SOME ASPECTS OF PRIMORDIAL BLACK HOLES PHYSICS

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1 SOME ASPECTS OF PRIMORDIAL BLACK HOLES PHYSICS Aurélien Barrau Laboratory for Subatomic Physics and Cosmology CNRS/INP3 Université Joseph Fourier Grenoble, France 1 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

2 The interval Special relativity : - Space-time homogeneity - Space isotropy - Same laws in all inertial frames group structure : Lorentz matrix conserved quantity : ds c dt dx dy dz Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

3 Equivalence principle All the test masses behave identically in the gravitational fiels ( mg ma!) Gravitational strength can be seen as a movement of the frame New equation for the interval ds g μν dx μ dx ν 3 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

4 Aurelien Barrau LPSC-Grenoble (CNRS / UJF) Riemann λ μα σ βλ λ μβ σ βα σ μα β σ μβ α σ μαβ Γ Γ Γ + Γ Γ Γ R λ ν μλ ν μ ν μ V V V D Γ + Curvature : Riemann where ( ) ν ν μ ν μ μ ν μ ν ν μ μ ν ν ν μ μ

4 4 Aurelien Barrau LPSC-Grenoble (CNRS / UJF) Riemann λ μα σ βλ λ μβ σ βα σ μα β σ μβ α σ μαβ Γ Γ Γ + Γ Γ Γ R λ ν μλ ν μ ν μ V V V D Γ + Curvature : Riemann where ( ) ν ν μ ν μ μ ν μ ν ν μ μ ν ν ν μ μ μ ν μ ν μ V x x x x x V x x x x V x x x x V V + ' ' ' ' ' ' ' ' Riemann vanishes if and only if spacetime is flat View as an «operator» : R(.,.,. ) so that R(u,ξ,u) gives the Opposite of the geodesic acceleration τ τ τ ξ τ τ ξ β α β α δ γ β α βγδ d dx af d x D m d dx d dx R d D + 0 and

5 Stress energy At each spacetime point, there exist a rank tensor containing all the information about energy and momentum T μν T(u,. ) T(.,u) -{4-momentum density} T α β u β dp dv α T(u,n) T(n,u) -{component of 4-momentum in direction n} T(u,u) {mass-energy density} Conservation : div(t)0 5 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

Einstein From geometrical ingrediants we try to build a tensor that: (1) Vanishes in flat spacetime () Uses ony Riemann and metric (3) Is specific because of (a)

6 Einstein From geometrical ingrediants we try to build a tensor that: (1) Vanishes in flat spacetime () Uses ony Riemann and metric (3) Is specific because of (a) linearity in Riemann, (b) symmetry and rank, (c) divergence free. Only one solution : G μν R μν 1 Rg μν où α R μν R μαν et R μ R μ 6 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

7 Field equations The simplest : G α T!!! 8 G μν 4 π c G T μν Exemple : black holes ds MG 1 c dt dr MG 1 rc rc 7 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

8 PBH could have formed in the early Universe * Standard mass spectrum in a radiation dominated era P δ 1 σ ( δ ) e π σ W e γ δ n BH M M BH ( M BH ) ( α ) M * ρcωpbh * α Near critical phenomena * Bubbles collisions, cosmic strings, etc. γ M BH κ ( δ ' δ ) c k 8 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

9 Hawking evaporation law d N dqdt h e Q Γ hκ / 4π c s ( 1) s d N dqdt M Q e Q T dm dt α ( M M ) T 3 hc 16πkGM M g T 10 1 GeV t 10 1 s M 10 9 g T 10 4 GeV t 1s S. Hawking, Comm. Math. Phys. 43 (1975) Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

10 BH thermodynamics 0th law : The surface gravity of a stationary BH is constant everywhere on the horizon 1st law: dmtds+ωdj+φdq nd law: ΔS>0 T hκ π kc, S Α 4l 3rd law: it is impossible to reduce the BH temperature du zero by a finit sequence of operations Generalized entropy SgS+Sm. ΔSg>0 10 Aurelien Barrau LPSC-Grenoble (CNRS / UJF), p E Mc Complementarity, UV/IR connection, holographic principle

11 constant term in the mass loss rate α g s 8 t+h W+Z b c+τ q+u+d+s+μ M(g) T(GeV) 11 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

12 Antiproton individual emission d N _ Q 1 p Γj kt s α j ( 1) j Q E dedt Q, T ) e h dg ( _ j p ( Q, E) de dq σ Γ/M Q Jet energy Antiproton energy MQ 1 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

13 Mass spectrum Convolution of the individual flux with the mass spectrum d N(M, E) d n(r, z) q prim (r, z, E) dm dedt dmdv Initial spectrum Today : dn dm dn dm init dm dm init dn dm M M < M * Hawking evolution law M init ( + 3 1/ 3 3 αt m ) 13 Aurelien Barrau LPSC-Grenoble (CNRS / UJF) M g Initial mass of a black hole with lifetime ~ age of the Univers

Cumulative source FLUX () (1) (4) (3) Flux total (1) () (3) (4) M [M Pl M [ 10 1 1,10 g,10 g] 13 g] 13 M [ 10 g, 5 10 M 13 > 5 10 g 13 g] Énergie

14 Cumulative source FLUX () (1) (4) (3) Flux total (1) () (3) (4) M [M Pl M [ ,10 g,10 g] 13 g] 13 M [ 10 g, 5 10 M 13 > 5 10 g 13 g] Énergie cinétique des antiprotons (GeV) Contribution essentielle: Masses de trous noirs entre 10 1 et g 14 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

15 Horizon size after inflation? Flux M 1 8 M t Pl Pl t t RH 0.3g 1 M T Pl RH Antiprotons kinetic energy (GeV) 15 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

16 What about a QCD halo? Flux Effet du halo Sans halo d N dedt e E T 0 P( T ) 8.6 T (1GeV ) Antiprotons kinetic energy (GeV) 16 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

17 Now, let the antiprotons propagate in the Milky way Drawing by D. Maurin Maurin, Taillet, Donato, Salati, Barrau, Boudoul, review article for Research Signapost (00) [astro-ph/01111] 17 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

18 18 Aurelien Barrau LPSC-Grenoble (CNRS / UJF) Secondary antiprotons ),, ( 1 ),0, ( ) ( ),0, ( ) ( _ E z r N r r r z z K z V E r N z h E r q z h c ine p + + Γ δ δ { } ' '), ( 4 ') ( ), ( _ de E r n p H E p de d E r q Threshlod p H ISM Φ + π σ { } { } ), ( ' '), ( ' ' ), ( E r N v n E de E r N v n E E de d E r q p H p X p H E p H p X p H σ σ p-p interactions : p-he, He-p and He-He interactions : evaluated with DTUNUC Tertiaries : Salati, Maurin, Taillet, Donato model

19 Secondary antiprotons flux Experimental data Antiprotons flux p-p component p-he component He-p component He-He component F.Donato, D. Maurin, P. Salati, A. Barrau, G. Boudoul, R.Taillet Astrophy. J. (001) 536, Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

20 Top of atmosphere spectrum A. Barrau, et al., Astronom. Astrophys., 388, 767 (00) 0 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

21 Upper limit on the PBH density ρ < g. cm n < 4 10 cm ( L 3kpc) Ω < Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

22 Gamma-ray new upper limit Taking into account the expected background from (Pavlidou & fields, ApJ 575, L5-8 (00)): -galaxies - quasars The EGRET gamma-ray flux at 100 MeV can be converted into (after integration over redshift, evolution and absorption) : Omega_PBH < 3.3 E 9, improving by a factor 3 the Page & MacGibbon upper limit. This limit is nearly the same as with antiprotons but it relies on very different physics and assumptions. Barrau & Boudoul, IRCR 003 proc., [asto-ph/030458] Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

23 Cosmological consequences Unlike the CMB or the large scale structures, PBH give informations on small scale PRIMORDIAL BLACK HOLES ARE A UNIQUE COSMOLOGICAL PROBE 3 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

24 Cosmological consequences HYPOTHESIS: Bump in the mass variance Starobinski et al. Phys. Rev. D 67 (003) 0404 Near critial phenomena M κ M H ( δ δ ) γ c Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

25 Constraints on the PBH fraction β β Contrainte Gravitationnelle Mpeak (g) Contrainte due aux antiprotons Barrau, Blais, Boudoul, Polarski, Phys. Lett. B, 551, 18 (003) 5 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

26 Amplitude of the jump 6 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

27 A new hope for detection? Antideuterons! Secondary noise very small (kinematics) A few events expected within the AMS detector 7 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

28 Antideuteron source term d N D dedt Γ ( Q, T ) dg ( Q, E, P0 ) h de ( ) s 1 Q / kt j D e ( 1) j dq j Q Eα j j p P 0 Fragmentation function into antideuterons For a given coalescence momentum P_0 n D 8 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

29 Antideuteron spectrum Window for detection Evaporation New computation of the secondary flux Secondary anti(d) More events in the Low energy tail 9 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

30 Parameters space {L - P 0 - ρ} P 0 (MeV/c) AMS excluded Zone in case of no-detection ρ (g/cm 3 ) L (kpc) A. Barrau et al. Astronom. Astrophys. 398, 403 (003) 30 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

31 The AMS experiment AMS-01: test fly in 1998 In AMS-0 on the ISS! 31 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

32 Main physics topics for AMS Search for antimatter Search for CDM Cosmic-rays Gamma-rays 3 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

33 The AMS-0 spectrometer TRD - e+/p & e-/p Discrim P<300GeV/c Cryostat & Aimant SC (B 1T) Trajectomètre (P & de/dx ) 3m Calorimetre electrom. (ID em particules) TOF Hodoscopes (TOF & de/dx) VETO RICH (particule ID A<~7, Z<~6) 33 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

34 Particles identification 34 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

35 What can de done? Bouchet et al. Nucl. Phys A 688,417 (001) Antimatter Cosmic-rays 35 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

36 The RICH Counter Calorimetre Number of photons Z Ring size V radiator mirror PMTs 36 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

37 If PBHs don t exist, let s create them! Hierarchy problem : M_Planck >> E_EW Two interesting ways to address this problem are : - Warped extra dimensional geometries (RS) Randall & Sundrum, Phys. Rev. Lett. 83, 3370 (1999) - Large extra dimension Harkani-Hamed, Dimopoulos & Dvali, Phys. Lett. B 49, 57 (1998) If the spacetime structure is made of numerous large dimensions : Mp ~ TeV if D10 and V61fm 6 37 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

38 Generalized Schwarschild solution r h 4(π ) Ω J 0 ( D ) D 4 D M M D Pl 1/( D 3) T H J 0 D 3 4πr h Myers & Perry, Amm. Phys. 17, 304 (1986) NS exp( M ( D ) /( D 3) ) Experimental detection 38 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

39 Detection at the LHC If the center of mass energy is > E_Planck for an impact parameter < R_S Black Hole! EASY EXPERIMENTAL SIGNATURE T. Banks & W. Fischler, hep-th/ Dimopoulos & Landsberg, Phys. Rev. Lett. 85, 499 (001) Giddings & Thomas, Phys. Rev. D 65, (00) 39 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

40 The LHC as a BH factory Need for PDF Dimopoulos & Landsberg, Phys. Rev. Lett. 85, 499 (001) 40 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

41 Dimensionality of space / new particles Plot from Dimopoulos & Landsberg The dimensionality of space can be reconstructed in most cases There is also a promising possibility to search for new particles ~ 100 GeV (e.g. a 130 GeV Higgs boson) PB : inelasticity Landsberg, Phys. Rev. Lett. 88, 18 (004) 41 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

42 The Gauss Bonnet term From General Relativity : To the Gauss-Bonnet action : - Phenomenological approach: only ghost-free quadratic correction - String theoretical approach: leading order in heterotic string models Successfully used Cosmology (e.g. Deruelle et al.) and BH Physics (e.g. Alexeyev et al.) 4 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

43 Gauss Bonnet BH thermodynamics Boulware & Deser, Phys. Rev. Lett., 88, 3370 (1985) Cai, Phys. Rev. D, 65, (00) 43 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

44 Temperature behaviour Non monotomic behaviour integration over time Barrau et al. Phys. Lett. B 584 (004) Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

45 Flux computation Multi-D grey body factors Taken at the relativistic limit (Kanti, Harris, Grain, Barrau) 45 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

46 ATLAS detection - Mp ~ 1 TeV - Rs (and production rate) modified by the GB term -Hard electrons and photons kept for determining the spectrum - Energy resolution taken into account 46 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

47 Results : beyond the dimensionality of space In any case, D And the GB coupling constant can be reconstructed Barrau, Grain, Alexeyev, Phys. Lett. B 584 (004) Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

48 EDGB cosmic black holes S S GB d 4 R x ijkl R ijkl g { μ Φ R + Φ + e S } λ 4R ij R ij μ + R σ ds Δdt dr r ( dϑ + sin Δ GB θdϕ ) Effects of Moduli fields, higher order curvature corrections and time perturbations OK Alexeyev, Barrau, Class. & Quantum Grav., 19, 4431 (00) 48 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

49 49 Aurelien Barrau LPSC-Grenoble (CNRS / UJF) Metric functions revisited ( ) Φ Φ h h r 6 4 inf λ... ) ( ) (... ) (... ) ( ) ( Δ h h h h h r r r r r r s s r r d r r d φ φ φ φ σ Alexeyev, Barrau, Boudoul et al., Astronom. Lett., 8, 7, (00)

50 Evaporation law in the Planck era Im( S) Im M ω r M out r in dr r dh Hawking law Im( S) k( M M 3 min ) 50 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

51 51 Aurelien Barrau LPSC-Grenoble (CNRS / UJF) Integrated relic flux t M G M c k M M Pl min 5 min 8 9 h π + Θ E t G M M c k E t k M M c G dedt N d Pl Pl min min h h π π π + max 0 4 ) ( tan ) ( ), (1 R univ dr R R R c R t z E dedt N d F π ϑ π ρ sr m s J F

52 BH from CR in the atmopshere Anchordoqui et al., Phys. ReV. D, 65 (00) 1407 Source of EHECR? (a different problem) A. Barrau, Astropart. Phys. 1 (000) 69 5 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

53 D-dimensional BH created on the ISM RC+ISM BH Cross section ~ 100 pbarn low amplitude But hard spectrum d de _ p 3 n _ p dtdv dσ dg nh 4 RC ( E _ πφ, Q( T, D, M dm de p _ p D ), E RC ) de RC dm Flux ~ 1/E dσ ( pp BH ) σ dm partons M s a, b 1 M s dx x M f ( x) f ( sx ) 53 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

54 Spectra after propagation Primordial universe production OK. Dark matter < 10^1g / galaxy A. Barrau, C. Féron, J. Grain, Astrophys. Journal, 630 (005) Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

55 gravitinos in cosmology dn dt 3/ + 3 Hn 3/ < Σ v > n rad m E 3/ 3/ n τ 3/ 3/ Photons : - gamma-gamma pair creation - pair creation on nuclei - Scattering -Compton -Inverse-compton D+gamma->n+p T+gamma->n+D T+gamma->p+n+n 3He+gamma->p+D 4He+gamma->p+T 4He+gamma->n+3He 4He+gamma->p+n+D 55 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

56 Constraints on SUGRA Lower limit on the reheating temperature as a function of the 100 MeV antideuteron flux Barrau & Ponthieu, Phys. Rev. D 69 (004) Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

57 Gravitino mass 57 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

58 Gravitinos from PBHs Khlopov & Barrau, submitted to Class. Quantum Grav. (005) n<1.18 : the most stringent limit at small scale Positive running excluded 58 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

59 Dark Matter In the BSI framework, PBHs can be reconsidered as CDM candidates In two different scenarii A. Barrau, D.Blais, G.Boudoul, D. Polarski Ann. Phys. 13, 115 (004) If M RH is very large (greater than g), PBHs become good candidates p 6 σ H, COBE LW δ Ω min π PBH M 15 H, e 3 Pour M H,e g p Experimental investigations possible above 10 g by detection of gravitational waves 59 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

60 Relics dark matter If M RH is small (smaller than 10 9 g), stable relics become good canidates p 6 σ H, COBE M rel 10 LW δ Ω min π PBH M p M 15 H, e 3 Pour M rel M P < p < A. Barrau, D.Blais, G.Boudoul, D. Polarski, Ann. Phys. 13, 115 (003) [astro-ph/ ] 60 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

61 (A)dS Universe 1 Rμν gμν R + Λgμν 8πT μν Cosmological constant De Sitter (ds) Universe Positive cosmological constant Presenceof an event horizon at Anti-De Sitter (AdS) Universe Negative cosmological constant Presence of closed geodesics ( d 1)( d ) Λ R ds 61 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

62 Black Holes in such a space-time ds (1 r μ Λ ( d 1)( d ) r ) dt (1 d 1 r μ d 1 dr Λ ( d 1)( d ) r ) r dω d Metric function h(r) De Sitter (ds) Universe Two event horizons R and H R ds Anti-De Sitter (AdS) Universe One event horizon RH No solution for with R T Tcrit H R crit Exist only for H with R crit ( d 3)( d Λ ) T crit 1 π Λ ( d ( d 3) ) 6 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

63 Calculation of Greybody factors (1) A potential barrier appears in the equation of motion of fields around a black hole: 1 r d dy r dr dy l( l + 1) + ω h( r) R r Tortoise coordinate Black holes radiation spectrum is decomposed into three part: dn dt e ω T H 1 ± 1 l Potential barrier σ l ( ω ) d 3 k 0 Black hole s horizon De Sitter horizon Break vacuum fluctuations Cross the potential barrier Phase space term 63 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

64 Calculation of Greybody factors () l + 1 σ l( ω) A l ω A l F F ( h ) in ( ) in F ( ) out 1 ( ) Fin (h) F in ( ) F in ( ) F out 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 64 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

65 Calculation of Greybody factors -results for scalar in ds universed4 Λ 10 The divergence comes from the presence of two horizons P. Kanti, J. Grain, A. Barrau, Phys. Rev. D 71 (005) Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

66 Flux Greybody factors in ds spacetime : 66 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

67 Experimental detection 67 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

68 What about the endpoint? 68 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

69 Conclusion Big black-holes are fascinating But small black holes are far more fascinating! 69 Aurelien Barrau LPSC-Grenoble (CNRS / UJF)

ANTIMATTER FROM PRIMORDIAL BLACK HOLES

ANTIMATTER FROM PRIMORDIAL BLACK HOLES Aurélien Barrau Institut des Sciences Nucléaires & UJF 53, av des Martyrs, 38026 Grenoble cedex, France XIVth RENCONTRES DE BLOIS, MATTER-ANTIMATTER ASYMMETRY Antiprotons