Cosmological Constraints on Supersymmetric Models. Frank Daniel Steffen

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1 Cosmological Constraints on Supersymmetric Models Frank Daniel Steffen Cosmology at the Beach, Jan 14, 2011

2 The Standard Model Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 2 GAUGE Gauge bosons Gauginos `SU(3) c, SU(2) L Y forces B-boson, bino W-bosons, winos gluon, gluino A (1) a µ = B µ λ (1) a = e B ( 1, 1 ) 0 A (2) a µ = W a µ λ (2) a = f W a ( 1, 3 ) 0 A (3) a µ = G a µ λ (3) a = eg a ( 8, 1 ) 0 matter MATTER Sfermions Fermions leptons I = 1, 2, 3 quarks I = 1, 2, 3 ( 3 colors) el I eνi L e I L ee I = e I R 0 A L I = eq I eui LA Q I = ed I L eu I = eu I R νi L e I L A `SU(3) c, SU(2) L Y ( 1, 2 ) 1 E c I = e c I R ( 1, 1 ) +2 ui L d I L 1 A ( 3, 2 ) U c I = u c I R ( 3, 1 ) 4 3 ed I = e d I R D c I = d c I R ( 3, 1 ) HIGGS Higgs, higgsinos φ = Higgs Boson 0 φ+ φ 0 A e Hd = e H 0 d eh d 1 `SU(3) c, SU(2) L Y A ( 1, 2 ) +1

3 Supersymmetry GAUGE Gauge bosons Gauginos B-boson, bino W-bosons, winos gluon, gluino `SU(3) c, SU(2) L Y A (1) a µ = B µ δ a1 λ (1) a = e B δ a1 ( 1, 1 ) 0 A (2) a µ = W a µ λ (2) a = f W a ( 1, 3 ) 0 A (3) a µ = G a µ λ (3) a = eg a ( 8, 1 ) 0 MATTER Sfermions Fermions sleptons, leptons I = 1, 2, 3 squarks, quarks I = 1, 2, 3 ( 3 colors) el I eνi L A L I = e I L ee I = e I R 0 eq I eui LA Q I = ed I L eu I = eu I R ed I = e d I R Higgs, higgsinos H d = H u = H0 d H d 0 H+ u Hu 0 1 A e Hd = νi L e I L A `SU(3) c, SU(2) L Y ( 1, 2 ) 1 E c I = e c I R ( 1, 1 ) +2 ui L d I L 1 A ( 3, 2 ) U c I = u c I R ( 3, 1 ) 4 3 D c I = d c R I ( 3, 1 ) e d 0 eh d 0 A ( 1, 2 ) 1 H A Hu e e u + A ( 1, 2 ) +1 eh 0 u 1 Minimal Supersymmetric Extension of the Standard Model Every Particle of the Standard Model has a Superpartner

4 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models Why Supersymmetry? Gauge Couplings Mα [GeV] Gaugino Mass Parameters Extension of Space-Time Symmetry 1000 Gauge Coupling Unification M 3 (Q) g s (Q) 800 M 2 (Q)/x Hierarchy Stabilization 2 [Lecture by Mark Trodden] 600 g(q) (Super-) Gravity M 1 (Q)/x M 2 (Q) 5/3 g (Q) M 1 (Q) 200 m 1/2 = 400 GeV Consistent String Theory M GUT Q [GeV] M GUT Q [GeV] Dark Matter Gauge Coupling Unification at M GUT GeV

5 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 5 Conservation of R-Parity [Lecture by Mark Trodden] superpotential: W MSSM W L + W B non-observation of L & B violating processes (proton stability,...) postulate conservation of R-Parity multiplicative quantum number P R = ( 1) 3(B L)+S = 2 +1 for SM, H u, H d 1 for X superpartners SUSY 2 SM1 SUSY 1 SUSY R-Parity SM R-Parity SM2 The lightest supersymmetric particle (LSP) is stable!!!

6 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 6 Cosmological Constraints Dark Matter Density Structure Formation Big Bang Nucleosynthesis Baryogenesis / Leptogenesis

7 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 6 Cosmological Constraints Dark Matter Density Structure Formation Big Bang Nucleosynthesis Baryogenesis / Leptogenesis

8 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 7 LSP Density DM Density photons Ωγ = % baryons ΩB = 4 %? baryon asymmetry? neutrinos 0.1 % Ων 1.5 %? neutrino mass? Standard Model particles 73% dark energy 5% dark matter 22% dark energy ΩDE = 73 %? vacuum energy? dark matter ΩDM = 22 %? identity?

9 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 8 focus point region Neutralino LSP Case annihilation funnel bulk region coannihilation region [see Baltz, Battaglia, Peskin, Wizansky, 06] [Battaglia]

10 Standard Thermal History of the Universe inflation slow roll ρϕ a 0 V reheat phase radiation dominated mat. dom. Λ dom. ρrad a -4 ρmat a -3 ρλ a 0 neutralino pair annihilation Cold Thermal Relic eχ 0 1 eχ 0 1 SM 1 SM 2 6!7 direct detection (CRESST, EDELWEISS,...) elastic eq. 6E7 neutralino scattering eχ 0 1 A eχ 0 1 A freeze out prod.@colliders (Tevatron, LHC, ILC,...) m/tf ~ 20 6L7 neutralino pair production p p eχ 0 1 eχ (Tevatron, LHC) e + e eχ 0 1 eχ (ILC) Standard Model particles 75% dark energy 5% dark matter 20% TR=? reheating temp. [Talk by Manuel Drees] [..., Jungman, Kamionkowski, Griest, 96,...] Supersymmetric Dark Matter in Cosmology and at Colliders 10 GeV WIMP freeze out 1s 1 MeV BBN y 1eV t0=14 Gy T0=2.73 K LHC Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 9 18 t T a

11 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 10 focus point region Neutralino LSP Case annihilation funnel bulk region coannihilation region [see Baltz, Battaglia, Peskin, Wizansky, 06] [Battaglia]

12 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 10 focus point region Neutralino LSP Case annihilation funnel bulk region poster by Jonas Lindert coannihilation region [see Baltz, Battaglia, Peskin, Wizansky, 06] [Battaglia]

13 Frank D. Steffen (Max Planck Institute for Physics, Munich) Dark Matter Candidates 11 Other well-motivated candidates Extremely Weakly Interacting Particles (EWIPs) Extensions of the Standard Model Peccei-Quinn Symmetry & Supersymmetry spin mass int. Axions Axinos Gravitinos fa >10 9 GeV fa >10 9 GeV MPl =2.4 x10 18 GeV 0 1/2 3/2 <10 mev? ev-tev (p/fa) n (p/fa) n (p/mpl) n

14 Frank D. Steffen (Max Planck Institute for Physics, Munich) Dark Matter Candidates 11 Other well-motivated candidates Extremely Weakly Interacting Particles (EWIPs) Extensions of the Standard Model Peccei-Quinn Symmetry & Supersymmetry spin mass int. Axions Axinos Gravitinos fa >10 9 GeV fa >10 9 GeV 0 1/2 3/2 <10 mev? MPl =2.4 x10 18 GeV poster by Peter Graf ev-tev (p/fa) n (p/fa) n (p/mpl) n

15 Frank D. Steffen (Max Planck Institute for Physics, Munich) Dark Matter Candidates 11 Other well-motivated candidates Extremely Weakly Interacting Particles (EWIPs) Extensions of the Standard Model Peccei-Quinn Symmetry & Supersymmetry spin mass int. Axions Axinos Gravitinos fa >10 9 GeV fa >10 9 GeV MPl =2.4 x10 18 GeV 0 1/2 3/2 <10 mev? ev-tev (p/fa) n (p/fa) n (p/mpl) n

16 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 12 Axino & Gravitino LSP Cases Extremely Weakly Interacting Particles (EWIPs) Extensions of the Standard Model Peccei-Quinn Symmetry & Supersymmetry spin mass int. Axions Axinos Gravitinos fa >10 9 GeV fa >10 9 GeV MPl >2.4 x10 18 GeV 0 1/2 3/2 <10 mev? ev-tev (p/fa) n (p/fa) n (p/mpl) n

17 inflation slow roll ρϕ a 0 V reheat phase TR=? reheating temp. radiation dominated ( mat. dom. Λ dom. ρrad a -4 ) ρmat a -3 ρλ a 0 eτ prod. at colliders (LHC, ILC,...) + eτ collection + eτ decay analysis: NLSP m! eg, LSP M + Pl (?), SM... T < 10 GeV e eq. NLSP freeze out m/tf ~ 20 [Covi, Kim, Roszkowski, 99] ) ( e 10 GeV WIMP freeze out ) 1s 1 MeV BBN y 1eV 75% dark energy t0=14 Gy T0=2.73 K LHC dark matter 20% Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 13 Standard Model particles 5% t T a

18 inflation slow roll ρϕ a 0 V reheat phase prod. Very at Early colliders Hot (LHC, Universe ILC,...) Thermal Axino/ Gravitino Production + eτ collection T ~ 10 7 GeV + eτ g a decay analysis: G a e m eg, M Pl (?), g c +... g b TR=? reheating temp. g c radiation dominated ( mat. dom. Λ dom. ρrad a -4 ) ρmat a -3 ρλ a 0 eτ prod. at colliders (LHC, ILC,...) + eτ collection + eτ decay analysis: NLSP m! eg, LSP M + Pl (?), SM... T < 10 GeV e eq. NLSP freeze out m/tf ~ 20 [Covi, Kim, Roszkowski, 99] ) ( e 10 GeV WIMP freeze out ) 1s 1 MeV BBN y 1eV 75% dark energy t0=14 Gy T0=2.73 K LHC dark matter 20% Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 13 Standard Model particles 5% t T a

19 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models Gravitino LSP Case Thermal G Production τ NLSP G + τ [Pradler, FDS, 07] [...; see Bolz, also Brandenburg, [Moroi, Murayama, Buchmüller, Yamguchi, 93, 01] Asaka, Hamaguchi, Suzuki, 00, Roszkowski et al., 05, [Pradler, FDS, 06] Cerdeno et al., 06, FDS 06, Rychkov, Strumia, 07] [FDS 06] [... ; see Borgani, also [Borgani, Masiero, Masiero, Yamaguchi, Yamguchi, 96, 96;...] Asaka, Hamaguchi, Suzuki, 00, Ellis et al., 04, [... ; Covi, Kim, Roszkowski, 99;...] Feng, Su, Takayama, 04]

20 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models a Axino LSP Case Thermal G Production a τ NLSP G + τ !6 10!4 10!2 CDM (mã, [Brandenburg, T R ) (100 FDS, kev, 04] 10 6 GeV) HDM (mã, T R ) (100 ev, 10 9 GeV) [...; Bolz, see Brandenburg, also [Covi et al., Buchmüller, 01] 01] CDM (m eg identical, T R ) (10 to MeV the, 10 6 GeV CDM (mg e, gravitino T R) (100 case GeV, 10 9 GeV [... ; Borgani, Masiero, Yamaguchi, 96;...] [Pradler, FDS, 06] [... ; Covi, Kim, Roszkowski, 99;...] [... ; Brandenburg, FDS, 04] [... ; Pradler, FDS, hep-ph/ ] a

21 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 16 Cosmological Constraints Dark Matter Density Structure Formation Big Bang Nucleosynthesis Baryogenesis / Leptogenesis

22 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 16 Cosmological Constraints Dark Matter Density Structure Formation Big Bang Nucleosynthesis Baryogenesis / Leptogenesis

23 Big Bang Nucleosynthesis inflation slow roll ρϕ a 0 V reheat phase radiation dominated mat. dom. Λ dom. ρrad a -4 ρmat a -3 ρλ a 0 /0(+ /0(* /0() C & /0(' " /0(!./!./ './ )./ - ) + B=$"%& (././ /0//) ' &! "#$"% & %>#9?=;7%Ω 3! ( /0/. /0/( /0/! BBN Standard Model particles 75% dark energy 5% dark matter 20%. (! ' ) * +, -./ :;8:&<8;89%65;=8%η././ TR=? reheating temp. 10 GeV WIMP freeze out 1s 1 MeV BBN y 1eV t0=14 Gy T0=2.73 K LHC Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 17 t T a

24 C & " + B=$"%& /0(+ /0(* /0() /0(' /0(!./!./ './ )./ - ) (././ Big-Bang Nucleosynthesis. /0//) ' &! "#$"% & and Cosmological Constraints 20. Big-Bang time nucleosynthesis delay after t (i). When 3 this concentration is reached the two-body DD deut become more Deriving efficientthis than formula the pn deuterium I used the relations production (19) with κ and 1.11, Xand D begins (28); theto obtaine decr %>#9?=;7%Ω 3! ( was solved by iterations assuming that 10 1 < η 10 < 10. /0/. /0/( /0/! After deuterium 10-6 abundance reaches the value given by (34) everything proceed In fact, if η 10 = 1 then according to (28) the equilibrium concentration X D should in 10 4 to when -7 the temperature drops from 0.08 MeV to 0.07 MeV. This incr means that the 10-8 reaction rates converting the deuterium to more heavy elements, wh portional to XD 2, at T 0.07 MeV become times bigger than the rate of the expa clear that this system is far from the equilibrium and the deuterium supplied by pn r converted very fast to more heavy elements. This doesn t allow the deuterium conce increase to the values bigger than The details of the nonequilibrium processes ar by a complicated system of kinetic equations which can be solved only numerically. I results of numerical calculations for the time evolution of the element abundances in t with Ω B h are shown [5] (! ' ) * +, -./ :;8:&<8;89%65;=8%η././ 4 Why it is so can be understooddd2 even withoutt analyzing D He T the rates of reactions. Actually, if [Particle Data Book 2006] [Kawasaki, 4 He would be in the equilibrium with the other 7 light e Kohri, Moroi, T 05; Cyburt et al., Li be dominating at low temperatures because of its high binding energy 03] (28.3 four times bigger than the binding energies of the figure [V. intermediate Mukhanov, 1 elements, 04] 3 He T (6.92 MeV ). The system which is away from equilibrium always tends th Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 4 18 re 20.1: The abundances of 4 He, D, 3 He and 7 Li as predicted by the standard el of big-bang nucleosynthesis. Boxes indicate the observed light element dances (smaller boxes: 2σ statistical errors; larger boxes: ±2σ statistical and matic errors). The narrow vertical band indicates the CMB measure of the ic baryon density. See full-color version on color pages at end of book. In this Figure to every element corresponds its own reservoir. All these SBBN Below I present the calculations which explain the time behavior of these abun derive the formulae for the final freeze-out abundances of light elements up to 7 Be. T 4 He, deuterium 10-6 (D), helium-3 ( 3 He), tritium (T ), Lithium-7 ( 7 Li) and Beryllium other light elements 10-7 as, for instance, 8 Li, 8 B etc. are produced in very small amoun be ignored. The most important nuclear reactions involving the light elements are schem picted in Fig.1, which I recommend to keep in front of the eyes reading the rest of th 3 figure He2 D p DD1 [Burles et al., 99] 3 He D 3 4 He He The concentration of the p,n free neutrons during this period strongly decr first to the deuterium 10 p,n reservoir -15 and 4 Dthen proceed 3 7 He He 10 6 n further through the Be n pipe D! elements. For most neutrons the final destination is the He reservoir Li p 7 Be

25 C & " + B=$"%& /0(+ /0(* /0() /0(' /0(!./!./ './ )./ - ) (././ Big-Bang Nucleosynthesis. /0//) ' &! "#$"% & 20. Big-Bang nucleosynthesis %>#9?=;7%Ω 3! ( /0/. /0/( /0/! (! ' ) * +, -./ :;8:&<8;89%65;=8%η././ [Particle Data Book 2006] re 20.1: The abundances of 4 He, D, 3 He and 7 Li as predicted by the standard el of big-bang nucleosynthesis. Boxes indicate the observed light element dances (smaller boxes: 2σ statistical errors; larger boxes: ±2σ statistical and matic errors). The narrow vertical band indicates the CMB measure of the ic baryon density. See full-color version on color pages at end of book. Frank D. Steffen (Max-Planck-Institute for Physics, Munich) and Cosmological Constraints He e H D h e e H Standard Model particles D e He He [Kawasaki, Kohri, Moroi, 05; Cyburt et al., 03] Li Cosmological Constraints on Supersymmetric Models e H e stau D e e e gravitino e e H e 19

26 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 20 Catalyzed BBN [Pospelov, 06] 1h stau He Li gravitino D Standard Model particles stau 10 h [b] [Cyburt et al., 06; FDS, 06; Pradler, FDS, 07; Hamaguchi et al., 07; Kawasaki, Kohri, Moroi, 07; Takayama, 07; Jedamzik, 07; Pradler, FDS, 08] CBBN of 9 Be: [Pospelov, 07; Pospelov, Pradler, FDS, 08]

27 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 21 Gravitino LSP Case with a Charged Slepton NLSP (C)BBN Constaints [Pospelov, Pradler, FDS, 08] disfavored by cosmological constraints see also [FDS, hep-ph/ ]

28 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 22 [Freitas, FDS, Tajuddin, Wyler, ] Axino LSP Case with a Charged Slepton NLSP fa[gev] (a) He/D 10 6 s D sev em 10 4 s 10 2 s D cons em 6 Li D sev had 9 Be e Q = 1/3 m B = 1.1 m τ m 2 ã /m2 τ 1 Y τ = (m τ /1 TeV) m τ [TeV] D cons had Upper Limits on the Peccei-Quinn Scale fa[gev] (b) f a GeV [Raffelt, 06] D sev em 3 He/D 10 6 s 10 4 s ev D cons em mev ev D sev had 10 2 s D cons had e Q = 1/3 m B = 1.02 m τ m 2 ã /m2 τ 1 Y τ = (m τ /1 TeV) kev ma ADMX CAST Telescope Laboratory ColdDM Excessradiation HotDM Globularclusterstars(photons) GCstars&Whitedwarfcooling(electrons) SN 1987A Toomanyevents Burstduration m τ [TeV] Astrophysical Axion Bounds Bounds from Axion Searches 6 Li 9 Be

29 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 23 Cosmological Constraints Dark Matter Density Structure Formation Big Bang Nucleosynthesis Baryogenesis / Leptogenesis

30 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 24 Supersymmetric Dark Matter Candidates LSP interaction production constraints experiments eχ 0 1 g, g WIMP cold indirect detection (EGRET, GLAST,...) weak freeze out direct detection (CRESST, EDELWEISS,...) M W 100 GeV prod.@colliders (Tevatron, LHC, ILC,...) eg p M Pl n therm. prod. cold eτ prod. at colliders (LHC, ILC,...) extremely weak NLSP decays warm + eτ collection M Pl = GeV... BBN + eτ decay analysis: m eg, M Pl (?) ea p f a n therm. prod. cold eτ prod. at colliders (LHC, ILC,...) extremely weak NLSP decays warm + eτ collection fa 10 9 GeV... BBN + eτ decay analysis: mã, f a

31 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 24 Supersymmetric Dark Matter Candidates LSP interaction production constraints experiments eχ 0 1 g, g WIMP cold indirect detection (EGRET, GLAST,...) For a review (including an extensive list of references), The European Physical Journal C EPJ C weak freeze out direct detection (CRESST, EDELWEISS,...) RecognizedbyEuropeanPhysicalSociety volume 59 number 2 january 2009 M W 100 GeV prod.@colliders (Tevatron, LHC, ILC,...) Particles and Fields eg ea p M Pl n therm. prod. cold eτ prod. at colliders (LHC, ILC,...) extremely weak NLSP decays warm + eτ collection M Pl = GeV... BBN + eτ decay analysis: m eg, M Pl (?) p see [FDS, Dark Matter Candidates, Eur. Phys. J. C59 (2009) 557, arxiv: ] in Supersymmetry at the dawn of the LHC f a n therm. prod. cold eτ prod. at colliders (LHC, ILC,...) extremely weak NLSP decays warm + eτ collection Present limits on the spin-independent neutralino nucleon cross section from direct searches. From F.D. Steffen: Dark-matter candidates fa 10 9 GeV... BBN + eτ decay analysis: mã, f a

32 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 24 Supersymmetric Dark Matter Candidates LSP interaction production constraints experiments eχ 0 1 g, g WIMP cold indirect detection (EGRET, GLAST,...) weak freeze out direct detection (CRESST, EDELWEISS,...) M W 100 GeV prod.@colliders (Tevatron, LHC, ILC,...) eg p M Pl n therm. prod. cold eτ prod. at colliders (LHC, ILC,...) extremely weak NLSP decays warm + eτ collection M Pl = GeV... BBN + eτ decay analysis: m eg, M Pl (?) ea p f a n therm. prod. cold eτ prod. at colliders (LHC, ILC,...) extremely weak NLSP decays warm + eτ collection fa 10 9 GeV... BBN + eτ decay analysis: mã, f a

33 Bonus Material Frank D. Steffen (Max-Planck-Institute of Physics, Munich) Probing the Reheating Temperature at Colliders and with BBN 25

34 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 26 Cosmological Constraints Dark Matter Density Structure Formation Big Bang Nucleosynthesis Baryogenesis / Leptogenesis

35 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 26 Cosmological Constraints Dark Matter Density Structure Formation Big Bang Nucleosynthesis Baryogenesis / Leptogenesis

36 Thermal Leptogenesis inflation slow roll ρϕ a 0 V reheat phase radiation dominated mat. dom. Λ dom. ρrad a -4 ρmat a -3 ρλ a 0 Standard Model particles 75% dark energy 5% dark matter 20% TR > 10 9 GeV reheating temp. 10 GeV WIMP freeze out 1s 1 MeV BBN y 1eV t0=14 Gy T0=2.73 K LHC Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 27 t T a

37 Thermal Leptogenesis inflation slow roll ρϕ a 0 V reheat phase radiation dominated mat. dom. Λ dom. ρrad a -4 ρmat a -3 ρλ a 0 Standard Model particles 75% dark energy 5% dark matter 20%??? TR > 10 9 GeV reheating temp. 10 GeV WIMP freeze out 1s 1 MeV BBN y 1eV t0=14 Gy T0=2.73 K LHC Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 27 t T a

38 Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 28 The gravitino can become a problem...

39 Frank D. Steffen (Max-Planck-Institute of Physics, Munich) Probing the Reheating Temperature at Colliders and with BBN 29 Thermal Gravitino Production Stable Gravitino gravitino LSP gauge-field of local SUSY (supergravity) Unstable Gravitino neutralino LSP Very Hot Early Universe eτ collection T ~ 10 7 GeV eτ g a decay analysis: G a e m eg, M Pl (? g c +... g b g c gauge-invariant treatment (hard thermal loop resummation) gravitino DM late NLSP decays NLSP bound states neutralino DM late gravitino decays BBN constraints SUSY QCD [Bolz, Brandenburg, Buchmüller, 01] + electroweak contributions [Pradler, Steffen, 06 & 07]

40 Frank D. Steffen (Max-Planck-Institute of Physics, Munich) Probing the Reheating Temperature at Colliders and with BBN 29 Thermal Gravitino Production Stable Gravitino gravitino LSP gauge-field of local SUSY (supergravity) Unstable Gravitino neutralino LSP Very Hot Early Universe eτ collection T ~ 10 7 GeV eτ g a decay analysis: G a e m eg, M Pl (? g c +... g b g c gauge-invariant treatment (hard thermal loop resummation) gravitino DM late NLSP decays NLSP bound states neutralino DM late gravitino decays BBN constraints SUSY QCD [Bolz, Brandenburg, Buchmüller, 01] + electroweak contributions [Pradler, Steffen, 06 & 07]

41 Frank D. Steffen (Max-Planck-Institute of Physics, Munich) Probing the Reheating Temperature at Colliders and with BBN 29 Thermal Gravitino Production Stable Gravitino gravitino LSP gauge-field of local SUSY (supergravity) Unstable Gravitino neutralino LSP Very Hot Early Universe eτ collection T ~ 10 7 GeV eτ g a decay analysis: G a e m eg, M Pl (? g c +... g b g c gauge-invariant treatment (hard thermal loop resummation) gravitino DM late NLSP decays NLSP bound states neutralino DM late gravitino decays BBN constraints SUSY QCD [Bolz, Brandenburg, Buchmüller, 01] + electroweak contributions [Pradler, Steffen, 06 & 07]

42 Upper Limits on the Reheating Temperature Neutralino LSP Unstable Gravitino 226 J. Pradler, F.D. Steffen / Physics Letters B 648 (2007) Late Decaying Gravitinos from Thermal Production resulting gravitino yield from thermal production reads Y TP G (T low) G (T low) ntp C G (T R) s(t low ) s(t R )H (T R ) 3 ( = y i gi 2 (T R) 1 + M2 i (T ) R) i=1 3m 2 G Thermal Leptogenesis ( )( ) ki T R ln (3) g BBN constraints i (T R ) 10 10, GeV + ΩDM where the constants y constraint i are given in Table 1. These constants are obtained with for neutralino DM [Pradler, the Hubble FDS, parameter 07] describing the radiationdominated epoch, H rad (T ) = g (T )π 2 /90 T 2 /M P, the entropy density s(t ) = 2π 2 g S (T )T 3 /45, and an effective numberthermal of relativistic Leptogenesis degrees of freedom of requires g T >10 9 (T R ) = g S (T R ) = GeV We evaluate g i (T R ) and M i (T R ) using the one-loop evolution described by the renormalization group equation in [Kohri, Moroi, Yotsuyanagi, 05] Frank D. Steffen (Max-Planck-Institute for Physics, Munich) Cosmological Constraints on Supersymmetric Models 30

43 Frank D. Steffen (Max-Planck-Institute of Physics, Munich) Probing the Reheating Temperature at Colliders and with BBN 31 Thermal Gravitino Production Stable Gravitino gravitino LSP gauge-field of local SUSY (supergravity) Unstable Gravitino neutralino LSP Very Hot Early Universe eτ collection T ~ 10 7 GeV eτ g a decay analysis: G a e m eg, M Pl (? g c +... g b g c gauge-invariant treatment (hard thermal loop resummation) gravitino DM late NLSP decays NLSP bound states neutralino DM late gravitino decays BBN constraints SUSY QCD [Bolz, Brandenburg, Buchmüller, 01] + electroweak contributions [Pradler, Steffen, 06 & 07]

44 ! Product Thermal G Upper Limits on the Reheating Temperature Thermal Leptogenesis[Josef Pradler, FDS, hep-ph/ ] Thermal Leptogenes [Josef Pradler, FDS, hep-ph/ ]! Dark Matter Upper Bounds TR in the CMSSM with G! on! τ NLSP!"##$%&"'(&$)*+,"! + τ with- G Thermal G Production! Upper Bounds on T"R in the G CMSSM Dark Matter Stable Gravitino LSP Unstable!"#$%$&#'()*+,-./#0"123#(/#4.*5 Gravitino ! 20!"##$%&"'(&$)*+," " - $%$&#61/*#7.#7)"8.25#7).(8+29#6.,:(2+/6#3.*.)6+2./#':.2"6.2"-"94 ;").#*:(2#<==#'()(6.*.)/#.>.2#+2#6+2+6(-#?;$$;@#6"3.-/A ! 1000 Thermal Leptoge msugra / CMSSM!"#$%$&#'()*+,-./#0"123#(/#4.*5!"##$%&'&(#)%*&&&" (+,-./ # Thermal Leptogenesis Thermal Leptogenesis Furthermore, wecmssm only need to take into account the pro# $%$&#61/*#7.#7)"8.25#7).(8+29#6.,:(2+/6#3.*.)6+2./#':.2"6 ;").#*:(2#<==#'()(6.*.)/#.>.2#+2#6+2+6(-#?;$$;@#6"3.-/A! 500!.B#/1'.)0+.-3/#+2#C:+33.2D#/.,*")# 500! 2000 E2*.)(,*#9)(>+*(*+"2(--4#B+*:#;$$;# 2000 # $"0*#$%$&#7).(8+29 $ 0* $%$& 7 8+!"##$%&'&(#)%*&&& duction of the spin-1/2 components of the gravitino since" (+,-./ (11) implies Mi2 /3m2Ge! 1 0&1'2'(%3%2$&'3&-,4&$!'*% for mge! 1 GeV.#!.B#/1'.)0+.-3/#+2#C:+33.2D#/.,*")# Electronic address: j # E2*.)(,*#9)(>+*(*+"2(--4#B+*:#;$$;# For a given m1/2, the reheating temperature TR is lim Electronic address: s # $"0*#$%$&#7).(8+29 $ 0* $%$& 7 8+ ited from above because ΩTP cannot exceed the dark [1] M. Pospelov, Phys. R e G 0&1'2'(%3%2$&'3&-,4&$!'*% 567&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&-, [2] K. Kohri and F. Ta matter density [25] Ω3σ h is the =,"2/.)>(*+" E2 h E2#J#'()+*4#,"2/.)>(*+"2#/,.2()+"L#*:.#Q$R#+/#*:.#2.1*)(-+2"##" J '()+*4 /,.2()+" *:.where Q$R +/ *:.<F#%2+0+.3#9(19+2"#6(//#6 2.1*)(-+2" " dm (2007). HF#%2+0+.3#/,(-()#6(//#6 Hubble constant in units of 100 km Mpc 1 s 1. Requiring IF#J(*+"#"0#K L#K >.>/#*(2! <F#%2+0+.3#9(19+2"#6(//#6<GH HF#%2+0+.3#/,(-()#6(//#6= IF#J(*+"#"0#K<L#KH >.>/#*(2! M N +-+ MF#N)+-+2.()#,"1'-+29#O -+ O= PF#K+99/#6(//#*.)6#/92?µ@ <GH !"#$%&'()*#"+,$" /012'3&,45,678'9:;01; = : [3] M. Kaplinghat and M N +-+ MF#N)+-+2.()#,"1'-+29#O -+ O PF#K+99/#6(//#*.)6#/92?µ@ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(2006). 2 ΩTP h (13) 7 e G [4]*:.R.Q$RH. Cyburt, J. R. E x TRE2#J#'()+*4#,"2/.)>(*+"2#/,.2()+"L#*:.#Q$R#+/#*:.#2.1*)(-+2"##"!'()+*410 GeV E2 J,"2/.)>(*+"2 /,.2()+"Murayama, +/ *:.Yamguchi, 2.1*)(-+2" 93] " see also [Moroi, V.Rychkov, C. Spanos, JCAP [Cerdeno et al., 06, Stumia, 07] Frankthe D. Steffen (Max-Planck-Institute of Physics, Munich) Dark Matter in Cosmology and exat Colliders 44!"#$%&'()*#"+,$" and using derived lower bound (11) allows us to -.-/012'3&,45,678'9:;01;9001 [FDS 06] [5] K. Hamaguchi, T. Ha [Pradler, FDS, 07] ΩDM constraint + BBN constraints BBN constraints tract the conservative upper limit: T. T. Yanagida, Phy alsobrandenburg, [Moroi, Murayama, Yamguchi, 93, 01] also [Borgani, Masiero, Yamguchi, 96, 7Figure [... ;see Borgani, Masiero, Yamaguchi, 96;bound...] on the reheating temperature [...; see Bolz, Buchm uller, 7: Upper for the Case 1 for gravitino DM x Asaka, Hamaguchi, Suzuki, 00, Roszkowski et al., 05, Asaka, Suzuki, 00, Ellis et al., 04, [6]constraint C. Bird, K. Koopma R; Hamaguchi, + Ω DM! "1/5 gravitino mass. [Pradler, FDS, 06] [... Covi, Kim, Roszkowski, 99;...] also [Moroi, Murayama, Yamguchi, 93, see also [Borgani, Masiero, Yamguchi, 96, [... ; Borgani, Masiero, Yamaguchi, 96;...] olz, Brandenburg, Buchm u ller, 01] m Cerdeno[Pradler, et al., 06, FDS 06, Rychkov, Feng, e 7 Su, Takayama, 04] G ph/ FDS, 07] Strumia, 07] TR " GeV. (14) also [Moroi, Murayama, Yamguchi, 9 [...; see Bolz, Brandenburg, Buchm uller for DM amaguchi, Suzuki, 00, Roszkowski et al., 05, Asaka, Hamaguchi, Suzuki, 00,neutralino Ellis et Kawasaki, al., 04, [7] M. K. 07 Koh GeV Frank D. Steffen (Max-Planck-Institute of Physics, Munich) Dark Matter in Cosmology and10 at Colliders 29 [Pradler, FDS, [Pradler, FDS, 06] [... ; Covi, Kim, Roszkowski,...] 05] et Asaka, Suzuki, 00, 99; Roszkowski 436 (2007). [Kohri, Moroi, Yotsuyanagi, o et al., 06, FDS 06, Rychkov, Strumia, 07] FDS, arxiv: ] Feng,Hamaguchi, Su, Takayama, 04] [Pradler, [Pradler, FDS, 06] Strum This constraint is a slowly varying function of al., m :are e 06, Cerdeno et FDS Rychkov, see alsoineffective. [Moroi, Murayama, [8] 06, T. Jittoh et Buchm al.yamgu (2007 photo- and hadro-dissociations Then, overproductio [...; Bolz, Brandenburg, G 1/5 p m neconversion becomes the most important. For 00, the observation (mge /10 GeV) = Dark for 1 GeV 1 TeV. [9] K. Jedamzik (2007), Asaka, Hamaguchi, Suzuki, Roszkow fen (Max-Planck-Institute of Physics, Munich) Matter Cosmology and at Colliders 29 G = in 4 [Pradler, FDS, 06] mass fraction of He, we consider three different observational results 9 [10] 06, J. FDS R. of Ellis, K. A. OlS Therefore, (14) poses a strong bound on TD.R Steffen for the natu- et al., Frank (Max-Planck-Institute Physics, Munic Cerdeno 06, Rychkov, (5.10). As one can see, the upper bound on T in this case is sensitive R Phys. Lett. B588, 7 ral gravitino LSP mass range inconstraint gravity-mediated superon the primordial abundance of 4 He; for the case of m3/2 = [11] D. G. Cerdeno,Physics K.-Y. Steffen (Max-Planck-Institute 7 symmetry breaking scenarios. TR is required to befrank lowerd.than 3 10 GeV if we use the of lowest val and R. Ruiz de Aust < 100 [Pradler, FDS, 07] = T! 10 GeV H 1000 [FDS 06] [Pradler, FDS, 07]! Talk by Josef Pradler Thermal Leptogenesis requires T >10 GeV (5.8) while,on with the highest given in Eq. Models (5.10), the upper32 bou Frank D. Steffen (Max-Planck-Institute Physics, Constraints onvalue Supersymmetric Noteforthat themunich) constraint (14)Cosmological relies thermal grav-