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Mini Black Holes and extra-dimensions

Aurélien BARRAU & Julien GRAIN

Small black holes in astrophysics : PBHs

J. Grain, A. Barrau, LPSC-Grenoble

PBH could have formed in the early universe

- Standard mass spectrum in the early universe
- Softening of the equation of state (Canuto , Khlopov)
- Quasi-critical phenomenon (Choptuik)
- Double inflation (Khlopov)
- Phase transition (Hawking , Steinhardt , Khlopov)

J. Grain, A. Barrau, LPSC-Grenoble

Direct antiprotons emission

- Individual emission
- Convoluted with the mass spectrum today

Initial spectrum

J. Grain, A. Barrau, LPSC-Grenoble

Source flux

(1)

(2)

(3)

FLUX

(4)

main contribution from :

antiprotons kinetic energy (GeV)

No influence of the details of the formation mechanism

J. Grain, A. Barrau, LPSC-Grenoble

Let antiprotons propagate in the Milky Way

Diffusive halo with convection and nuclear reactions

Galactic disc where sources are located

Drawing by D. Maurin

Maurin, Taillet, Donato, Salati, Barrau, Boudoul, review article for

“Research Signapost” (2002) [astro-ph/0212111]

J. Grain, A. Barrau, LPSC-Grenoble

Primary and secondary antiprotons

- Solve a diffusion equation for PBHs antiprotons AND secondary antiprotons coming from nuclear reaction on the ISM:
- And taking into account the diffusion in energy (tertiary contribution)

p-p interaction

p-He interaction

He-p interaction

He-He interaction

J. Grain, A. Barrau, LPSC-Grenoble

TOA fluxes and upper limit on PBH density

Experimental data points

Secondary antiprotons flux : “standard” physics only

PBH antiprotons flux for different values of PBH’s density

F.Donato, D. Maurin, P. Salati, A. Barrau, G. Boudoul, R.Taillet

Astrophy. J. (2001) 536, 172

A. Barrau, G. Boudoul et al.,

Astronom. Astrophys., 388, 767 (2002)

J. Grain, A. Barrau, LPSC-Grenoble

Another probe : gamma rays

- Data
- EGRET flux at 100 MeV
- “Gamma rays noise”
- (Pavlidou & Fields, ApJ 575, L5-8 (2002)):
- - galaxies
- - quasars

PBH emission (direct + neutral pions decay), with an integration over redshift :

+

PBH < 3.310 –9

A. Barrau & G. Boudoul, ICRC 2003 proc., [astro-ph/0304528]

J. Grain, A. Barrau, LPSC-Grenoble

Unlike the CMB or the large scale structures, PBH give informations on small scale

PRIMORDIAL BLACK HOLES ARE A UNIQUE COSMOLOGICAL PROBE

J. Grain, A. Barrau, LPSC-Grenoble

Cosmological constrain:PBH fraction β

PBHs are the only way to constrain small scales in the primordial power spectrum

Hypothesis: bump in the mass variance

( Starobinsky , Polarski )

Antiprotons constrains

Barrau, Blais, Boudoul, Polarski,

Phys. Lett. B, 551, 218 (2003)

J. Grain, A. Barrau, LPSC-Grenoble

Particle physics beyond the standard model with black holes ?

- To avoid entropy overproduction, an upper limit on Trh is obtainted with gravitinos
- If cosmic-rays from PBHs are detected, it leads to an upper limit on the Hubble mass at reheating so it leads to a lower limit on Trh
- Combining both lead to constrains on the gravitino mass

Lower limit on the gravitino

mass as a function of the PBH

induced cosmic rays flux

A. Barrau & N. Ponthieu

Phys. Rev. D 69, 085010 (2004) , hep-ph/0402187

J. Grain, A. Barrau, LPSC-Grenoble

PERSPECTIVES

Gravitinos emission from PBHs

- n<1.18 : the most stringent limit at small scale
- Positive running excluded

M. Khlopov, A. Barrau, astro-ph/0406621

J. Grain, A. Barrau, LPSC-Grenoble

Detection of PBH:Antideuterons

- Future experiment like AMS will measure the antideuteron flux
- Improvement ~ factor 10 in sensitivity

evaporation

Window for detection

New physics

Secondary anti(D)

A. Barrau, S. Alexeyev, et al. Class. Quantum Grav. 19 (2002) 4431

A. Barrau, G. Boudoul, et al. Astronom. Astrophys. 398, 403 (2003)

J. Grain, A. Barrau, LPSC-Grenoble

A. Barrau, J. Grain & S. Alexeev

Phys. Lett. B 584, 114-122 (2004)

Mini Black holes at the LHC :a delight for new physics !J. Grain, A. Barrau, LPSC-Grenoble

Arkani-Hamed, Dimopoulos, Dvali Phys. Lett. B 429, 257 (1998)

Black Holes at the LHC ?Hierarchy problem in standard physics:

One of the solutions:

Large extra dimensions

J. Grain, A. Barrau, LPSC-Grenoble

Black Holes Creation

- Two partons with a center-of-mass energy moving in opposite direction
- A black hole of mass and horizon radius is formed if the impact parameter is lower than

From Giddings & al. (2002)

J. Grain, A. Barrau, LPSC-Grenoble

Precursor Works

Giddings, Thomas Phys. Rev. D 65, 056010 (2002)

Dimopoulos, Landsberg Phys. Rev. Lett 87, 161602 (2001)

- Computation of the black hole’s formation cross-section
- Derivation of the number of black holes produced at the LHC
- Determination of the dimensionnality of space using Hawking’s law

J. Grain, A. Barrau, LPSC-Grenoble

From Dimopoulos & al. 2001

Interesting idea : using mini black holes a resonances

- Search for SUSY particles
- Search for light Higgs

Sigma ~ 1 TeV ^-2 ~ 400 pbarn !

J. Grain, A. Barrau, LPSC-Grenoble

From Dimopoulos & al. 2001

Gauss-Bonnet Black Holes?

- All previous works have used D-dimensionnal Schwarzschild black holes
- General Relativity:
- Low energy limit of String Theory:

A. Barrau, J. Grain & S. Alexeev

Phys. Lett. B 584, 114-122 (2004)

J. Grain, A. Barrau, LPSC-Grenoble

Gauss-Bonnet Black Holes’ Thermodynamic (1)

Properties derived by:

Boulware, Deser Phys. Rev. Lett. 83, 3370 (1985)

Cai Phys. Rev. D 65, 084014 (2002)

Expressed in function of the horizon radius

J. Grain, A. Barrau, LPSC-Grenoble

Gauss-Bonnet Black holes’ Thermodynamic (2)

Non-monotonic behaviour

taking full benefit of evaporation process

(integration over black hole’s lifetime)

J. Grain, A. Barrau, LPSC-Grenoble

The flux Computation

- Analytical results in the high energy limit

The grey-body factors are constant

- is the most convenient variable

Harris, Kanti JHEP 010, 14 (2003)

J. Grain, A. Barrau, LPSC-Grenoble

The Flux Computation (ATLAS detection)

- Planck scale = 1TeV
- Number of Black Holes produced at the LHC derived by Landsberg
- Hard electrons, positrons and photons sign the Black Hole decay spectrum
- ATLAS resolution

J. Grain, A. Barrau, LPSC-Grenoble

The Results -measurement procedure-

- For different input values of (D,), particles emitted by the full evaporation process are generated

spectra are reconstructed for each mass bin

- A analysis is performed

J. Grain, A. Barrau, LPSC-Grenoble

The Results-discussion-

- For a planck scale of order a TeV, ATLAS can distinguish between the case with and the case without Gauss-Bonnet term.

Important progress in the construction of a full quantum theory of gravity

- The results can be refined by taking into account more carefully the endpoint of Hawking evaporation

Barrau, Grain & Alexeyev

Phys. Lett. B 584, 114 (2004)

+ Dark matter candidate

Barrau et al., Ann. Phys. (2004)

J. Grain, A. Barrau, LPSC-Grenoble

Let’s add a cosmological constant

J. Grain, A. Barrau, LPSC-Grenoble

Positive cosmological constant

Presence of an event horizon at

Negative cosmological constant

Presence of closed geodesics

(A)dS UniverseCosmological constant

De Sitter (dS) Universe

Anti-De Sitter (AdS) Universe

J. Grain, A. Barrau, LPSC-Grenoble

Two event horizons and

No solution for with

One event horizon

Exist only for with

Black Holes in such a space-timeMetric function h(r)

De Sitter (dS) Universe

Anti-De Sitter (AdS) Universe

J. Grain, A. Barrau, LPSC-Grenoble

Calculation of Greybody factors (1)

- A potential barrier appears in the equation of motion of fields around a black hole:
- Black holes radiation spectrum is decomposed into three part:

De Sitter horizon

Tortoise coordinate

Potential barrier

Black hole’s horizon

Break vacuum fluctuations

Cross the potential barrier

Phase space term

J. Grain, A. Barrau, LPSC-Grenoble

Calculation of Greybody factors (2)

De Sitter horizon

Analytical calculations

Numerical calculations

Equation of motion analytically solved at the black hole’s and the de Sitter horizon

Equation of motion numerically solved from black hole’s horizon to the de Sitter one

J. Grain, A. Barrau, LPSC-Grenoble

Calculation of Greybody factors -results for scalar in dS universe-

d=4

The divergence comes from the presence of two horizons

P. Kanti, J. Grain, A. Barrau, Phys. Rev. D 71 (2005) 104002

J. Grain, A. Barrau, LPSC-Grenoble

Flux

Greybody factors in dS spacetime :

http://lpsc.in2p3.fr/ams/greybody

J. Grain, A. Barrau, LPSC-Grenoble

Perspectives

Compatibility with astrophysical and cosmological data OK

A. Barrau, C. feron, J. Grain, in press for Astrophys. J. (2005)

- Computations for fermions in dS spacetime (Grain, Kanti, Barrau)
- Computations for bosons and fermions in AdS spacetime (Grain, Kanti, Barrau)
- Investigation of the LHC signals (Labbé, Grain, Barrau)
- Gravitationnal blueshift (Barrau, Muteau-Jaouen)

J. Grain, A. Barrau, LPSC-Grenoble

Conclusion

Big black holes are fascinating…

But small black holes are far more fascinating!!!

J. Grain, A. Barrau, LPSC-Grenoble

Primordial Black holes in our Galaxy

F.Donato, D. Maurin, P. Salati, A. Barrau, G. Boudoul, R.Taillet

Astrophy. J. (2001) 536, 172

A. Barrau, G. Boudoul et al.,

Astronom. Astrophys., 388, 767 (2002)

Astrophys. 398, 403 (2003)

Barrau, Blais, Boudoul, Polarski,

Phys. Lett. B, 551, 218 (2003)

J. Grain, A. Barrau, LPSC-Grenoble

Cosmological constrain using PBH

- Small black holes could have been formed in the early universe
- Stringent constrains on the amount of PBH in the galaxy:

The anti-proton flux emitted by PBH is evaluating using an improved propagation scheme for cosmic rays

- This leads to constrain on the PBH fraction
- New window of detection using low energy anti-deuteron

J. Grain, A. Barrau, LPSC-Grenoble

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