const. À

PBHs form

Friedmann eq.

Primordial Black HoleCarr (1975)

t = th

[Carr (1975), Guedens et al. (2002), Kawasaki (2004)]

> c

a(t)/k

H(t)-1 / t

k = aH

In RD: Jeans length ~ Hubble radius ~ Schwarzschild radius

BH

5D Schwarzschild (rS¿ℓ)

Accretion

(t)

Fcdt

Radiation accretes due to “slow” expansion in 5d era

[Guedens et al., Majumdar (2002)]

Efficiency (0 < F < 1)

Brane

Mass growth

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=1.60

Primordial Mass Function

Scale invariant

“Tilt”

(Normalised at Ly Forest)

Accretion leadsto a huge increase

i: Initial PBH abundance

[YS et al., JCAP 0606 (2006) 003]Formula to calculate from inflationary perturbation

Hawking Radiation

S2

S3

D=5 (RS) D=4

¿

4D particles

KK graviton

Black body

Temperature and mass of a “critical” PBH lifetime being 13.7Gyr

Galactic Antiprotons[YS et al., PRD 71 (2005) 063512]

[Asaoka (2002)]

http://www.kek.jp/newskek/2002/mayjun/bess1.html

Observations

Excess?

Propagation

p

r

z

Solar wind

p_ p

_

Convection

B

¯

primarysecondary

Source• NFW density profile• QCD Jets treated with

PYTHIA

[Ginzburg, Khazan & Ptuskin (1980), Berezinskii et al. (1991)]

Diffusion eq

[Webber, Lee & Gupta (1992)]

(+Solar modulation)

Typical Flux

10-4

10-3

10-2

10-1

0.1 1.0 10.0

Ant

ipro

ton

flux

[m-2

s-1sr

-1G

eV-1

]

Kinetic energy [GeV]

BESS 1995BESS 1997BESS 1998

CAPRICE1994CAPRICE 1998

totalsecondary

primaryprimary (4D)

No effect from extra dim?

Positive detection?

Fitted to solar-minimum data

Extra-dim Dependence

E0

Flux

• Contribution only from those currently evaporating• But spectrum unchanged• Flux proportional to →decreasing function of ℓ

106 108 1010 1012 1014 1016 1018

PB

H m

ass

spec

trum

dn/

dM [a

rb. u

nit]

PBH mass [g]

5D primordial5D present4D present

ℓ small

ℓ large

TH & GeV

Diffusion

Mass function (present-day)

M*

i is same

1018

1020

1022

1024

1026

1028

1030

1032

0.0 0.2 0.4 0.6 0.8 1.0

Siz

e of

the

extr

a di

men

sion

l/l

4

Accretion efficiency F

10-13

10-14

10-22

10-23

Effectively 4D

Constraints on i or ℓGi = Extr

a d

im (

ℓ/l 4

)

Accretion (F)

Large ℓ= weaker bound on PBH

×○

Density contrast G » 105

Extragalactic X/-ray Background

[YS et al., PRD 68 (2003) 103510]

10-1 100 101 102 103 104 105 106 107 108 109

Photon Energy (keV)

0.1

1.0

10.0

100.0

E2 d

J/dE

(keV

2 /(cm

2 -s-k

eV-s

r)

HEAO A2,A4(LED)

ASCA HEAO-A4 (MED)

COMPTEL

v

EGRET

http://cossc.gsfc.nasa.gov/docs/cgro/images/home/Cartoon_CGRO.jpghttp://heasarc.gsfc.nasa.gov/Images/heao1/heao1_sat_small2.gif

[Strong et al. (2003)]

keV GeVMeV

Observations

Spectrum

Superposing blackbody spectra

log E0

log I

TH/(1+z)

/ Mbh/TH

I / nbh/(1+z)3 ℓ1/2 Mbh3/2

Lifetime=Cosmic age

Heavy (still exist)Light (already died)

Sensitive to extra dimension I » U0/E0

I[k

eV c

m

ssr

ke

V

]

E [keV]

l=ll=l

l=l

i= , F=., f=

(b)

I[k

eV c

m

ssr

ke

V

]

E [keV]

i= , F=, f=l=ll=ll=l

4D

I[k

eV c

m

ssr

ke

V

]

E [keV]

l=l

l=l

l=l

i= , F=., f=

(a)

ℓ ↗Temp ↘ 4

D

Extra-dim Dependence

F=1

F=0

F=0.5

Potential to detect the extra dimAccretion takes important role

0.1mm

Safe

Dangerous

1018

1020

1022

1024

1026

1028

1030

1032

0.0 0.2 0.4 0.6 0.8 1.0

l/l4

F

10-23

10-24

10-25

10-26

10-27

10-28

10-29

10-30

10-31

Effectively 4D

ConstraintsExtr

a d

im (

ℓ/l 4

)

Accretion(F)

Small ℓweakensbound

Large ℓ weakens upper bound on PBH

×○

i =

Conclusions

1018

1020

1022

1024

1026

1028

1030

1032

0.0 0.2 0.4 0.6 0.8 1.0

Siz

e of

the

extr

a di

men

sion

l/l

4

Accretion efficiency F

10-26

10-27 10-28

Effectively 4DPhoton

Antiproton

(G = 105)

i > 10-27

Always

i<10-28

Always i =10-27 » 10-

28

Cooperative

As the constraint on ℓ

Comparison

Firm Limit on Inflation

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

pbar

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

Seljak et al. 200510-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

pbar

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

Seljak et al. 200510-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

10-6

10-5

10-4

10-3

10-2

10-1

100

100 105 1010 1015 1020 1025 1030

Pow

er s

pect

rum

PR

c

1/2

Comoving scale k -1 [m]

F=1 F=0 4D

WMAPLy

Cu

rvatu

re p

ert

ura

bati

on

n=1.28 1.35 1.39

1018

1020

1022

1024

1026

1028

1030

1032

0.0 0.2 0.4 0.6 0.8 1.0

Siz

e of

the

extr

a di

men

sion

l/l

4

Accretion efficiency F

10-26

10-27 10-28

Effectively 4DPhoton

Antiproton

10-4

10-3

10-2

10-1

0.1 1.0 10.0

Ant

ipro

ton

flux

[m-2

s-1sr

-1G

eV-1

]

Kinetic energy [GeV]

BESS 1995BESS 1997BESS 1998

CAPRICE1994CAPRICE 1998

totalsecondary

primaryprimary (4D)

Best-fit

If the sub-GeV pbar excess is real, allowed parameter region is very restrictive

i » 10-27

¼ 0.05

pbar visible

invisibleℓ . 1 pm

Braneworld disfavoured?Bess-Polar 2007 should give a hint

Being Speculative