Making Dark Matter. Manuel Drees. Bonn University & Bethe Center for Theoretical Physics. Making Dark Matter p. 1/35

Transcription

1 Making Dark Matter Manuel Drees Bonn University & Bethe Center for Theoretical Physics Making Dark Matter p. 1/35

2 Contents 1 Introduction: The need for DM Making Dark Matter p. 2/35

3 Contents 1 Introduction: The need for DM 2 Particle Dark Matter candidates Making Dark Matter p. 2/35

4 Contents 1 Introduction: The need for DM 2 Particle Dark Matter candidates 3 Making particle DM Making Dark Matter p. 2/35

5 Contents 1 Introduction: The need for DM 2 Particle Dark Matter candidates 3 Making particle DM a) WIMPs at low T R Making Dark Matter p. 2/35

6 Contents 1 Introduction: The need for DM 2 Particle Dark Matter candidates 3 Making particle DM a) WIMPs at low T R b) Thermal WIMPs (freeze out) Making Dark Matter p. 2/35

7 Contents 1 Introduction: The need for DM 2 Particle Dark Matter candidates 3 Making particle DM a) WIMPs at low T R b) Thermal WIMPs (freeze out) c) FIMPs (freeze in) Making Dark Matter p. 2/35

8 Contents 1 Introduction: The need for DM 2 Particle Dark Matter candidates 3 Making particle DM a) WIMPs at low T R b) Thermal WIMPs (freeze out) c) FIMPs (freeze in) d) Thermal gravitino production Making Dark Matter p. 2/35

9 Contents 1 Introduction: The need for DM 2 Particle Dark Matter candidates 3 Making particle DM a) WIMPs at low T R b) Thermal WIMPs (freeze out) c) FIMPs (freeze in) d) Thermal gravitino production e) Production in inflaton decay Making Dark Matter p. 2/35

10 Contents 1 Introduction: The need for DM 2 Particle Dark Matter candidates 3 Making particle DM a) WIMPs at low T R b) Thermal WIMPs (freeze out) c) FIMPs (freeze in) d) Thermal gravitino production e) Production in inflaton decay 4 Summary Making Dark Matter p. 2/35

11 Introduction: the need for Dark Matter Several observations indicate existence of non-luminous Dark Matter (DM) (more exactly: missing force) Making Dark Matter p. 3/35

12 Introduction: the need for Dark Matter Several observations indicate existence of non-luminous Dark Matter (DM) (more exactly: missing force) Galactic rotation curves imply Ω DM h Ω: Mass density in units of critical density; Ω = 1 means flat Universe. h: Scaled Hubble constant. Observation: h = 0.72 ± 0.07 Making Dark Matter p. 3/35

13 Introduction: the need for Dark Matter Several observations indicate existence of non-luminous Dark Matter (DM) (more exactly: missing force) Galactic rotation curves imply Ω DM h Ω: Mass density in units of critical density; Ω = 1 means flat Universe. h: Scaled Hubble constant. Observation: h = 0.72 ± 0.07 Models of structure formation, X ray temperature of clusters of galaxies,... Making Dark Matter p. 3/35

14 Introduction: the need for Dark Matter Several observations indicate existence of non-luminous Dark Matter (DM) (more exactly: missing force) Galactic rotation curves imply Ω DM h Ω: Mass density in units of critical density; Ω = 1 means flat Universe. h: Scaled Hubble constant. Observation: h = 0.72 ± 0.07 Models of structure formation, X ray temperature of clusters of galaxies,... Cosmic Microwave Background anisotropies (WMAP etc.) imply Ω DM h 2 = ± PDG, 2012 edition Making Dark Matter p. 3/35

15 Need for non baryonic DM Total baryon density is determined by: Big Bang Nucleosynthesis Making Dark Matter p. 4/35

16 Need for non baryonic DM Total baryon density is determined by: Big Bang Nucleosynthesis Analyses of CMB data Making Dark Matter p. 4/35

17 Need for non baryonic DM Total baryon density is determined by: Big Bang Nucleosynthesis Analyses of CMB data Consistent result: Ω bar h Making Dark Matter p. 4/35

18 Need for non baryonic DM Total baryon density is determined by: Big Bang Nucleosynthesis Analyses of CMB data Consistent result: Ω bar h = Need non baryonic DM! Making Dark Matter p. 4/35

19 Need for exotic particles Only possible non baryonic particle DM in SM: Neutrinos! Making Dark Matter p. 5/35

20 Need for exotic particles Only possible non baryonic particle DM in SM: Neutrinos! Make hot DM: do not describe structure formation correctly = Ω ν h Making Dark Matter p. 5/35

21 Need for exotic particles Only possible non baryonic particle DM in SM: Neutrinos! Make hot DM: do not describe structure formation correctly = Ω ν h = Need exotic particles as DM! Making Dark Matter p. 5/35

22 Need for exotic particles Only possible non baryonic particle DM in SM: Neutrinos! Make hot DM: do not describe structure formation correctly = Ω ν h = Need exotic particles as DM! Possible loophole: primordial black holes; not easy to make in sufficient quantity sufficiently early. Making Dark Matter p. 5/35

23 What we need Since h 2 0.5: Need 20% of critical density in Matter (with negligible pressure, w 0) Making Dark Matter p. 6/35

24 What we need Since h 2 0.5: Need 20% of critical density in Matter (with negligible pressure, w 0) which still survives today (lifetime τ yrs) Making Dark Matter p. 6/35

25 What we need Since h 2 0.5: Need 20% of critical density in Matter (with negligible pressure, w 0) which still survives today (lifetime τ yrs) and does not couple to elm radiation Making Dark Matter p. 6/35

26 Remarks Precise WMAP determination of DM density hinges on assumption of standard cosmology, including assumption of nearly scale invariant primordial spectrum of density perturbations: almost assumes inflation! Making Dark Matter p. 7/35

27 Remarks Precise WMAP determination of DM density hinges on assumption of standard cosmology, including assumption of nearly scale invariant primordial spectrum of density perturbations: almost assumes inflation! Evidence for Ω DM > 0.2 much more robust than that! (Does, however, assume standard law of gravitation.) Making Dark Matter p. 7/35

28 Particle DM: Possibilities Theorist s tasks: Introduce right kind of particle (stable, neutral, non relativistic) Making Dark Matter p. 8/35

29 Particle DM: Possibilities Theorist s tasks: Introduce right kind of particle (stable, neutral, non relativistic) Make enough (but not too much) of it in early universe Making Dark Matter p. 8/35

30 Particle DM: Possibilities Theorist s tasks: Introduce right kind of particle (stable, neutral, non relativistic) Make enough (but not too much) of it in early universe There are many possible ways to solve these tasks! Making Dark Matter p. 8/35

31 Particle DM: Possibilities Theorist s tasks: Introduce right kind of particle (stable, neutral, non relativistic) Make enough (but not too much) of it in early universe There are many possible ways to solve these tasks! = Use theoretical prejudice as guideline: Only consider candidates that solve (at least) one additional problem! Making Dark Matter p. 8/35

32 Particle Candidates 1 Axion a: Pseudoscalar pseudo-goldstone boson Making Dark Matter p. 9/35

33 Particle Candidates 1 Axion a: Pseudoscalar pseudo-goldstone boson Introduced to solve strong CP problem Making Dark Matter p. 9/35

34 Particle Candidates 1 Axion a: Pseudoscalar pseudo-goldstone boson Introduced to solve strong CP problem Mass m a < 10 3 ev Making Dark Matter p. 9/35

35 Particle Candidates 1 Axion a: Pseudoscalar pseudo-goldstone boson Introduced to solve strong CP problem Mass m a < 10 3 ev Direct detection difficult, but possible Making Dark Matter p. 9/35

36 Particle Candidates 1 Axion a: Pseudoscalar pseudo-goldstone boson Introduced to solve strong CP problem Mass m a < 10 3 ev Direct detection difficult, but possible Neutralino χ : Majorana spin 1/2 fermion Making Dark Matter p. 9/35

37 Particle Candidates 1 Axion a: Pseudoscalar pseudo-goldstone boson Introduced to solve strong CP problem Mass m a < 10 3 ev Direct detection difficult, but possible Neutralino χ : Majorana spin 1/2 fermion Required in supersymmetrized SM Making Dark Matter p. 9/35

38 Particle Candidates 1 Axion a: Pseudoscalar pseudo-goldstone boson Introduced to solve strong CP problem Mass m a < 10 3 ev Direct detection difficult, but possible Neutralino χ : Majorana spin 1/2 fermion Required in supersymmetrized SM 50 GeV < m χ < 1 TeV Making Dark Matter p. 9/35

39 Particle Candidates 1 Axion a: Pseudoscalar pseudo-goldstone boson Introduced to solve strong CP problem Mass m a < 10 3 ev Direct detection difficult, but possible Neutralino χ : Majorana spin 1/2 fermion Required in supersymmetrized SM 50 GeV < m χ < 1 TeV Direct detection probably difficult, but possible Making Dark Matter p. 9/35

40 Particle Candidates 2 Gravitino G: Majorana spin 3/2 fermion Making Dark Matter p. 10/35

41 Particle Candidates 2 Gravitino G: Majorana spin 3/2 fermion Required in supersymmetrized theory of gravity Making Dark Matter p. 10/35

42 Particle Candidates 2 Gravitino G: Majorana spin 3/2 fermion Required in supersymmetrized theory of gravity 100 ev < m G < 1 TeV Making Dark Matter p. 10/35

43 Particle Candidates 2 Gravitino G: Majorana spin 3/2 fermion Required in supersymmetrized theory of gravity 100 ev < m G < 1 TeV Direct detection is virtually impossible Making Dark Matter p. 10/35

44 Particle Candidates 2 Gravitino G: Majorana spin 3/2 fermion Required in supersymmetrized theory of gravity 100 ev < m G < 1 TeV Direct detection is virtually impossible Here: focus on WIMP (e.g. Neutralino) and Gravitino. Making Dark Matter p. 10/35

45 Making DM Principal possibilities: DM was in thermal equilibrium: Making Dark Matter p. 11/35

46 Making DM Principal possibilities: DM was in thermal equilibrium: Implies lower bounds on temperature T R and χ production cross section Making Dark Matter p. 11/35

47 Making DM Principal possibilities: DM was in thermal equilibrium: Implies lower bounds on temperature T R and χ production cross section Ω depends on particle physics and expansion history [Hubble parameter H(T) ] Making Dark Matter p. 11/35

48 Making DM Principal possibilities: DM was in thermal equilibrium: Implies lower bounds on temperature T R and χ production cross section Ω depends on particle physics and expansion history [Hubble parameter H(T) ] Example: Neutralino χ Making Dark Matter p. 11/35

49 Making DM Principal possibilities: DM was in thermal equilibrium: Implies lower bounds on temperature T R and χ production cross section Ω depends on particle physics and expansion history [Hubble parameter H(T) ] Example: Neutralino χ DM production from thermal plasma: Making Dark Matter p. 11/35

50 Making DM Principal possibilities: DM was in thermal equilibrium: Implies lower bounds on temperature T R and χ production cross section Ω depends on particle physics and expansion history [Hubble parameter H(T) ] Example: Neutralino χ DM production from thermal plasma: Thermal equilibrium may never have been achieved (low T R and/or low interaction rate) Making Dark Matter p. 11/35

51 Making DM Principal possibilities: DM was in thermal equilibrium: Implies lower bounds on temperature T R and χ production cross section Ω depends on particle physics and expansion history [Hubble parameter H(T) ] Example: Neutralino χ DM production from thermal plasma: Thermal equilibrium may never have been achieved (low T R and/or low interaction rate) Ω depends on particle physics, T R and H(T) Making Dark Matter p. 11/35

52 Making DM Principal possibilities: DM was in thermal equilibrium: Implies lower bounds on temperature T R and χ production cross section Ω depends on particle physics and expansion history [Hubble parameter H(T) ] Example: Neutralino χ DM production from thermal plasma: Thermal equilibrium may never have been achieved (low T R and/or low interaction rate) Ω depends on particle physics, T R and H(T) Example: Gravitino G with m G > 0.1 kev Making Dark Matter p. 11/35

53 Making DM (cont. d) Non thermal production: Making Dark Matter p. 12/35

54 Making DM (cont. d) Non thermal production: From decay of heavier particle ( χ, G) Making Dark Matter p. 12/35

55 Making DM (cont. d) Non thermal production: From decay of heavier particle ( χ, G) During phase transition (axion a) Making Dark Matter p. 12/35

56 Making DM (cont. d) Non thermal production: From decay of heavier particle ( χ, G) During phase transition (axion a) During (p)reheating at end of inflation ( G, χ) Making Dark Matter p. 12/35

57 Making DM (cont. d) Non thermal production: From decay of heavier particle ( χ, G) During phase transition (axion a) During (p)reheating at end of inflation ( G, χ) Depends strongly on details of particle physics and cosmology Making Dark Matter p. 12/35

58 Making DM (cont. d) Non thermal production: From decay of heavier particle ( χ, G) During phase transition (axion a) During (p)reheating at end of inflation ( G, χ) Depends strongly on details of particle physics and cosmology Via particle antiparticle asymmetry: Making Dark Matter p. 12/35

59 Making DM (cont. d) Non thermal production: From decay of heavier particle ( χ, G) During phase transition (axion a) During (p)reheating at end of inflation ( G, χ) Depends strongly on details of particle physics and cosmology Via particle antiparticle asymmetry: Assume symmetric contribution annihilates away: only particles left (see: baryons) Making Dark Matter p. 12/35

60 Making DM (cont. d) Non thermal production: From decay of heavier particle ( χ, G) During phase transition (axion a) During (p)reheating at end of inflation ( G, χ) Depends strongly on details of particle physics and cosmology Via particle antiparticle asymmetry: Assume symmetric contribution annihilates away: only particles left (see: baryons) If same mechanism generates baryon asymmetry: Naturally explains Ω DM 5Ω baryon, if m χ 5m p Making Dark Matter p. 12/35

61 Making DM (cont. d) Non thermal production: From decay of heavier particle ( χ, G) During phase transition (axion a) During (p)reheating at end of inflation ( G, χ) Depends strongly on details of particle physics and cosmology Via particle antiparticle asymmetry: Assume symmetric contribution annihilates away: only particles left (see: baryons) If same mechanism generates baryon asymmetry: Naturally explains Ω DM 5Ω baryon, if m χ 5m p For WIMPs: Order of magnitude of Ω DM is understood; Ω baryon isn t Making Dark Matter p. 12/35

62 Thermal history of the Universe Currently: Universe dominated by dark energy ( 75%) and non relativistic matter ( 25%); Ω rad (Radiation relativistic particles.) Making Dark Matter p. 13/35

63 Thermal history of the Universe Currently: Universe dominated by dark energy ( 75%) and non relativistic matter ( 25%); Ω rad (Radiation relativistic particles.) Dependence on scale factor R: ρ m R 3, ρ rad R 4 ρ: energy density, units GeV 4 Making Dark Matter p. 13/35

64 Thermal history of the Universe Currently: Universe dominated by dark energy ( 75%) and non relativistic matter ( 25%); Ω rad (Radiation relativistic particles.) Dependence on scale factor R: ρ m R 3, ρ rad R 4 ρ: energy density, units GeV 4 Implies ρ rad > ρ m for R < R 0, i.e. T > 1 ev Making Dark Matter p. 13/35

65 Thermal history of the Universe Currently: Universe dominated by dark energy ( 75%) and non relativistic matter ( 25%); Ω rad (Radiation relativistic particles.) Dependence on scale factor R: ρ m R 3, ρ rad R 4 ρ: energy density, units GeV 4 Implies ρ rad > ρ m for R < R 0, i.e. T > 1 ev Early Universe was dominated by radiation! (Except in some extreme quintessence or brane cosmology models.) Making Dark Matter p. 13/35

66 Thermal DM production Let χ be a generic DM particle, n χ its number density (unit: GeV 3 ). Assume χ = χ, i.e. χχ SM particles is possible, but single production of χ is forbidden by some symmetry. Making Dark Matter p. 14/35

67 Thermal DM production Let χ be a generic DM particle, n χ its number density (unit: GeV 3 ). Assume χ = χ, i.e. χχ SM particles is possible, but single production of χ is forbidden by some symmetry. Evolution of n χ determined by Boltzmann equation: dn χ dt + 3Hn χ = σ ann v ( n 2 χ ) n2 χ, eq H = Ṙ/R : Hubble parameter... : Thermal averaging σ ann = σ(χχ SM particles) v : relative velocity between χ s in their cms n χ,eq : χ density in full equilibrium Making Dark Matter p. 14/35

68 dn ( χ + 3Hn dt χ = σ ann v n 2 n χ 2 ) χ, eq 2 nd lhs term: Describes χ dilution by expansion of Universe: = 3R 4 Ṙ = 3HR 3 dr 3 dt Making Dark Matter p. 15/35

69 dn ( χ + 3Hn dt χ = σ ann v n 2 n χ 2 ) χ, eq 2 nd lhs term: Describes χ dilution by expansion of Universe: = 3R 4 Ṙ = 3HR 3 dr 3 dt 1 st rhs term: describes χ pair annihilation; assumes shape of n χ same as that of n χ, eq : reactions χ + f χ + f are very fast (f : some SM particle). Making Dark Matter p. 15/35

70 dn ( χ + 3Hn dt χ = σ ann v n 2 n χ 2 ) χ, eq 2 nd lhs term: Describes χ dilution by expansion of Universe: = 3R 4 Ṙ = 3HR 3 dr 3 dt 1 st rhs term: describes χ pair annihilation; assumes shape of n χ same as that of n χ, eq : reactions χ + f χ + f are very fast (f : some SM particle). 2 nd rhs term: describes χ pair production; assumes CP conservation (= same matrix element). Making Dark Matter p. 15/35

71 dn ( χ + 3Hn dt χ = σ ann v n 2 n χ 2 ) χ, eq 2 nd lhs term: Describes χ dilution by expansion of Universe: = 3R 4 Ṙ = 3HR 3 dr 3 dt 1 st rhs term: describes χ pair annihilation; assumes shape of n χ same as that of n χ, eq : reactions χ + f χ + f are very fast (f : some SM particle). 2 nd rhs term: describes χ pair production; assumes CP conservation (= same matrix element). Check: creation and annihilation balance iff n χ = n χ, eq. Making Dark Matter p. 15/35

72 Rewriting the Boltzmann equation In order to get rid of the 3Hn χ term: introduce Y χ n χ s (s: entropy density) Making Dark Matter p. 16/35

73 Rewriting the Boltzmann equation In order to get rid of the 3Hn χ term: introduce Y χ n χ s (s: entropy density) For adiabatic expansion of the Universe: ds dt = 3Hs Making Dark Matter p. 16/35

74 Rewriting the Boltzmann equation In order to get rid of the 3Hn χ term: introduce Y χ n χ s (s: entropy density) For adiabatic expansion of the Universe: ds dt = 3Hs dy χ dt = 1 s dn χ dt n χ ds s 2 dt Making Dark Matter p. 16/35

75 Rewriting the Boltzmann equation In order to get rid of the 3Hn χ term: introduce Y χ n χ s (s: entropy density) For adiabatic expansion of the Universe: ds dt = 3Hs dy χ dt = 1 s = 1 s dn χ dt n χ ds s 2 dt [ 3Hnχ σ ann v ( n 2 χ n 2 χ, eq )] + n χ s 2 3Hs Making Dark Matter p. 16/35

76 Rewriting the Boltzmann equation In order to get rid of the 3Hn χ term: introduce Y χ n χ s (s: entropy density) For adiabatic expansion of the Universe: ds dt = 3Hs dy χ dt = 1 s dn χ dt n χ ds s 2 dt = 1 [ s 3Hnχ σ ann v ( n 2 χ n 2 χ, eq = s σ ann v ( Yχ 2 Yχ, 2 ) eq. s = 2π2 45 g T 3 (g : no. of relativistic d.o.f.) )] + n χ s 2 3Hs Making Dark Matter p. 16/35

77 Rewriting the Boltzmann equation In order to get rid of the 3Hn χ term: introduce Y χ n χ s (s: entropy density) For adiabatic expansion of the Universe: ds dt = 3Hs dy χ dt = 1 s dn χ dt n χ ds s 2 dt = 1 [ s 3Hnχ σ ann v ( n 2 χ n 2 χ, eq = s σ ann v ( Yχ 2 Yχ, 2 ) eq. s = 2π2 45 g T 3 (g : no. of relativistic d.o.f.) )] + n χ s 2 3Hs If interactions are negligible: Y χ const., i.e. χ density in co moving volume is unchanged Making Dark Matter p. 16/35

78 Rewriting the Boltzmann equation (cont d) Write lhs entirely in terms of dimensionless quantities: introduce x = m χ T. Making Dark Matter p. 17/35

79 Rewriting the Boltzmann equation (cont d) Write lhs entirely in terms of dimensionless quantities: introduce x = m χ T. Had: ṡ = 3Hs Making Dark Matter p. 17/35

80 Rewriting the Boltzmann equation (cont d) Write lhs entirely in terms of dimensionless quantities: introduce x = m χ T. Had: ṡ = 3Hs ( g T 3) = 3H ( g T 3) = d dt Making Dark Matter p. 17/35

81 Rewriting the Boltzmann equation (cont d) Write lhs entirely in terms of dimensionless quantities: introduce x = m χ T. Had: ṡ = 3Hs ( g T 3) = 3H ( g T 3) = d dt = ġ T 3 + 3g T 2 T = 3Hg T 3 Making Dark Matter p. 17/35

82 Rewriting the Boltzmann equation (cont d) Write lhs entirely in terms of dimensionless quantities: introduce x = m χ T. Had: ṡ = 3Hs ( g T 3) = 3H ( g T 3) = d dt = ġ T 3 + 3g T 2 T = 3Hg T 3 = T ( ) = H + ġ 3g T Making Dark Matter p. 17/35

83 Rewriting the Boltzmann equation (cont d) Write lhs entirely in terms of dimensionless quantities: introduce x = m χ T. Had: ṡ = 3Hs ( g T 3) = 3H ( g T 3) = d dt = ġ T 3 + 3g T 2 T = 3Hg T 3 = T ( ) = H + ġ 3g T From now on: set ġ = 0, since g changes only slowly with time. (Except during QCD phase transition.) Making Dark Matter p. 17/35

84 Rewriting the Boltzmann equation (cont d) Write lhs entirely in terms of dimensionless quantities: introduce x = m χ T. Had: ṡ = 3Hs ( g T 3) = 3H ( g T 3) = d dt = ġ T 3 + 3g T 2 T = 3Hg T 3 = T ( ) = H + ġ 3g T From now on: set ġ = 0, since g changes only slowly with time. (Except during QCD phase transition.) = ẋ = m χ T 2 T = x T T = xh Making Dark Matter p. 17/35

85 Boltzmann equation (cont d) dy χ dx = 1 ẋ dy χ dt Making Dark Matter p. 18/35

86 Boltzmann equation (cont d) dy χ dx = 1 ẋ dy χ dt = 1 Hx s σ annv ( Y 2 χ Y 2 χ, eq ) Making Dark Matter p. 18/35

87 Boltzmann equation (cont d) dy χ dx = 1 ẋ dy χ dt = 1 Hx s σ annv ( Y 2 χ Y 2 χ, eq ) Use s = 2π2 45 g T 3 H = ρ rad 3M 2 P = π 90 g M P T 2 for flat, rad. dom. Universe Making Dark Matter p. 18/35

88 Boltzmann equation (cont d) dy χ dx = 1 ẋ dy χ dt = 1 Hx s σ annv ( Y 2 χ Y 2 χ, eq Use s = 2π2 45 g T 3 H = ρ rad 3M 2 P = π 90 g M P T 2 = dy χ dx = 4π g m χ M P 90 x 2 ) for flat, rad. dom. Universe σ ann v ( Yχ 2 Yχ, 2 ) eq Making Dark Matter p. 18/35

89 Boltzmann equation (cont d) dy χ dx = 1 ẋ dy χ dt = 1 Hx s σ annv ( Y 2 χ Y 2 χ, eq Use s = 2π2 45 g T 3 H = ρ rad 3M 2 P = π 90 g M P T 2 = dy χ dx = 4π g m χ M P 90 x 2 ) for flat, rad. dom. Universe σ ann v ( Yχ 2 Yχ, 2 ) eq For T > 200 MeV: 10 < 4π g 90 < 20 (SM, MSSM) Making Dark Matter p. 18/35

90 Condition for thermal equilibrium n χ σ ann v > H for some T! Making Dark Matter p. 19/35

91 Condition for thermal equilibrium n χ σ ann v > H for some T! For renormalizable interactions: easiest to satisfy for T m χ = σ ann v (T m χ ) > 1 m χ M P (See: freeze in). Making Dark Matter p. 19/35

92 Condition for thermal equilibrium n χ σ ann v > H for some T! For renormalizable interactions: easiest to satisfy for T m χ = σ ann v (T m χ ) > 1 m χ M P (See: freeze in). For non renormalizable interactions: easiest to satisfy at maximal temperature, T T R. (See: G) Making Dark Matter p. 19/35

93 Condition for thermal equilibrium n χ σ ann v > H for some T! For renormalizable interactions: easiest to satisfy for T m χ = σ ann v (T m χ ) > 1 m χ M P (See: freeze in). For non renormalizable interactions: easiest to satisfy at maximal temperature, T T R. (See: G) For T R < m χ : Easiest to satisfy for T T R (see: WIMP at low T R ). Making Dark Matter p. 19/35

94 Example 1: WIMP Decouple (freeze out) at temperature T m χ (see below). (N.B. Means χ makes cold DM!) Making Dark Matter p. 20/35

95 Example 1: WIMP Decouple (freeze out) at temperature T m χ (see below). (N.B. Means χ makes cold DM!) χ s are non relativistic: 2 consequences Making Dark Matter p. 20/35

96 Example 1: WIMP Decouple (freeze out) at temperature T m χ (see below). (N.B. Means χ makes cold DM!) χ s are non relativistic: 2 consequences 1) n χ g χ ( mχ T 2π ) 3/2 e x σ ann v x3/2 2 π 0 dv v 2 (σ ann v)e xv2 /4 Making Dark Matter p. 20/35

97 Example 1: WIMP Decouple (freeze out) at temperature T m χ (see below). (N.B. Means χ makes cold DM!) χ s are non relativistic: 2 consequences 1) n χ g χ ( mχ T 2π ) 3/2 e x σ ann v x3/2 2 π 0 dv v 2 (σ ann v)e xv2 /4 2) Most of the time: can expand cross section in χ velocity: σ ann v = a + bv = σ ann v = a + 6 b x +... Making Dark Matter p. 20/35

98 Example 1: WIMP Decouple (freeze out) at temperature T m χ (see below). (N.B. Means χ makes cold DM!) χ s are non relativistic: 2 consequences 1) n χ g χ ( mχ T 2π ) 3/2 e x σ ann v x3/2 2 π 0 dv v 2 (σ ann v)e xv2 /4 2) Most of the time: can expand cross section in χ velocity: σ ann v = a + bv = σ ann v = a + 6 b x +... Typically, a,b < α 2 m 2 χ, α2 10 3, unless a is suppressed by some symmetry; e.g. for χ χ f f : a m 2 f. Making Dark Matter p. 20/35

99 Case 1: Low reheat temperature Let T R be the highest temperature of the radiation dominated universe (after inflation). Making Dark Matter p. 21/35

100 Case 1: Low reheat temperature Let T R be the highest temperature of the radiation dominated universe (after inflation). Boundary condition: n χ (T R ) = 0 (??) Making Dark Matter p. 21/35

101 Case 1: Low reheat temperature Let T R be the highest temperature of the radiation dominated universe (after inflation). Boundary condition: n χ (T R ) = 0 (??) Assume T R < m χ /20 = χ annihilation is negligible (see below): ignore 1 st rhs term in Boltzmann equation! Making Dark Matter p. 21/35

102 Case 1: Low reheat temperature Let T R be the highest temperature of the radiation dominated universe (after inflation). Boundary condition: n χ (T R ) = 0 (??) Assume T R < m χ /20 = χ annihilation is negligible (see below): ignore 1 st rhs term in Boltzmann equation! = dy χ dx = 4π g m χ M P 90 x 2 ( a + 6b x ) Y 2 χ, eq. Making Dark Matter p. 21/35

103 Case 1: Low reheat temperature Let T R be the highest temperature of the radiation dominated universe (after inflation). Boundary condition: n χ (T R ) = 0 (??) Assume T R < m χ /20 = χ annihilation is negligible (see below): ignore 1 st rhs term in Boltzmann equation! = dy χ dx = 4π g m χ M P 90 x 2 = 4π g 90 m χ M P x 2 ( a + 6b x ) Y 2 χ, eq. ( a + 6b x ) m 6 χ (2π) 3 x 3 e 2x 452 x 6 (2π 2 ) 2 g 2 m 6 χ Making Dark Matter p. 21/35

104 Case 1: Low reheat temperature Let T R be the highest temperature of the radiation dominated universe (after inflation). Boundary condition: n χ (T R ) = 0 (??) Assume T R < m χ /20 = χ annihilation is negligible (see below): ignore 1 st rhs term in Boltzmann equation! = dy χ dx = 4π g m χ M P 90 x 2 = 4π g 90 m χ M P x 2 ( a + 6b x ) Y 2 χ, eq. ( a + 6b x ) m 6 χ (2π) 3 x 3 e 2x 452 x 6 (2π 2 ) 2 g 2 m 6 χ = g 3/2 π 6g2 χm χ M P (ax + 6b)e 2x. Making Dark Matter p. 21/35

105 Case 1: Low reheat temperature Let T R be the highest temperature of the radiation dominated universe (after inflation). Boundary condition: n χ (T R ) = 0 (??) Assume T R < m χ /20 = χ annihilation is negligible (see below): ignore 1 st rhs term in Boltzmann equation! = dy χ dx = 4π g m χ M P 90 x 2 = 4π g 90 m χ M P x 2 ( a + 6b x ) Y 2 χ, eq. ( a + 6b x ) m 6 χ (2π) 3 x 3 e 2x 452 x 6 (2π 2 ) 2 g 2 m 6 χ = g 3/2 π 6g2 χm χ M P (ax + 6b)e 2x. = Y χ (x x R ) = 452 g 2 χ 8 90g 3/2 π 6m χm P e 2x R [ a2 ( xr 1 2 ) + 3b ]. Making Dark Matter p. 21/35

106 To get current Ω χ h 2 Saw: Y χ Y χ,0 = const. for x x R. Making Dark Matter p. 22/35

107 To get current Ω χ h 2 Saw: Y χ Y χ,0 = const. for x x R. = Ω χ h 2 = ρ χ ρ crit. h 2 = n χm χ 3H 2 0 M2 P H 2 0 (100kmMpc 1 sec 1 ) 2 Making Dark Matter p. 22/35

108 To get current Ω χ h 2 Saw: Y χ Y χ,0 = const. for x x R. = Ω χ h 2 = ρ χ ρ crit. h 2 = n χm χ 3H 2 0 M2 P H 2 0 (100kmMpc 1 sec 1 ) 2 = Y χ,0 s 0 m χ 3M 2 P (100kmMpc 1 sec 1 ) 2 Making Dark Matter p. 22/35

109 To get current Ω χ h 2 Saw: Y χ Y χ,0 = const. for x x R. = Ω χ h 2 = ρ χ ρ crit. h 2 = n χm χ 3H 2 0 M2 P H 2 0 (100kmMpc 1 sec 1 ) 2 = Y χ,0 s 0 m χ 3M 2 P (100kmMpc 1 sec 1 ) 2 Use 1 Mpc = km, 1 sec 1 = GeV, s 0 = cm 3 = GeV 3, and introduce dimensionless quantities â = am 2 χ, ˆb = bm 2 χ Making Dark Matter p. 22/35

110 To get current Ω χ h 2 Saw: Y χ Y χ,0 = const. for x x R. = Ω χ h 2 = ρ χ ρ crit. h 2 = n χm χ 3H 2 0 M2 P H 2 0 (100kmMpc 1 sec 1 ) 2 = Y χ,0 s 0 m χ 3M 2 P (100kmMpc 1 sec 1 ) 2 Use 1 Mpc = km, 1 sec 1 = GeV, s 0 = cm 3 = GeV 3, and introduce dimensionless quantities â = am 2 χ, ˆb = bm 2 χ = Ω χ h 2 = m χ Y χ, GeV 1 Making Dark Matter p. 22/35

111 To get current Ω χ h 2 Saw: Y χ Y χ,0 = const. for x x R. = Ω χ h 2 = ρ χ ρ crit. h 2 = n χm χ 3H 2 0 M2 P H 2 0 (100kmMpc 1 sec 1 ) 2 = Y χ,0 s 0 m χ 3M 2 P (100kmMpc 1 sec 1 ) 2 Use 1 Mpc = km, 1 sec 1 = GeV, s 0 = cm 3 = GeV 3, and introduce dimensionless quantities â = am 2 χ, ˆb = bm 2 χ = Ω χ h 2 = m χ Y χ, GeV 1 = Ω χ h 2 = e 2m χ/t R [â 2 ( ) mχ T R 1 2 ] + 3ˆb Making Dark Matter p. 22/35

112 To get current Ω χ h 2 Saw: Y χ Y χ,0 = const. for x x R. = Ω χ h 2 = ρ χ ρ crit. h 2 = n χm χ 3H 2 0 M2 P H 2 0 (100kmMpc 1 sec 1 ) 2 = Y χ,0 s 0 m χ 3M 2 P (100kmMpc 1 sec 1 ) 2 Use 1 Mpc = km, 1 sec 1 = GeV, s 0 = cm 3 = GeV 3, and introduce dimensionless quantities â = am 2 χ, ˆb = bm 2 χ = Ω χ h 2 = m χ Y χ, GeV 1 = Ω χ h 2 = e 2m χ/t R [â 2 ( ) mχ T R 1 2 ] + 3ˆb Example: â = 0, ˆb = 10 4 = need T R 0.04m χ Making Dark Matter p. 22/35

113 Case 2: Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Making Dark Matter p. 23/35

114 Case 2: Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Requires n χ σ ann v > H Making Dark Matter p. 23/35

115 Case 2: Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Requires n χ σ ann v > H For T < m χ : n χ n χ, eq T 3/2 e m χ/t, H T 2 Making Dark Matter p. 23/35

116 Case 2: Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Requires n χ σ ann v > H For T < m χ : n χ n χ, eq T 3/2 e m χ/t, H T 2 Inequality cannot be true for arbitrarily small T ; point where inequality becomes (approximate) equality defines decoupling (freeze out) temperature T F. Making Dark Matter p. 23/35

117 Case 2: Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Requires n χ σ ann v > H For T < m χ : n χ n χ, eq T 3/2 e m χ/t, H T 2 Inequality cannot be true for arbitrarily small T ; point where inequality becomes (approximate) equality defines decoupling (freeze out) temperature T F. For T < T F : WIMP production negligible, only annihilation relevant in Boltzmann equation. Making Dark Matter p. 23/35

118 Thermal WIMP: solution of Boltzmann eq. Had dy χ dx = 4π g 90 m χ M P x 2 σ ann v ( Yχ 2 Yχ, 2 ) eq Making Dark Matter p. 24/35

119 Thermal WIMP: solution of Boltzmann eq. Had dy χ dx = 4π g 90 m χ M P x 2 σ ann v ( Yχ 2 Yχ, 2 ) eq High temperature, T > T F : write Y χ = Y χ, eq. +, ignore 2 term Making Dark Matter p. 24/35

120 Thermal WIMP: solution of Boltzmann eq. σ ann v ( Yχ 2 Yχ, 2 ) eq Had dy χ dx = 4π g m χ M P 90 x 2 High temperature, T > T F : write Y χ = Y χ, eq. +, ignore 2 term = d dx = dy χ, eq dx + dy χ dx dy χ,eq dx 4π g 90 m χ M P x 2 σ ann v (2Y χ, eq ) Making Dark Matter p. 24/35

121 Thermal WIMP: solution of Boltzmann eq. σ ann v ( Yχ 2 Yχ, 2 ) eq Had dy χ dx = 4π g m χ M P 90 x 2 High temperature, T > T F : write Y χ = Y χ, eq. +, ignore 2 term = d dx = dy χ, eq dx + dy χ dx dy χ,eq dx 4π g 90 m χ M P x 2 σ ann v (2Y χ, eq ) Use dy χ, eq dx = 3 2 Y χ, eq x Y χ, eq Y χ, eq (x 1): Making Dark Matter p. 24/35

122 Thermal WIMP: solution of Boltzmann eq. σ ann v ( Yχ 2 Yχ, 2 ) eq Had dy χ dx = 4π g m χ M P 90 x 2 High temperature, T > T F : write Y χ = Y χ, eq. +, ignore 2 term = d dx = dy χ, eq dx + dy χ dx dy χ,eq dx 4π g 90 m χ M P x 2 σ ann v (2Y χ, eq ) Use dy χ, eq dx = 3 2 To keep d dx = 0 : need Y χ, eq x Y χ, eq Y χ, eq (x 1): x m χ M P g σ ann v Making Dark Matter p. 24/35

123 Low T solution Y χ, eq 0 = can ignore production term in Boltzmann eq. Making Dark Matter p. 25/35

124 Low T solution Y χ, eq 0 = can ignore production term in Boltzmann eq. d dx 1.32m χ M P g x 2 σ ann v 2 Making Dark Matter p. 25/35

125 Low T solution Y χ, eq 0 = can ignore production term in Boltzmann eq. d dx 1.32m χ M P g x 2 σ ann v 2 = 1 (x F ) 1 ( ) = 1.32m χm P g x F dxx 2 σ ann v 1.32m χ M P g J(x F ) Making Dark Matter p. 25/35

126 Low T solution Y χ, eq 0 = can ignore production term in Boltzmann eq. d dx 1.32m χ M P g x 2 σ ann v 2 = 1 (x F ) 1 ( ) = 1.32m χm P g x F dxx 2 σ ann v Assume ( ) (x F ) = Y χ,0 = g m χ M P J(x F ) 1.32m χ M P g J(x F ) Making Dark Matter p. 25/35

127 Low T solution Y χ, eq 0 = can ignore production term in Boltzmann eq. d dx 1.32m χ M P g x 2 σ ann v 2 = 1 (x F ) 1 ( ) = 1.32m χm P g x F dxx 2 σ ann v Assume ( ) (x F ) = Y χ,0 = g m χ M P J(x F ) 1.32m χ M P g J(x F ) = Ω χ h GeV 2 g J(x F ) Making Dark Matter p. 25/35

128 Low T solution Y χ, eq 0 = can ignore production term in Boltzmann eq. d dx 1.32m χ M P g x 2 σ ann v 2 = 1 (x F ) 1 ( ) = 1.32m χm P g x F dxx 2 σ ann v Assume ( ) (x F ) = Y χ,0 = g m χ M P J(x F ) 1.32m χ M P g J(x F ) = Ω χ h GeV 2 g J(x F ) Typically, x F 22; depends only logarithmically on σ ann. Making Dark Matter p. 25/35

129 Low T solution Y χ, eq 0 = can ignore production term in Boltzmann eq. d dx 1.32m χ M P g x 2 σ ann v 2 = 1 (x F ) 1 ( ) = 1.32m χm P g x F dxx 2 σ ann v Assume ( ) (x F ) = Y χ,0 = g m χ M P J(x F ) 1.32m χ M P g J(x F ) = Ω χ h GeV 2 g J(x F ) Typically, x F 22; depends only logarithmically on σ ann. Non-relativistic expansion: J(x F ) = a x F + 3b x 2 F... Making Dark Matter p. 25/35

130 Ω χ h GeV 2 g J(x F ) Solution validated numerically. Making Dark Matter p. 26/35

131 Ω χ h GeV 2 g J(x F ) Solution validated numerically. Density has no explicit dependence on m χ. Making Dark Matter p. 26/35

132 Ω χ h GeV 2 g J(x F ) Solution validated numerically. Density has no explicit dependence on m χ. Density has no dependence on reheat temperature T R, if T R > T F. Making Dark Matter p. 26/35

133 Ω χ h GeV 2 g J(x F ) Solution validated numerically. Density has no explicit dependence on m χ. Density has no dependence on reheat temperature T R, if T R > T F. Density scales like inverse of annihilation cross section: The stronger the WIMPs annihilate, the fewer are left. Making Dark Matter p. 26/35

134 Ω χ h GeV 2 g J(x F ) Solution validated numerically. Density has no explicit dependence on m χ. Density has no dependence on reheat temperature T R, if T R > T F. Density scales like inverse of annihilation cross section: The stronger the WIMPs annihilate, the fewer are left. Smooth transition to previous case (T R < T F ): MD, Iminniyaz, Kakizaki, hep-ph/ Making Dark Matter p. 26/35

135 Co annihilation Is important for SUSY scenarios with small mass splitting between LSP and NLSP: δm m χ m χ m χ Making Dark Matter p. 27/35

136 Co annihilation Is important for SUSY scenarios with small mass splitting between LSP and NLSP: δm m χ m χ m χ Rate ( χ + f χ + f ) Rate( χ χ ff), by factor e (2m χ m χ )/T (f, f : SM particles) Making Dark Matter p. 27/35

137 Co annihilation Is important for SUSY scenarios with small mass splitting between LSP and NLSP: δm m χ m χ m χ Rate ( χ + f χ + f ) Rate( χ χ ff), by factor e (2m χ m χ )/T (f, f : SM particles) χ, χ retain relative equilibrium well after sparticles decouple from SM particles: n χ = n χ e δm/t Making Dark Matter p. 27/35

138 Co annihilation Is important for SUSY scenarios with small mass splitting between LSP and NLSP: δm m χ m χ m χ Rate ( χ + f χ + f ) Rate( χ χ ff), by factor e (2m χ m χ )/T (f, f : SM particles) χ, χ retain relative equilibrium well after sparticles decouple from SM particles: n χ = n χ e δm/t Previous treatment still applies, with replacement: σ ann σ eff σ ann + f B σ( χ χ SM) + fb 2 σ( χ χ SM) ( ) 3/2 f B : relative Boltzmann factor = 1 + δm m χ e δm/t Making Dark Matter p. 27/35

139 Co annihilation Is important for SUSY scenarios with small mass splitting between LSP and NLSP: δm m χ m χ m χ Rate ( χ + f χ + f ) Rate( χ χ ff), by factor e (2m χ m χ )/T (f, f : SM particles) χ, χ retain relative equilibrium well after sparticles decouple from SM particles: n χ = n χ e δm/t Previous treatment still applies, with replacement: σ ann σ eff σ ann + f B σ( χ χ SM) + fb 2 σ( χ χ SM) ( ) 3/2 f B : relative Boltzmann factor = 1 + δm m χ e δm/t σ( χ χ ), σ( χ χ ) σ( χ χ) possible! Making Dark Matter p. 27/35

140 Case 3: Freeze in Hall et al., arxiv: Assume very weak, renormalizable interaction (Feebly Interacting Massive Particle, FIMP): never achieved thermal equilibrium Making Dark Matter p. 28/35

141 Case 3: Freeze in Hall et al., arxiv: Assume very weak, renormalizable interaction (Feebly Interacting Massive Particle, FIMP): never achieved thermal equilibrium χ pair production dominated by reactions at T m χ : independent of T R as long as T R m χ Making Dark Matter p. 28/35

142 Case 3: Freeze in Hall et al., arxiv: Assume very weak, renormalizable interaction (Feebly Interacting Massive Particle, FIMP): never achieved thermal equilibrium χ pair production dominated by reactions at T m χ : independent of T R as long as T R m χ Final relic density proportional to cross section, independent of FIMP mass Making Dark Matter p. 28/35

143 Thermal WIMPs, FIMPs: Assumptions χ is effectively stable, τ χ τ U : partly testable at colliders Making Dark Matter p. 29/35

144 Thermal WIMPs, FIMPs: Assumptions χ is effectively stable, τ χ τ U : partly testable at colliders No entropy production after χ decoupled: Not testable at colliders Making Dark Matter p. 29/35

145 Thermal WIMPs, FIMPs: Assumptions χ is effectively stable, τ χ τ U : partly testable at colliders No entropy production after χ decoupled: Not testable at colliders H at time of χ decoupling is known: partly testable at colliders Making Dark Matter p. 29/35

146 Thermal Gravitino Dark Matter Each gravitino coupling gives factor m sparticles m GM P section, if m G s, m sparticle in cross Making Dark Matter p. 30/35

147 Thermal Gravitino Dark Matter Each gravitino coupling gives factor m sparticles m GM P section, if m G s, m sparticle in cross = Most important G production mechanism for m > G MeV: associated ( production with ) other sparticle! 1 σ G 26g 2 24π(m GM P ) sm 2 g Making Dark Matter p. 30/35

148 Thermal Gravitino Dark Matter Each gravitino coupling gives factor m sparticles m GM P section, if m G s, m sparticle in cross = Most important G production mechanism for m > G MeV: associated ( production with ) other sparticle! 1 σ G 26g 2 24π(m GM P ) sm 2 g G annihilation can be ignored; write Boltzmann eq. for Ỹ G n G/n γ : dỹ G dt = n γσ G 4TH(T) Making Dark Matter p. 30/35

149 Gravitino DM (cont. d) Solution of Boltzmann eq.: Ỹ G,0 = 4n γ(t R )σ G 4H(T R ) T R (assuming Ỹ G(T R ) = 0) Making Dark Matter p. 31/35

150 Gravitino DM (cont. d) Solution of Boltzmann eq.: Ỹ G,0 = 4n γ(t R )σ G 4H(T R ) T R (assuming Ỹ G(T R ) = 0) = Ω Gh ( M g ) 2 1 GeV 1 TeV m G T R GeV Making Dark Matter p. 31/35

151 Gravitino DM (cont. d) Solution of Boltzmann eq.: Ỹ G,0 = 4n γ(t R )σ G 4H(T R ) T R (assuming Ỹ G(T R ) = 0) = Ω Gh ( M g ) 2 1 GeV 1 TeV m G T R GeV Inclusion of thermal corrections: e.g. Pradler & Steffen, hep-ph/ Making Dark Matter p. 31/35

152 Gravitino DM (cont. d) Solution of Boltzmann eq.: Ỹ G,0 = 4n γ(t R )σ G 4H(T R ) T R (assuming Ỹ G(T R ) = 0) = Ω Gh ( M g ) 2 1 GeV 1 TeV m G T R GeV Inclusion of thermal corrections: e.g. Pradler & Steffen, hep-ph/ m In general, have to add Ω G NLSP m NLSP from (late) decays of NLSPs. (BBN!) Making Dark Matter p. 31/35

153 DM Production from Inflaton Decay Only consider perturbative decays here. Making Dark Matter p. 32/35

154 DM Production from Inflaton Decay Only consider perturbative decays here. χ : DM particle; φ : inflaton Making Dark Matter p. 32/35

155 DM Production from Inflaton Decay Only consider perturbative decays here. χ : DM particle; φ : inflaton B(φ χ) : Average number of χ particles produced per φ decay Making Dark Matter p. 32/35

156 DM Production from Inflaton Decay Only consider perturbative decays here. χ : DM particle; φ : inflaton B(φ χ) : Average number of χ particles produced per φ decay Instantaneous φ decay approximation: all inflatons decay at T = T R. Making Dark Matter p. 32/35

157 DM Production from Inflaton Decay Only consider perturbative decays here. χ : DM particle; φ : inflaton B(φ χ) : Average number of χ particles produced per φ decay Instantaneous φ decay approximation: all inflatons decay at T = T R. Inflatons are non relativistic when they decay. Making Dark Matter p. 32/35

158 DM Production from Inflaton Decay (cont. d) Energy conserved during φ decay = n φ m φ = ρ rad (T R ) = π2 30 g T 4 R Making Dark Matter p. 33/35

159 DM Production from Inflaton Decay (cont. d) Energy conserved during φ decay = n φ m φ = ρ rad (T R ) = π2 30 g T 4 R = Y χ (T R ) = n χ(t R ) s(t R ) = B(φ χ)n φ(t R ) s(t R ) Making Dark Matter p. 33/35

160 DM Production from Inflaton Decay (cont. d) Energy conserved during φ decay = n φ m φ = ρ rad (T R ) = π2 30 g T 4 R = Y χ (T R ) = n χ(t R ) s(t R ) = B(φ χ)n φ(t R ) s(t R ) = B(φ χ)ρ rad(t R ) m φ s(t R ) Making Dark Matter p. 33/35

161 DM Production from Inflaton Decay (cont. d) Energy conserved during φ decay = n φ m φ = ρ rad (T R ) = π2 30 g T 4 R = Y χ (T R ) = n χ(t R ) s(t R ) = B(φ χ)n φ(t R ) s(t R ) = B(φ χ)ρ rad(t R ) m φ s(t R ) = 3 4 T R m φ B(φ χ) Making Dark Matter p. 33/35

162 DM Production from Inflaton Decay (cont. d) Energy conserved during φ decay = n φ m φ = ρ rad (T R ) = π2 30 g T 4 R = Y χ (T R ) = n χ(t R ) s(t R ) = B(φ χ)n φ(t R ) s(t R ) = B(φ χ)ρ rad(t R ) m φ s(t R ) = 3 4 T R m φ B(φ χ) If χ production and annihilation at T < T R is negligible, universe evolves adiabatically: = Ω χ h 2 = m χ m φ T R 1 GeVB(φ χ) Making Dark Matter p. 33/35

163 Possibilities for B(φ χ) If χ = LSP: expect B(φ χ) 1: Excludes charged LSP for m φ > 2m χ, T R > 1 MeV! Making Dark Matter p. 34/35

164 Possibilities for B(φ χ) If χ = LSP: expect B(φ χ) 1: Excludes charged LSP for m φ > 2m χ, T R > 1 MeV! Democratic coupling: B(φ χ) g χ /g Making Dark Matter p. 34/35

165 Possibilities for B(φ χ) If χ = LSP: expect B(φ χ) 1: Excludes charged LSP for m φ > 2m χ, T R > 1 MeV! Democratic coupling: B(φ χ) g χ /g φ f fχχ (4 body): ( ) 2 ( ) 5/2 B(φ χ) α2 χ 96π 1 4m2 χ 1 2m χ 3 m 2 m φ φ (Assumes σ(χχ f f) α2 χ m 2 χ, φ f f dominates.) Making Dark Matter p. 34/35

166 Possibilities for B(φ χ) If χ = LSP: expect B(φ χ) 1: Excludes charged LSP for m φ > 2m χ, T R > 1 MeV! Democratic coupling: B(φ χ) g χ /g φ f fχχ (4 body): ( ) 2 ( ) 5/2 B(φ χ) α2 χ 96π 1 4m2 χ 1 2m χ 3 m 2 m φ φ (Assumes σ(χχ f f) α2 χ m 2 χ, φ f f dominates.) Can be most important production mechanism for superheavy Dark Matter (m χ GeV) in chaotic inflation (m φ GeV); for LSP if T R < 0.03m χ ;... Making Dark Matter p. 34/35

167 Summary Different production mechanisms give very different results for Ω χ h 2 : Making Dark Matter p. 35/35

168 Summary Different production mechanisms give very different results for Ω χ h 2 : Thermal WIMP: Ω χ h 2 1 σ eff v, independent of T R: most frequently studied case; needs T R > 0.05m χ. Making Dark Matter p. 35/35

169 Summary Different production mechanisms give very different results for Ω χ h 2 : Thermal WIMP: Ω χ h 2 1 σ eff v, independent of T R: most frequently studied case; needs T R > 0.05m χ. WIMP that never was in equilibrium: Ω χ h 2 e 2m χ/t R m 2 χ σ ann v Making Dark Matter p. 35/35

170 Summary Different production mechanisms give very different results for Ω χ h 2 : Thermal WIMP: Ω χ h 2 1 σ eff v, independent of T R: most frequently studied case; needs T R > 0.05m χ. WIMP that never was in equilibrium: Ω χ h 2 e 2m χ/t R m 2 χ σ ann v Thermal gravitino production: Ω Gh 2 T R m G. Making Dark Matter p. 35/35

171 Summary Different production mechanisms give very different results for Ω χ h 2 : Thermal WIMP: Ω χ h 2 1 σ eff v, independent of T R: most frequently studied case; needs T R > 0.05m χ. WIMP that never was in equilibrium: Ω χ h 2 e 2m χ/t R m 2 χ σ ann v Thermal gravitino production: Ω Gh 2 T R m G. Production from inflaton decay: Ω χ h 2 m χt R B(φ χ) m φ. Making Dark Matter p. 35/35

172 Summary Different production mechanisms give very different results for Ω χ h 2 : Thermal WIMP: Ω χ h 2 1 σ eff v, independent of T R: most frequently studied case; needs T R > 0.05m χ. WIMP that never was in equilibrium: Ω χ h 2 e 2m χ/t R m 2 χ σ ann v Thermal gravitino production: Ω Gh 2 T R m G. Production from inflaton decay: Ω χ h 2 m χt R B(φ χ) m φ. Only the thermal WIMP scenario can be tested using collider data and results from WIMP search experiments. Other scenarios can only be tested with additional input to constrain cosmology (T R,...). Making Dark Matter p. 35/35