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  1. Mini Black Holes and extra-dimensions Aurélien BARRAU & Julien GRAIN

  2. Black Holes evaporate • Radiation spectrum • Hawking evaporation law J. Grain, A. Barrau, LPSC-Grenoble

  3. Small black holes in astrophysics : PBHs J. Grain, A. Barrau, LPSC-Grenoble

  4. 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

  5. Direct antiprotons emission • Individual emission • Convoluted with the mass spectrum today Initial spectrum J. Grain, A. Barrau, LPSC-Grenoble

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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 < 3.310 –9 A. Barrau & G. Boudoul, ICRC 2003 proc., [astro-ph/0304528] J. Grain, A. Barrau, LPSC-Grenoble

  11. Cosmological consequences 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. Let’s add a cosmological constant J. Grain, A. Barrau, LPSC-Grenoble

  29. Positive cosmological constant Presence of an event horizon at Negative cosmological constant Presence of closed geodesics (A)dS Universe Cosmological constant De Sitter (dS) Universe Anti-De Sitter (AdS) Universe J. Grain, A. Barrau, LPSC-Grenoble

  30. Two event horizons and No solution for with One event horizon Exist only for with Black Holes in such a space-time Metric function h(r) De Sitter (dS) Universe Anti-De Sitter (AdS) Universe J. Grain, A. Barrau, LPSC-Grenoble

  31. 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

  32. 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

  33. 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

  34. Flux Greybody factors in dS spacetime : http://lpsc.in2p3.fr/ams/greybody J. Grain, A. Barrau, LPSC-Grenoble

  35. 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

  36. Conclusion Big black holes are fascinating… But small black holes are far more fascinating!!! J. Grain, A. Barrau, LPSC-Grenoble

  37. 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

  38. 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