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Constraints on Mixed / Dark

André Lessa University of São Paulo

Moriond - March 11th, 2013

H. Baer, K. J. Bae, AL, arXiv:1301.7428 Outline

What is Dark Radiation?

Axions and Dark Radiation Supersymmetric Axion

CMB Constraints

Conclusions What is Dark Radiation? What is Dark Radiation?

◮ Number of relativistic species during matter-radiation decoupling (T ∼eV):

ρR = ργ + Nν ρν + ???

"Radiation" Dark Radiation What is Dark Radiation?

◮ Number of relativistic species during matter-radiation decoupling (T ∼eV):

ρR = ργ + Nν ρν + ???

"Radiation" Neutrinos Dark Radiation

◮ N Nν ρν +ρX 3 04 Or: eff = ρν → . (SM) What is Dark Radiation?

◮ Number of relativistic species during matter-radiation decoupling (T ∼eV):

ρR = ργ + Nν ρν + ???

"Radiation" Neutrinos Dark Radiation

◮ N Nν ρν +ρX 3 04 Or: eff = ρν → . (SM)

6000 Neff and CMB:

5000 )

2 Neff = 2

• Affects expansion rate K µ 4000 N = 3.04

) ( eff

→ shifts peak π

/(2 N = 4.34 3000 eff • Changes time of matter-radiation equality TT l → enhances 1st and 2nd peaks 2000 l(l+1)C

• ... 1000

102 103 Multipole Moment (l) Dark Radiation

2011: WMAP7 Neff = 4.34 ± 0.88 arXiv:1212.5226 SPT Neff = 3.86 ± 0.42 ACT Neff = 4.6 ± 0.80

2012-2013: WMAP9 Neff = 3.84 ± 0.40 WMAP9 NSPT 3 71 ± 0 35 SPT eff = . . ACT ACT Neff = 3.50 ± 0.42

2013-: Planck Neff =?? ± 0.2 Dark Radiation

2011: WMAP7 Neff = 4.34 ± 0.88 arXiv:1212.5226 SPT Neff = 3.86 ± 0.42 ACT Neff = 4.6 ± 0.80

2012-2013: WMAP9 Neff = 3.84 ± 0.40 WMAP9 NSPT 3 71 ± 0 35 SPT eff = . . ACT ACT Neff = 3.50 ± 0.42

2013-: Planck Neff =?? ± 0.2

SM → ✞∆Neff ≡ Neff − Neff < 1.6 (95% C.L.) ☎ ✝ ✆ Dark Radiation

2011: WMAP7 Neff = 4.34 ± 0.88 arXiv:1212.5226 SPT Neff = 3.86 ± 0.42 ACT Neff = 4.6 ± 0.80

2012-2013: WMAP9 Neff = 3.84 ± 0.40 WMAP9 NSPT 3 71 ± 0 35 SPT eff = . . ACT ACT Neff = 3.50 ± 0.42

2013-: Planck Neff =?? ± 0.2

SM → ✞∆Neff ≡ Neff − Neff < 1.6 (95% C.L.) ☎ ✝ ✆ ◮ What if the excess is real? Dark Radiation

2011: WMAP7 Neff = 4.34 ± 0.88 arXiv:1212.5226 SPT Neff = 3.86 ± 0.42 ACT Neff = 4.6 ± 0.80

2012-2013: WMAP9 Neff = 3.84 ± 0.40 WMAP9 NSPT 3 71 ± 0 35 SPT eff = . . ACT ACT Neff = 3.50 ± 0.42

2013-: Planck Neff =?? ± 0.2

SM → ✞∆Neff ≡ Neff − Neff < 1.6 (95% C.L.) ☎ ✝ ✆ ◮ What if the excess is real? • New relativistic species at T & eV

• mDR . eV (usually) → suppressed interactions with SM Dark Radiation

2011: WMAP7 Neff = 4.34 ± 0.88 arXiv:1212.5226 SPT Neff = 3.86 ± 0.42 ACT Neff = 4.6 ± 0.80

2012-2013: WMAP9 Neff = 3.84 ± 0.40 WMAP9 NSPT 3 71 ± 0 35 SPT eff = . . ACT ACT Neff = 3.50 ± 0.42

2013-: Planck Neff =?? ± 0.2

SM → ✞∆Neff ≡ Neff − Neff < 1.6 (95% C.L.) ☎ ✝ ✆ ◮ What if the excess is real? • New relativistic species at T & eV

• mDR . eV (usually) → suppressed interactions with SM • DR candidates: () sterile neutrinos, , , ... Axion = Dark Radiation?

◮ QCD axion (Strong CP Problem)

6 ◮ 10 GeV ma ∼ 6 eV fa

g ◮ 9 fa & 10 GeV (astrophysical bounds) a αs ∝ ✔ fa → ma . meV g → small couplings ✔ Axion = Dark Radiation?

◮ QCD axion (Strong CP Problem)

6 ◮ 10 GeV ma ∼ 6 eV fa

g ◮ 9 fa & 10 GeV (astrophysical bounds) a αs ∝ ✔ fa → ma . meV g → small couplings ✔

◮ Coherent Oscillations → CDM Axion = Dark Radiation?

◮ QCD axion (Strong CP Problem)

6 ◮ 10 GeV ma ∼ 6 eV fa

g ◮ 9 fa & 10 GeV (astrophysical bounds) a αs ∝ ✔ fa → ma . meV g → small couplings ✔

◮ Coherent Oscillations → CDM

◮ Also produced thermally: g a Relativistic ✔

g

g g Axion = Dark Radiation?

◮ QCD axion (Strong CP Problem)

6 ◮ 10 GeV ma ∼ 6 eV fa

g ◮ 9 fa & 10 GeV (astrophysical bounds) a αs ∝ ✔ fa → ma . meV g → small couplings ✔

◮ Coherent Oscillations → CDM

◮ Also produced thermally: g a Relativistic ✔

−2 g → ✞∆Neff < 10 ☎→ Below CMB sensitivity

g g (Can✝ not explain possible✆ excess) Axion = Dark Radiation?

◮ QCD axion (Strong CP Problem)

6 ◮ 10 GeV ma ∼ 6 eV fa

g ◮ 9 fa & 10 GeV (astrophysical bounds) a αs ∝ ✔ fa → ma . meV g → small couplings ✔

◮ Coherent Oscillations → CDM

◮ Also produced thermally: g a Relativistic ✔

−2 g → ✞∆Neff < 10 ☎→ Below CMB sensitivity

g g (Can✝ not explain possible✆ excess)

◮ Non-thermal production? Supersymmetric Axion

◮ fa ≫ EW scale → Supersymmetric Axion

◮ fa ≫ EW scale → Hierarchy Problem → Supersymmetry ◮ Supersymmetric Axion:

a → Aˆ → s + i a + a˜ axion

• SM + a → MSSM + a, s, a˜ = PQMSSM Supersymmetric Axion

◮ fa ≫ EW scale → Hierarchy Problem → Supersymmetry ◮ Supersymmetric Axion:

a → Aˆ → s + i a + a˜ saxion axion axino

• SM + a → MSSM + a, s, a˜ = PQMSSM

• Couplings:

g g g˜ g a → a, s s a˜

g g g˜ g˜

a˜ a + s s

a˜ a Supersymmetric Axion

◮ fa ≫ EW scale → Hierarchy Problem → Supersymmetry ◮ Supersymmetric Axion:

a → Aˆ → s + i a + a˜ saxion axion axino

• SM + a → MSSM + a, s, a˜ = PQMSSM

• Couplings:

g g g˜ g a → a, s s a˜

g g g˜ g˜

a˜ ✛ a✘ + s s → Non-thermal axion production (if ms > 2ma) a˜ a

✚ ✙ Supersymmetric Axion

◮ PQMSSM :

PQMSSM

q˜1,2, ˜l

Mass Scale g˜

˜t, b˜

LSP SM Supersymmetric Axion

◮ PQMSSM Masses:

PQMSSM

q˜1,2, ˜l s

Mass Scale g˜

˜t, b˜

LSP SM Supersymmetric Axion

◮ PQMSSM Masses:

PQMSSM

q˜1,2, ˜l s

Mass Scale g˜

˜t, b˜

LSP SM

a Supersymmetric Axion

◮ PQMSSM Masses:

PQMSSM

q˜1,2, ˜l s a˜ Mass Scale g˜

˜t, b˜

LSP SM

We assume: a

mLSP = me < m . ms ∼ mSUSY Z1 a˜ Supersymmetric Axion

s → a + a ◮ PQMSSM Masses: 1

PQMSSM 10-1 s → ~a + ~a q˜1 2, ˜l , 10-2 s BF a˜ s → g + g

Mass Scale -3 g˜ 10 m = 1.6 TeV ~g s → ~g + ~g ˜ -4 ˜t, b 10 m~a = 0.5 TeV

LSP 10-5 3 4 SM 10 10 ms (GeV) We assume: a

mLSP = me < m . ms ∼ mSUSY Z1 a˜ Supersymmetric Axion

= Neutralino + Axions • Neutralino production: TP (∼ MSSM) e a˜ → g + g˜ → ...Z1 + X • Axion production: coherent oscillations (CDM) Supersymmetric Axion

◮ Dark Matter = Neutralino + Axions • Neutralino production: TP (∼ MSSM) e a˜ → g + g˜ → ...Z1 + X • Axion production: coherent oscillations (CDM)

◮ Dark Radiation = Axions Supersymmetric Axion

◮ Dark Matter = Neutralino + Axions • Neutralino production: TP (∼ MSSM) e a˜ → g + g˜ → ...Z1 + X • Axion production: coherent oscillations (CDM)

◮ Dark Radiation = Axions • Production: TP s → a + a Supersymmetric Axion

◮ Dark Matter = Neutralino + Axions • Neutralino production: TP (∼ MSSM) e a˜ → g + g˜ → ...Z1 + X • Axion production: coherent oscillations (CDM)

◮ Dark Radiation = Axions • Production: TP s → a + a

• ∆Neff & 1 → large saxion production Supersymmetric Axion

◮ Dark Matter = Neutralino + Axions • Neutralino production: TP (∼ MSSM) e a˜ → g + g˜ → ...Z1 + X • Axion production: coherent oscillations (CDM)

◮ Dark Radiation = Axions • Production: TP s → a + a

• ∆Neff & 1 → large saxion production

• CMB constrains saxion production! Supersymmetric Axion

◮ Dark Matter = Neutralino + Axions • Neutralino production: TP (∼ MSSM) e a˜ → g + g˜ → ...Z1 + X • Axion production: coherent oscillations (CDM)

◮ Dark Radiation = Axions • Production: TP s → a + a

• ∆Neff & 1 → large saxion production

• CMB constrains saxion production!

How are saxions produced in the early ? Saxion Production

◮ Thermal Production g s

TP 2 g → ρs ∝ TR/fa

g g

g a˜

TP 2 g → ρa˜ ∝ TR/fa

g g˜ Saxion Production

◮ Thermal Production ◮ Coherent Oscillations: g s

TP 2 → ρ ∝ TR/f g s a CO 2 2 → ρs ∝ θs fa g g

• θs is UV dependent (inflation) g a˜ (θsfa ≡ s0)

TP 2 g → ρa˜ ∝ TR/fa

g g˜ Saxion Production

◮ Thermal Production ◮ Coherent Oscillations: g s

TP 2 → ρ ∝ TR/f g s a CO 2 2 → ρs ∝ θs fa g g

• θs is UV dependent (inflation) g a˜ (θsfa ≡ s0) • TP 2 Dominates at large fa and low TR g → ρa˜ ∝ TR/fa

g g˜

• Dominates at small fa and high TR CMB Constraints on TP

◮ Thermal Production of Saxions:

102 ∆ 10 CMB Excluded ( Neff > 1.6) 1 s(TP) 10-1 eff

N -2

∆ 10 10-3 10-4 10-5 107 108 109 1010 1011 1012 1013 T R (GeV)

• Saxion production increases with TR CMB Constraints on TP

◮ Thermal Production of Saxions:

102 ∆ 10 CMB Excluded ( Neff > 1.6) 1 s(TP) 10-1 eff

N -2

∆ 10 10-3 10-4 10-5 107 108 109 1010 1011 1012 1013 T R (GeV)

• Saxion production increases with TR ...but axino production increases at the same rate! CMB Constraints on TP

◮ Thermal Production of Saxions:

102 ∆ 10 CMB Excluded ( Neff > 1.6) 1 s(TP) 10-1 eff

N -2

∆ 10 10-3 10-4 10-5 107 108 109 1010 1011 1012 1013 T R (GeV)

• Saxion production increases with TR ...but axino production increases at the same rate!

ρ(s→aa) ∆Neff ∼ e ργ +ρ(a˜→Z1+γ) CMB Constraints on TP

◮ Thermal Production of Saxions:

102 ∆ 10 CMB Excluded ( Neff > 1.6) 1 s(TP) 10-1 eff

N -2

∆ 10 s(TP) + ~a(TP) 10-3 10-4 10-5 107 108 109 1010 1011 1012 1013 T R (GeV)

• Saxion production increases with TR ...but axino production increases at the same rate!

ρ(s→aa) ρ(s→aa) ∆Neff ∼ e → e ργ +ρ(a˜→Z1+γ) ρ(a˜→Z1+γ) CMB Constraints on TP

◮ Thermal Production of Saxions:

102 ∆ 10 CMB Excluded ( Neff > 1.6) 1 s(TP) 10-1 eff

N -2

∆ 10 s(TP) + ~a(TP) 10-3 10-4 10-5 107 108 109 1010 1011 1012 1013 T R (GeV)

• Saxion production increases with TR ...but axino production increases at the same rate!

ρ(s→aa) ρ(s→aa) ∆Neff ∼ e → e . 0.2 ργ +ρ(a˜→Z1+γ) ρ(a˜→Z1+γ) → Below WMAP9 sensitivity! CMB Constraints on CO

◮ Coherent Oscillation Production of Saxions: CMB Constraints on CO

◮ Coherent Oscillation Production of Saxions:

• Relevant at large fa → suppresses TP (no axino dilution) CMB Constraints on CO

◮ Coherent Oscillation Production of Saxions:

• Relevant at large fa → suppresses TP (no axino dilution)

CO 2 2 • ρs ∝ fa θs CMB Constraints on CO

◮ Coherent Oscillation Production of Saxions:

• Relevant at large fa → suppresses TP (no axino dilution)

CO 2 2 • ρs ∝ fa θs

• ∆Neff < 1.6 → Upper bound on fa! CMB Constraints on CO

◮ Coherent Oscillation Production of Saxions:

• Relevant at large fa → suppresses TP (no axino dilution)

CO 2 2 • ρs ∝ fa θs

• ∆Neff < 1.6 → Upper bound on fa!

1016 1016 θ θ s = 1 6 GeV) s fa = M /100 15 = 10 15 P 10 > 1.6 (T R 10 ∆ Neff 14 10 GeV) 14 10 = 10 10 > 1.6 (T R 13 ∆ Neff 13 10 |g |min = 6× 10-16 (ADMX) 10 |g |min = 6× 10-16 (ADMX) a γγ a γγ

(GeV) 12 (GeV) 12 -15 6 a 10 min × -15 a 10 min × GeV) f |g | = 6 10 (ADMX-II) f |g | = 6 10 (ADMX-II) a γγ a γγ = 10 10 GeV) 11 11 R 10 10 = 10 > 1.6 (T R eff 10 10 ∆ N 10 10 > 1.6 (T eff ∆ N

1 10 102 103 104 105 1 10 102 103 104 105 ms (GeV) ms (GeV) CMB Constraints

◮ Dark Matter:

e 2 • a˜ → ...Z1 + X → Ωe h enhancement Z1 2 • s → g + g → Ωe h dilution Z1 CMB Constraints

◮ Dark Matter:

e 2 • a˜ → ...Z1 + X → Ωe h enhancement Z1 2 • s → g + g → Ωe h dilution Z1

104 103 Xe100 Excluded 2 2 10 (Ω~ h > 0.026) Z 10 1 1 10-1 10-2 MSSM 2 -3 Ω~ h

2 10 Z1 -4 h

1 10 ~ Z 10-5 Ω 10-6 10-7 ∆ Neff > 1.6 10-8 10-9 10-10 10-11 10-12 109 1010 1011 1012 1013 1014 1015 1016 f a (GeV) Conclusions

◮ Current CMB data starts to become sensitive to SUSY axion models Conclusions

◮ Current CMB data starts to become sensitive to SUSY axion models

◮ In the mixed axion/neutralino DM scenario: Conclusions

◮ Current CMB data starts to become sensitive to SUSY axion models

◮ In the mixed axion/neutralino DM scenario: • TP of saxions is still unconstrained...... will start to be probed by Planck data Conclusions

◮ Current CMB data starts to become sensitive to SUSY axion models

◮ In the mixed axion/neutralino DM scenario: • TP of saxions is still unconstrained...... will start to be probed by Planck data

• Large CO saxion production is already excluded by ∆Neff < 1.6 13 (fa . 10 GeV) Conclusions

◮ Current CMB data starts to become sensitive to SUSY axion models

◮ In the mixed axion/neutralino DM scenario: • TP of saxions is still unconstrained...... will start to be probed by Planck data

• Large CO saxion production is already excluded by ∆Neff < 1.6 13 (fa . 10 GeV)

2 MSSM 2 • ∆Neff < 1.6 → Ωe h > Ωe h Z1 Z1 e → DM ∼ Z1 (WIMP Signal) Conclusions

◮ Current CMB data starts to become sensitive to SUSY axion models

◮ In the mixed axion/neutralino DM scenario: • TP of saxions is still unconstrained...... will start to be probed by Planck data

• Large CO saxion production is already excluded by ∆Neff < 1.6 13 (fa . 10 GeV)

2 MSSM 2 • ∆Neff < 1.6 → Ωe h > Ωe h Z1 Z1 e → DM ∼ Z1 (WIMP Signal)

◮ If Planck confirms the excess in ∆Neff : Conclusions

◮ Current CMB data starts to become sensitive to SUSY axion models

◮ In the mixed axion/neutralino DM scenario: • TP of saxions is still unconstrained...... will start to be probed by Planck data

• Large CO saxion production is already excluded by ∆Neff < 1.6 13 (fa . 10 GeV)

2 MSSM 2 • ∆Neff < 1.6 → Ωe h > Ωe h Z1 Z1 e → DM ∼ Z1 (WIMP Signal)

◮ If Planck confirms the excess in ∆Neff :

• ”evidence” for CO saxions (large fa → ADMX) or Conclusions

◮ Current CMB data starts to become sensitive to SUSY axion models

◮ In the mixed axion/neutralino DM scenario: • TP of saxions is still unconstrained...... will start to be probed by Planck data

• Large CO saxion production is already excluded by ∆Neff < 1.6 13 (fa . 10 GeV)

2 MSSM 2 • ∆Neff < 1.6 → Ωe h > Ωe h Z1 Z1 e → DM ∼ Z1 (WIMP Signal)

◮ If Planck confirms the excess in ∆Neff :

• ”evidence” for CO saxions (large fa → ADMX) or • axino LSP → no WIMP signal! What is Dark Radiation? Axions and Dark Radiation CMB Constraints Conclusions Backup

14/20 Cosmological Evolution

◮ Thermal Production:

1025

1021 Time 1015 SM

109 ) 4 103

1014

1013

-3 1012 (GeV 10

ρ 1011

1010

9 a (DR) -9 10 s ~ ~ 10 8 10 a Z1 7 10

106

-15 5 10 10 a (DM)

8 9 10 10

10-21

105 106 107 108 109 1010 1011 1012 1013 1014 R/R0 CMB Constraints

◮ Scan over parameter space:

104 CMB Excluded 103 ∆ ( Neff > 1.6) 102

10 ∆ Nmax(TP) 1 eff 10-1

-2

eff 10

N 10-3 ∆ 10-4

-5 -4 10 s0/fa = 10 10-6 s0/fa < 1 10-7 ≥ s0/fa 1 10-8 10-9 109 1010 1011 1012 1013 1014 1015 1016 f a (GeV) Experimental Constraints

L. Rosenberg’s talk @ Axions 2010, UF J.L. Hewett et al., arXiv:1205.2671 Dark Matter and Dark Radiation

MSSM 2 ◮ Bino LSP (Ωe h > 0.11) Z1

6 10 WMAP Excluded 5 10 Ω 2 4 ( ~ h > 0.12) 10 Z1 103 102 10 MSSM 2 1 Ω~ h Z

2 1 10-1 h 1 -2 ~ Z 10

Ω -3 10 BBN Allowed 10-4 10-5 BBN Excluded -6 ∆ 10 Neff > 1.6 10-7 10-8 10-9

109 1010 1011 1012 1013 1014 1015 1016 f a (GeV) Dark Matter and Dark Radiation

MSSM 2 ◮ LSP (Ωe h < 0.11) Z1

104 103 Xe100 Excluded 2 2 10 (Ω~ h > 0.026) Z 10 1 1 10-1 10-2 MSSM 2 -3 Ω~ h

2 10 Z1 -4 h

1 10 ~ Z 10-5 Ω 10-6 10-7 ∆ Neff > 1.6 10-8 10-9 10-10 10-11 10-12 109 1010 1011 1012 1013 1014 1015 1016 f a (GeV) Supersymmetric Axion

◮ Axion production: coherent oscillations** (CDM) T ≫ ΛQCD: ma = 0 T ≪ ΛQCD: ma =6 0

CO CO 2 2 2 ρa = 0 ρa ∝ V(ai) = maθi fa − ◮ CO behave as cold matter (ρ ∝ R 3)

◮ Saxions can also oscillate, if θs =6 0

◮ θi is a random number of order 1