Gravitino, dark matter candidate and BBN Sean Bailly LAPTH, Annecy April 5 2011 SB, K. Jedamzik, G. Moultaka, Phys.Rev.D80:063509,2009. SB, K.Y. Choi, K. Jedamzik, L. Roszkowski, JHEP 0905:103,2009. SB, JCAP 1103:022,2011. Sean Bailly Gravitino, dark matter candidate and BBN 1/ 40
Introduction: composition of Universe A few questions What is Dark Energy ? What is Dark Matter ? SUSY particles How is matter produced in the Early Universe ? Big Bang Nucleosynthesis Lithium problems Where is the antimatter ? Baryogenesis, leptogenesis Sean Bailly Gravitino, dark matter candidate and BBN 2/ 40
Introduction: composition of Universe A few questions What is Dark Energy ? What is Dark Matter ? SUSY particles How is matter produced in the Early Universe ? Big Bang Nucleosynthesis Lithium problems Where is the antimatter ? Baryogenesis, leptogenesis Sean Bailly Gravitino, dark matter candidate and BBN 2/ 40
Introduction: composition of Universe A few questions What is Dark Energy ? What is Dark Matter ? SUSY particles How is matter produced in the Early Universe ? Big Bang Nucleosynthesis Lithium problems Where is the antimatter ? Baryogenesis, leptogenesis Sean Bailly Gravitino, dark matter candidate and BBN 2/ 40
Introduction: composition of Universe A few questions What is Dark Energy ? What is Dark Matter ? SUSY particles How is matter produced in the Early Universe ? Big Bang Nucleosynthesis Lithium problems Where is the antimatter ? Baryogenesis, leptogenesis Sean Bailly Gravitino, dark matter candidate and BBN 2/ 40
Introduction: solving the matter problems A simple framework Extension of the Standard Model: Supersymmetry Constrained Minimal Supersymmetric Standard Model (CMSSM) Lightest Supersymmetric Particle (LSP): gravitino Conservation of R-parity In this scenario The gravitino is a good candidate for dark matter The decay of the Next-to-LSP to the LSP during BBN can solve the lithium problem However The constraints require low reheating temperature and heavy mass spectrum Non-standard cosmology with a modified Hubble parameter Sean Bailly Gravitino, dark matter candidate and BBN 3/ 40
Table of contents Supersymmetry 1 Dark matter 2 Big Bang Nucleosynthesis 3 Stau NLSP and gravitino LSP 4 Non-standard cosmology 5 Summary 6 Sean Bailly Gravitino, dark matter candidate and BBN 4/ 40
Table of contents Supersymmetry 1 Dark matter 2 Big Bang Nucleosynthesis 3 Stau NLSP and gravitino LSP 4 Non-standard cosmology 5 Summary 6 Sean Bailly Gravitino, dark matter candidate and BBN 5/ 40
Supersymmetry Symmetry between bosons and fermions Q | fermion � = | boson � Q | boson � = | fermion � New particles with same mass as SM partners Broken symmetry No observation of superpartners SUSY breaking mechanism is unknown Explicit breaking terms included in effective SUSY lagrangian m 1 / 2 , m 0 , A 0 , CMSSM: tan β, sgn µ R-parity conservation P R = ( − 1 ) 3 B + L + 2 S The lightest SUSY particle is stable Sean Bailly Gravitino, dark matter candidate and BBN 6/ 40
Gravitino Supergravity If supersymmetry is a broken local symmetry: supergravity Graviton and its superpartner, the gravitino ˜ G (3 / 2-spin particle) Super-Higgs mechanism: ˜ G becomes massive F m 3 / 2 = √ 3 M Pl √ F is the SUSY breaking scale where GMSB CMSSM AMSB F m 3 / 2 = √ 0.1 keV 100 GeV 10 TeV 3 M pl But here we will take the gravitino mass as a free parameter. Gravitino interactions Gravitational interactions ∝ m 2 m 2 soft soft ∝ F m 3 / 2 M Pl Sean Bailly Gravitino, dark matter candidate and BBN 7/ 40
Table of contents Supersymmetry 1 Dark matter 2 Big Bang Nucleosynthesis 3 Stau NLSP and gravitino LSP 4 Non-standard cosmology 5 Summary 6 Sean Bailly Gravitino, dark matter candidate and BBN 8/ 40
Evidence for dark matter First observations: F. Zwicky (1933) Study of galactic rotation curves: V. Rubin (1970’s) Other observations Large scale structure formation Gravitational lensing CMB Bullet Cluster . . . WMAP five-year data giving at 3 σ Komatsu et al. (2008) Ω DM h 2 = 0 . 1099 ± 0 . 0124 Sean Bailly Gravitino, dark matter candidate and BBN 9/ 40
Relic density calculation The Boltzmann equation X − n eq n X + 3 Hn X = − � σ v � � n 2 2 � ˙ X In a radiation dominated universe dY g 1 / 2 m X � π Y 2 − Y eq � 2 � < σ v > ∗ dx = − 45 G x 2 with x = m X / T and Y = n X / s m X The relic density reads: Ω X h 2 = 2 . 742 × 10 8 � � Y ( T 0 ) 1 GeV Sean Bailly Gravitino, dark matter candidate and BBN 10/ 40
Gravitino dark matter candidate and non-thermal production Good candidate No charges Super Weakly Interacting Massive Particle SUSY LSP with R-parity conservation: stable Gravitino production Non-thermal production Thermal production Non-thermal production from NLSP decay All SUSY particles decay to NLSP NLSP freeze-out NLSP decays to LSP 3 / 2 h 2 = m 3 / 2 Ω NTP m NLSP Ω NLSP h 2 Sean Bailly Gravitino, dark matter candidate and BBN 11/ 40
Gravitino dark matter: thermal production During reheating, gravitinos can be produced in scattering processes Bolz et al. (2001), Pradler & Steffen (2007) g + g g + ˜ G ˜ → q + g q + ˜ G ˜ → q + q g + ˜ G ˜ → . . . � k α 3 � M 2 � T R � � � Y PS ( T BBN ) = y α g 2 � α 1 + α ln g α 3 m 2 10 10 GeV 3 / 2 α = 1 Thermal contribution to relic density � � m 1 / 2 � 2 � T R � 10 GeV � 3 / 2 h 2 ≃ 0 . 32 Ω TP m 3 / 2 10 8 GeV 1 TeV Gravitino relic density Ω 3 / 2 h 2 = Ω TP 3 / 2 h 2 + Ω NTP 3 / 2 h 2 Sean Bailly Gravitino, dark matter candidate and BBN 12/ 40
Table of contents Supersymmetry 1 Dark matter 2 Big Bang Nucleosynthesis 3 Stau NLSP and gravitino LSP 4 Non-standard cosmology 5 Summary 6 Sean Bailly Gravitino, dark matter candidate and BBN 13/ 40
Big Bang Nucleosynthesis : SBBN (1/5) Before 1 s : weak interactions n + e + → p + ¯ 10 Abundances ν e 1 Y 10 -1 p Weak interaction freeze-out 10 -2 n / p = e − Q / T f ∼ 1 / 6 → 1 / 7 10 -3 10 -4 D 10 -5 3 He -6 10 Deuterium bottleneck 10 -7 n -8 10 p + n → γ + D 10 -9 7 Li p + n -10 10 γ + D → 10 -11 -12 10 Deuterium production starts at 200 s 10 -13 6 Li D + p → 3 He + γ , D + 3 He → 4 He + p -14 10 1 10 10 2 10 3 10 4 t(s) 4 He: most stable element, absorbs all No stable element at A = 5 neutrons and A = 8 2 n Y p = Small abundances of 6 Li, 7 Li p + n ≃ 0 . 25 Sean Bailly Gravitino, dark matter candidate and BBN 14/ 40
Big Bang Nucleosynthesis : predictions (2/5) SBBN has only one free parameter Measurement by WMAP η = n b n γ = ( 6 . 225 ± 0 . 170 ) × 10 − 10 Sean Bailly Gravitino, dark matter candidate and BBN 15/ 40
Big Bang Nucleosynthesis : observations (3/5) Element SBBN Observations � D � ( 2 . 60 ± 0 . 16 ) × 10 − 5 ( 2 . 68 + 0 . 27 − 0 . 25 ) × 10 − 5 H � 3 He � ( 1 . 05 ± 0 . 04 ) × 10 − 5 ( 1 . 1 ± 0 . 2 ) × 10 − 5 H Y p 0 . 2487 ± 0 . 0006 0 . 242 ± 0 . 002 � 6 Li 10 − 14 − 10 − 15 � ( 3 − 5 ) × 10 − 12 H � 7 Li � ( 4 . 26 + 0 . 91 − 0 . 86 ) × 10 − 10 ( 1 . 2 − 1 . 9 ) × 10 − 10 H Sean Bailly Gravitino, dark matter candidate and BBN 16/ 40
Big Bang Nucleosynthesis : lithium-7 (4/5) Spite plateau points to a primordial abundance which disagrees with SBBN Possible origin of discrepancy Nuclear rates (re-examined and restricted by solar neutrino flux Coc et al. (2003) , Cyburt et al. (2003) ) Stellar depletion Richard et al. (2004) , Korn et al. (2006) Star temperature scale Melendez & Ramirez (2004) Particle decay during BBN Moroi et al. (1993), Feng et al. (2003), Cerdeno et al. (2005) Sean Bailly Gravitino, dark matter candidate and BBN 17/ 40
Big Bang Nucleosynthesis : lithium-6 (5/5) Debate on the existence of plateau ? Li/H log ( 6 Li/H), log (Li/H) 6 Li/H Origin [Fe/H] Cosmic rays in the galactic formation Suzuki & Inoue (2002) Rollinde et al. (2006) Cosmic rays from Pop III stars Rollinde et al. (2006) Particle decay during BBN Sean Bailly Gravitino, dark matter candidate and BBN 18/ 40
Decay of relic particles Massive unstable particle X with lifetime τ X ∼ 10 2 − 10 6 s Decay to Standard Model particles Injection of photons and nucleons: photodisintegration, 4 He spallation. . . 6 Li production: n ( 4 He , pn ) 3 H ( α, n ) 6 Li 7 Li destruction: 7 Be ( n , p ) 7 Li ( p , α ) 4 He Abundance change is constrained by observations Sean Bailly Gravitino, dark matter candidate and BBN 19/ 40
Catalyzed BBN Negatively charged X particles: bound state formation Reactions catalyzed Pospelov (2006) D γ D 6 Li − 4 He 6 X − Li ( 4 He X ) σ CBBN ≃ 10 8 × σ SBBN Important production of lithium-6 for τ � 3000 s The BBN code developed by K. Jedamzik (2006) takes all CBBN effects into account (CBBN reaction rates Kamimura et al. (2008) ) Sean Bailly Gravitino, dark matter candidate and BBN 20/ 40
Table of contents Supersymmetry 1 Dark matter 2 Big Bang Nucleosynthesis 3 Stau NLSP and gravitino LSP 4 Non-standard cosmology 5 Summary 6 Sean Bailly Gravitino, dark matter candidate and BBN 21/ 40
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