Dark Radiation from Particle Decay

Jörn Kersten

University of Hamburg

Based on Jasper Hasenkamp, JK, JCAP 08 (2013), 024 [arXiv:1212.4160]

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 1 / 19 Outline

1 Introduction

2 Dark Radiation from Late Decays

3 Constraints for Model Building

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 2 / 19 1 Introduction

2 Dark Radiation from Late Decays

3 Constraints for Model Building

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 3 / 19 Dark Radiation

Radiation = relativistic particles Dark radiation: relativistic particles = ,⌫SM 6 Energy density (after e+e annihilation at T 0.5 MeV) ⇠ 4 7 T⌫ ⇢ 1 + N ⇢ rad ⌘ eff 8 T " ✓ ◆ # T T ⌘ ⇡2 4 ⇢ = 15 T Neff: effective number of neutrino species

Standard Model: Neff = 3.046 Existence of dark radiation N N 3.046 > 0 , eff ⌘ eff SM ⇢DR = 0.13 Neff ⇢rad

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 4 / 19 Cosmic Microwave Background (CMB) Increased Silk damping reduced power on small scales Hou et al., arXiv:1104.2333

Observable Effects

Big Bang Nucleosynthesis (BBN) ⇢ faster expansion rad " more n available for D fusion more 4He +0.8 Neff = 3.8 0.7 at 95% CL Izotov, Thuan, arXiv:1001.4440 N 1 at 95% CL eff  Mangano, Serpico, arXiv:1103.1261

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 5 / 19 Observable Effects

Big Bang Nucleosynthesis (BBN) ⇢ faster expansion rad " more n available for D fusion more 4He +0.8 Neff = 3.8 0.7 at 95% CL Izotov, Thuan, arXiv:1001.4440 N 1 at 95% CL eff  Mangano, Serpico, arXiv:1103.1261 Cosmic Microwave Background (CMB) Increased Silk damping reduced power on small scales Hou et al., arXiv:1104.2333

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 5 / 19 Selected Results from the CMB

N = 1.51 0.75 at 68% CL ACT, arXiv:1009.0866 eff ± N = 0.81 0.42 at 68% CL SPT, arXiv:1105.3182 eff ± +0.68 Neff = 0.31 0.64 at 95% CL Planck, arXiv:1303.5076 +0.48 Neff = 0.47 0.45 at 95% CL using H0 from HST Planck, arXiv:1303.5076 Neff < 0.71 at 95% CL Hojjati et al., arXiv:1304.3724 N = 0.61 0.30 at 68% CL Hamann, Hasenkamp, arXiv:1308.3255 eff ±

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 6 / 19 1 Introduction

2 Dark Radiation from Late Decays

3 Constraints for Model Building

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 7 / 19 Examples: Gravitino axion + axino ( m3 /M2 ) ! ⇠ 3/2 Pl Sneutrino gravitino + neutrino ! Modulino sneutrino + neutrino, axion + axino, . . . !

New Physics in the Later Early Universe

Late decays: after BBN, before recombination affect only CMB Mother 2 weakly interacting daughters ! Masses m, m1 < m2 m m 2 ⌘ m2 Daughters form dark radiation while relativistic Heavier daughter could form dark matter

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 8 / 19 New Physics in the Later Early Universe

Late decays: after BBN, before recombination affect only CMB Mother 2 weakly interacting daughters ! Masses m, m1 < m2 m m 2 ⌘ m2 Daughters form dark radiation while relativistic Heavier daughter could form dark matter Examples: Gravitino axion + axino ( m3 /M2 ) ! ⇠ 3/2 Pl Sneutrino gravitino + neutrino ! Modulino sneutrino + neutrino, axion + axino, . . . !

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 8 / 19 Two-body decay kinematics for m m : 1 ⌧ 2 2 NDR ( + 1) 1 ⇢DR(Td)= ⇢(Td) ⌦=⌦(Neff,⌧,) 2 ( + 1)2

NDR = 1, 2: number of relativistic dark particles during CMB times Free parameters in the following: ⌧,

Connecting Neff and Particle Physics

Neff measured know SM ⇢DR = 0.13 Neff ⇢rad Goal: Constrain model parameters ⌦: Energy density of the mother

Lifetime ⌧ (equivalently, temperature at decay Td) : Mass hierarchy between mother and heavier daughter

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 9 / 19 Connecting Neff and Particle Physics

Neff measured know SM ⇢DR = 0.13 Neff ⇢rad Goal: Constrain model parameters ⌦: Energy density of the mother

Lifetime ⌧ (equivalently, temperature at decay Td) : Mass hierarchy between mother and heavier daughter Two-body decay kinematics for m m : 1 ⌧ 2 2 NDR ( + 1) 1 ⇢DR(Td)= ⇢(Td) ⌦=⌦(Neff,⌧,) 2 ( + 1)2

NDR = 1, 2: number of relativistic dark particles during CMB times Free parameters in the following: ⌧,

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 9 / 19 Constraints from Dark Matter Density

Today’s density of heavier daughter ⌦ ⌦ lower limits 2  DM Decay before matter-radiation equality at teq: 1 t 2 0.3 N eq & eff ⌧ ✓ ◆

Decay after matter-radiation equality (now also ⌦ < ⌦DM): 2 t 3 0.15 N eq & eff ⌧ ✓ ◆

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 10 / 19 Constraints from Dark Matter Density

dmin t from different requirements

7 nr 10 t2 min teq H L tcmb 5 dpl 10 H L tg

103 min d 101

10-1

end tbbn te + e- tbbn 10-3

10-1 101 103 105 107 109 1011 1013 1015 1017 t s

Jörn Kersten (Uni Hamburg) Dark Radiation from@ ParticleD Decay 10 / 19 Heavier daughter too hot to form dark matter (or N 1) eff ⌧

Free Streaming of Heavier Daughter

Heavier daughter emitted with finite velocity washes out structure on scales smaller than free-streaming scale

t0 v fs = 2 dt 2 a Z⌧ Limit from Lyman-↵ forest:

fs 2 . 1 Mpc Abazajian, arXiv:astro-ph/0512631; Viel et al., arXiv:0709.0131; Boyarsky et al., arXiv:0812.0010

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 11 / 19 Free Streaming of Heavier Daughter

Heavier daughter emitted with finite velocity washes out structure on scales smaller than free-streaming scale

fs fs l2 min = l2 dmin t0 fs v2 2 = dt a 50 H L H L Z⌧ 20

Limit from Lyman-↵ forest: D 10 Mpc @

fs min

L 5 2 . 1 Mpc fs 2 l H

t dpl Abazajian, arXiv:astro-ph/0512631; 2 tcmb eq tg

Viel et al., arXiv:0709.0131; 1 nr Boyarsky et al., arXiv:0812.0010 t2 min 109 1011 1013 1015 1017 H L t s

Heavier daughter too hot to form dark matter (or Neff 1) @ D ⌧

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 11 / 19 Hot Dark Matter Constraint

Maximum amount of hot dark matter ⌦2 . 0.04 ⌦DM (corresponding to m⌫ < 0.44 eV Hamann et al., arXiv:1003.3999) lower limits on rise by factor 25 P Decay before matter-radiation equality at teq: 1 t 2 7 N eq & eff ⌧ ✓ ◆ Decay after matter-radiation equality: 2 t 3 3.5 N eq & eff ⌧ ✓ ◆

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 12 / 19 Hot Dark Matter Constraint

dmin t from different requirements

7 nr 10 t2 min teq H L tcmb 5 dpl 10 H L tg

103 min d 101

10-1

end tbbn te + e- tbbn 10-3

10-1 101 103 105 107 109 1011 1013 1015 1017 t s

Jörn Kersten (Uni Hamburg) Dark Radiation from@ ParticleD Decay 12 / 19 Hot Dark Matter Opportunities

1 Imagine conflict between future measurements: Cosmology ( m⌫)cosmo > 0 observed Laboratory upper limit < ( m⌫)cosmo P Indication for hot dark matter = ⌫ from decay 6 P 2 Heavier daughter may become non-relativistic during CMB times observable consequences for CMB likely

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 13 / 19 Examples: Saxion axion + axion, axino + axino ! Modulus gravitino + gravitino, axion + axion !

Two Decay Modes

1 Mother + , branching ratio B ! 1 2 Mother + , branching ratio B ! 2

Daughter masses m1 < m2 m x 2 2 ⌘ m Lighter daughter forms dark radiation

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 14 / 19 Two Decay Modes

1 Mother + , branching ratio B ! 1 2 Mother + , branching ratio B ! 2

Daughter masses m1 < m2 m x 2 2 ⌘ m Lighter daughter forms dark radiation Examples: Saxion axion + axion, axino + axino ! Modulus gravitino + gravitino, axion + axion !

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 14 / 19 Adjustable Free Streaming

B2 allows to adjust ⌦2 no dark matter density constraint on x2 fs 2 arbitrary

1.2 0.4 Mpc ⌧ 0.5 x2 0.1 5 ' fs ! 10 s 2 ⇣ ⌘ fs 2 3 2 1 ⌦DMh B 5.6 10 N 2 ' · 0.4 Mpc eff 0.1286 ! ✓ ◆ Heavier daughter may form dark matter Can be cold or warm

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 15 / 19 Adjustable Free Streaming -1 fs x 2 l2

103 H L end 5 tbbn 8¥10 s tcmb 1 2 - x

1 10 te + e-

101 103 105 107 109 1011 t s

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle@ D Decay 15 / 19 Solution of the Missing Satellites Problem

Simulations of structure formation more galactic satellites than observed Problem may well be solved by astrophysics . . . or by warm dark matter with 0.2 Mpc . fs . 1 Mpc Colín et al., arXiv:astro-ph/0004115; Lin et al., arXiv:astro-ph/0009003 possible in two-decay-mode scenario

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 16 / 19 1 Introduction

2 Dark Radiation from Late Decays

3 Constraints for Model Building

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 17 / 19 Constraints on Decays into Standard Model Particles

Br(Mother SM + SM) = 0 ! 6 Change of primordial abundances from BBN Jedamzik, arXiv:hep-ph/0604251; Kawasaki, Kohri, Moroi, arXiv:astro-ph/0408426 Spectral distortions of the CMB Hu, Silk, PRL 70 (1993); Chluba, Sunyaev, arXiv:1109.6552 Change of ionization history Slatyer, arXiv:1211.0283

strict upper limits on branching ratio

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 18 / 19 Constraints on Decays into Standard Model Particles

max Direct Bem t from BBN constraints 100

10-1 H L

10-2

10-3

10-4 max em B 10-5

10-6

-7 dpl 10 tcmb tg

-8 end 10 tbbn tbbn teq

10-9 10-1 101 103 105 107 109 1011 1013 1015 1017 t s

Jörn Kersten (Uni Hamburg) Dark Radiation from@ ParticleD Decay 18 / 19 Constraints on Decays into Standard Model Particles

max Direct Bvis t from CMB constraints 100

10-1 t dpl H L g 10-2

10-3

10-4

10-5 max vis

B 10-6

10-7

10-8

10-9

-10 end 10 tbbn tbbn tcmb teq 10-11 10-1 101 103 105 107 109 1011 1013 1015 1017 t s

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle@ D Decay 18 / 19 Constraints on Decays into Standard Model Particles

Br(Mother SM + SM) = 0 ! 6 Change of primordial abundances from BBN Jedamzik, arXiv:hep-ph/0604251; Kawasaki, Kohri, Moroi, arXiv:astro-ph/0408426 Spectral distortions of the CMB Hu, Silk, PRL 70 (1993); Chluba, Sunyaev, arXiv:1109.6552 Change of ionization history Slatyer, arXiv:1211.0283

strict upper limits on branching ratio . . . even if only suppressed decay possible (loop, 3- or 4-body decay)

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 18 / 19 Constraints on Decays into Standard Model Particles

max Bhad t from BBN constraints in considered scenarios 100

-1 end 10 H L tbbn

10-2

10-3

10-4 max had B 10-5

10-6

-7 dpl 10 tcmb tg

-8 10 tbbn teq

10-9 10-1 101 103 105 107 109 1011 1013 1015 1017 t s

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle@ D Decay 18 / 19 Conclusions

Dark universe may contain dark radiation Production in late decays different impact on BBN and CMB Energy density of mother determined by Neff, ⌧, Single dark decay mode: heavier daughter too hot for dark matter Two dark decay modes: heavier daughter may form dark matter and solve missing satellites problem Severe constraints on branching ratio into Standard Model particles input for construction of concrete models

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 19 / 19 Effects on the Cosmic Microwave Background (CMB)

⇢ later matter-radiation rad " equality 1st/3rd peak ratio no change ⇢ t unchanged m " eq ⇢ sound horizon r 1/H rad " s / # Peak positions no change of rs angular size ✓s = DA 1/H DA / # (by ⇢ ) ⇤ " Remaining effect: increased Silk damping reduced power on small scales Hou et al., arXiv:1104.2333

Jörn Kersten (Uni Hamburg) Dark Radiation from Particle Decay 20 / 19