Cosmology Falling in Love with Sterile Neutrinos

Home , Dark radiation

Jörn Kersten

Based on Torsten Bringmann, Jasper Hasenkamp, JK, JCAP 07 (2014) [arXiv:1312.4947]

Outline

1 Introduction

2 Self-Interacting Dark Matter

3 Dark Matter Interacting with Neutrinos

3 / 23 1 Introduction

2 Self-Interacting Dark Matter

3 Dark Matter Interacting with Neutrinos

4 / 23 Or does it? Tensions in ΛCDM cosmology

The Universe after Planck

Flat ΛCDM cosmology ﬁts data perfectly Planck, arXiv:1303.5062

5 / 23 The Universe after Planck

Flat ΛCDM cosmology ﬁts data perfectly Planck, arXiv:1303.5062 Or does it? Tensions in ΛCDM cosmology

5 / 23 Measurements of Cosmic Microwave Background (CMB):

∆Neff = 1.51 ± 0.75 at 68% CL ACT, ApJ 739 (2011)

∆Neff = 0.81 ± 0.42 at 68% CL SPT, ApJ 743 (2011) +0.68 ∆Neff = 0.31−0.64 at 95% CL Planck, arXiv:1303.5076

Hints for Dark Radiation

Dark radiation: relativistic particles 6= γ, νSM Parameterized via radiation energy density " # 7 T 4 ρ ≡ 1 + N ν ρ rad eff 8 T γ

T ≡ Tγ

Neff: effective number of neutrino species

Standard Model: Neff = 3.046

Existence of dark radiation ⇔ ∆Neff ≡ Neff − 3.046 > 0

6 / 23 Hints for Dark Radiation

Dark radiation: relativistic particles 6= γ, νSM Parameterized via radiation energy density " # 7 T 4 ρ ≡ 1 + N ν ρ rad eff 8 T γ

T ≡ Tγ

Neff: effective number of neutrino species

Standard Model: Neff = 3.046

Existence of dark radiation ⇔ ∆Neff ≡ Neff − 3.046 > 0 Measurements of Cosmic Microwave Background (CMB):

∆Neff = 1.51 ± 0.75 at 68% CL ACT, ApJ 739 (2011)

∆Neff = 0.81 ± 0.42 at 68% CL SPT, ApJ 743 (2011) +0.68 ∆Neff = 0.31−0.64 at 95% CL Planck, arXiv:1303.5076

6 / 23 Measurements

7 CDM+Neff+k+f+ns CDM+Neff+k+f+w CDM+Neff+f+w CDM+Neff+k+f CDM+Neff+k CDM+Neff+Yp CDM+Neff+f CDM+Neff 6

5 eff N 4

W7+SPT+BAO+H0+Union2W7+CMB+LRG+SN+H0W7+CMB+BAO+SN+H0W7+CMB+LRG+H0W7+CMB+BAO+H0W7+H0+WL+BAO+H(z)+Union2W7+SPT+WiggleZ+H(z)+BAO+SNLSW9+SPT+WiggleZ+H(z)+BAO+SNLSW7+SPT+BAO+H0W7+SPT+BAO+H0+Union2W7+ACT+SPT+BAO+H0W7+ACT+SPT+BAO+H0W7+BAO+H0W7+ACTW7+ACT+BAO+H0W7+SPT+WiggleZ+H(z)+BAO+SNLSW7+CMB+LRG+H0W7+CMB+BAO+H0W7+ACT+SPT+LRG+H0W7+SPTSZ+BAO+H0W7+SDSS+H0W7+SDSS+H0+Union2W7+SDSS+H0+Union2+W7+H0+WL+BAO+H(z)+Union2W7+SPT+BAO+H0W7+SNLS+BAO+BOSSW7+SPT+BAO+H0W9+STP+H0W9+STP+H0+BAOW9+ACT+H0W9+ACT+H0+BAOPl+WP+SPT+ACT+BAO4 D/H D/H+ W7+D/HW7+SPT(agnostic)W7+SPTW7+ACT+SPT+BAO+H0W7+ACT+SPT+LRG+H0W7+SPT+BAO+H0W7+SPTW7+ACT+BAO+H0W7+ACTW7+LRG+H0W7+BAO+H0W5+LRG+maxBGC+H0W5+CMB+BAO+fgas+H0W5+LRG+H0W5+BAO+SN+H0W7+H0+SDSS+SN+CHFTLSW7+SPT+H(z)+H0W7+H0+WL+BAO+H(z)+Union2W7+ACBAR+BAO+H0+ACTW7+ACBAR+ACT+SPT+SDSS+H0W7+ACBAR+ACT+SPT+SDSS+MSH0W7+SPT+BAO+H0W7+SPTW7+H0W7+SPT+BAO+H0W7+SPTW7+SPT+BAO+H0W9+ACT+SPT+BAO+H0W9+ACTW9+SPTW9+ACT+SPTW9+ACT+SPT+lensingPl+WP Pl+WP+SPT+ACT+BAO He

33 34

4 He 68 59

36 35 14 38 42 44 58 61 64 65

28 30 13 45 46 49

21 66

37 52 9 15 25 27 29 31 41 43 57 60 62 4 5 17 18

22 67 47 2 26 3 32 69 4 11 12 19 39 40 63 He+D/H 48

1 10 54

6 24 53

7 8 16

56 Modified from Riemer-Sørensen et al. (2013 review) arXiv:1301.7102 arXiv:1301.7102 review) (2013 al. et Riemer-Sørensen from Modified Resolved by hot dark matter component ' dark radiation Best ﬁt: ∆Neff = 0.61 3 meff ≡ Ts m = 0.41 eV s Tν s Hamann, Hasenkamp, JCAP 10 (2013) Wyman, Rudd, Vanderveld, Hu, PRL 112 (2014) Battye, Moss, PRL 112 (2014) Gariazzo, Giunti, Laveder, JHEP 11 (2013)

Hints for Hot Dark Matter

2 ... 3 σ tension: CMB (z > 1000) vs. local (z < 10) observations Expansion rate km Planck: H0 = (67.3 ± 1.2) s Mpc arXiv:1303.5076 km Hubble: H0 = (73.8 ± 2.4) s Mpc Riess et al., ApJ 730 (2011)

Magnitude of matter density ﬂuctuations( σ8)

8 / 23 Hints for Hot Dark Matter

2 ... 3 σ tension: CMB (z > 1000) vs. local (z < 10) observations Expansion rate km Planck: H0 = (67.3 ± 1.2) s Mpc arXiv:1303.5076 km Hubble: H0 = (73.8 ± 2.4) s Mpc Riess et al., ApJ 730 (2011)

Magnitude of matter density ﬂuctuations( σ8) Resolved by hot dark matter component ' dark radiation Best ﬁt: ∆Neff = 0.61 3 meff ≡ Ts m = 0.41 eV s Tν s Hamann, Hasenkamp, JCAP 10 (2013) Wyman, Rudd, Vanderveld, Hu, PRL 112 (2014) Battye, Moss, PRL 112 (2014) Gariazzo, Giunti, Laveder, JHEP 11 (2013)

8 / 23 on large scales

Astrophysics solutions or new particle physics?

Small-Scale Problems of Structure Formation

Numerical simulations of structure formation with cold dark matter

Springel, Frenk, White, Nature 440 (2006)

Excellent agreement with observations

9 / 23 Astrophysics solutions or new particle physics?

Small-Scale Problems of Structure Formation

Numerical simulations of structure formation with cold dark matter

Springel, Frenk, White, Nature 440 (2006)

Excellent agreement with observations on large scales

9 / 23 Astrophysics solutions or new particle physics?

Small-Scale Problems of Structure Formation

Missing satellites Cusp-core Too big to fail

Kravtsov, Adv. Astron. (2010) De Blok et al., ApJ 552 (2001) Boylan-Kolchin et al., Klypin et al., ApJ 522 (1999) MNRAS 422 (2011) More cuspy density More galactic Most massive proﬁles predicted satellites predicted satellites predicted than observed than observed denser than observed

9 / 23 Small-Scale Problems of Structure Formation

Missing satellites Cusp-core Too big to fail

9 / 23 1 Introduction

2 Self-Interacting Dark Matter

3 Dark Matter Interacting with Neutrinos

10 / 23 Not-so-WIMPy Dark Matter

Dark matter χ Standard Model singlet Charged under U(1)X gauge interaction Mass mχ ∼ TeV V ν χ χ χ χ Light gaugeχ boson V , mV ∼ MeV... ν¯ Long-range, velocity-dependentV ... interactionν V ... V Less cuspy density proﬁles ... χ¯ χ¯ χ¯ ν ν Cusp-core and too big to fail solvedV ν¯ Feng, Kaplinghat, Yu, PRL 104 (2010) Loeb, Weiner, PRL 106 (2011) Vogelsberger, Zavala, Loeb, MNRAS 423 (2012)

11 / 23 mχv TeV 10 km/s Here: ∼ 5 ∼ 30 1 mV MeV 3 · 10 km/s classical regime analytical approximations exist

Velocity-Dependent Self-Interactions

αX −mV r Described by Yukawa potential V (r) = ± r e Desired scattering cross section σT : Large in dwarf galaxies Small on larger scales to satisfy experimental limits Very different behavior depending on model parameters

100 D dwarf Milky Way cluster øøøø 7 only 10 øøøø 10 Classical Resonant Born øøø ø ø øø L 1 ø g 4 10 øø 2 0.1 ø cm attractive ø 10 H @ ø L

-2 X g ø

10 m 2 0.01

-3 Born T cm

H 10 mX=200 GeV resonant Σ -5 -2 X classical 10 Α =10 -4 X m 10 v=10 kms T -8

Σ 10 10-5 10 100 1000 0.001 0.01 0.1 1 v km s mΦ HGeVL Tulin, Yu, Zurek, PRL 110, PRD 87 (2013) H L

12 / 23 Velocity-Dependent Self-Interactions

100 D dwarf Milky Way cluster øøøø 7 only 10 øøøø 10 Classical Resonant Born øøø ø ø øø L 1 ø g 4 10 øø 2 0.1 ø cm attractive ø 10 H @ ø L

-2 X g ø

10 m 2 0.01

-3 Born T cm

H 10 mX=200 GeV resonant Σ -5 -2 X classical 10 Α =10 -4 X m 10 v=10 kms T -8

Σ 10 10-5 10 100 1000 0.001 0.01 0.1 1 v km s mΦ HGeVL Tulin, Yu, Zurek, PRL 110, PRD 87 (2013) H L mχv TeV 10 km/s Here: ∼ 5 ∼ 30 1 mV MeV 3 · 10 km/s classical regime analytical approximations exist

12 / 23 Simulating Self-Interacting Dark Matter

Simulation: formation of dwarf galaxy with dark matter + baryons

dA: SIDM10 109 DM:CDM-B stars:CDM-B DM:SIDM1-B stars:SIDM1-B DM:SIDM10-B stars:SIDM10-B DM:vdSIDMa-B stars:vdSIDMa-B DM:vdSIDMb-B stars:vdSIDMb-B ] 108 3 − c p k ¯ M

[ 7 10 ρ

6 1 0 1 2 10 −3 200 400 600 1000 3000 log[ρ/(M ⊙kpc )] r [pc] Vogelsberger, Zavala, Simpson, Jenkins, MNRAS 444 (2014)

Core, size depends on strength of self-interactions

13 / 23 1 Introduction

2 Self-Interacting Dark Matter

3 Dark Matter Interacting with Neutrinos

14 / 23 Problem: explicit breaking of SU(2)L

Late Kinetic Decoupling

Standard Model neutrinos coupled to V V ν χ χ χ χ χ Dark matter... scatters off neutrinos ν¯ V Tχ =...Tν until kinetic decouplingν V at T ...∼ 100 eV V Formation of... smaller structures suppressed χ¯ χ¯ χ¯ ν ν Missing satellitesV solvedν¯ Van den Aarssen, Bringmann, Pfrommer, PRL 109 (2012)

H L H L 5 van den Aarssen, Bringmann & Pfrommer 2012 5 van den Aarssen, Bringmann & Pfrommer 2012 mΧ = 10 TeV 70 not enough flattening mΧ = 500 GeV 60 7 M 50 of cuspy profiles 10 cutoff too small to 40 8 M address abundance 10 D 1 30 D 1 9 M 10 problem 0.5 10 M MeV 0.5 MeV 0.5 @ 20 1 @ 10 V V M ruled out by 2 11 m m 10 astrophysics 5 10 + 10 Ly-Α 0.1 2 -1 20 0.1 Σmax mΧ @cm g D excluded Υ @km s-1D 0.05 max 0.05 1 10 10-5 10-4 10-3 10-2 10-1 mΧ @TeVD gΝ

15 / 23 Late Kinetic Decoupling

Problem: explicit breaking of SU(2)L

15 / 23 Everything solved All small-scale problems of structure formation Hot dark matter hint (CMB-local tension) Neutrino oscillation anomalies (?) Bringmann, Hasenkamp, JK, JCAP 07 (2014)

Enter the Sterile Neutrino

Sterile neutrino N Mass m eV N . χ χ Standard Model singlet Charged under U(1)X V Forms hot dark matter N N Dark matter scatters off sterile neutrinos

16 / 23 Enter the Sterile Neutrino

Sterile neutrino N Mass m eV N . χ χ Standard Model singlet Charged under U(1)X V Forms hot dark matter N N Dark matter scatters off sterile neutrinos

Everything solved All small-scale problems of structure formation Hot dark matter hint (CMB-local tension) Neutrino oscillation anomalies (?) Bringmann, Hasenkamp, JK, JCAP 07 (2014)

16 / 23 Meet the Dark Side

Dirac fermion χ (dark matter), mχ ∼ TeV

Gauge boson V , mV ∼ MeV X µν X µν Kinetic mixing FµνF , FµνZ negligible Scalar Θ breaking U(1)X , hΘi ∼ MeV Light sterile neutrino N, mN . eV

Heavier sterile neutrino N2, mN2 ∼ MeV cancel anomalies Scalar ξ, hξi < hΘi active-sterile neutrino mixing Y Y 0 Y L ⊃ − M Θ† NcN − M Θ NcN − ν ξφ˜ ` N + h.c. N 2 2 2 2 Λ L

17 / 23 Tχ ∼ mχ/25: freeze-out (chemical decoupling) of dark matter

4 2 2 0.67 mχ ΩCDMh ∼ 0.11 gX TeV

V ν χ χ χ χ χ ... ν¯ V ... ν V ... V ... χ¯ χ¯ χ¯ ν ν V ν¯

Dark Matter Production

High temperatures: U(1)X sector thermalized via Higgs portal

2 2 LHiggs ⊃ κ|H| |Θ|

hΘi ∼ MeV breaks U(1)X

18 / 23 Dark Matter Production

High temperatures: U(1)X sector thermalized via Higgs portal

2 2 LHiggs ⊃ κ|H| |Θ|

hΘi ∼ MeV breaks U(1)X

Tχ ∼ mχ/25: freeze-out (chemical decoupling) of dark matter

4 2 2 0.67 mχ ΩCDMh ∼ 0.11 gX TeV

V ν χ χ χ χ χ ... ν¯ V ... ν V ... V ... χ¯ χ¯ χ¯ ν ν V ν¯

18 / 23 Cold Dark Matter Parameter Space

10 L 2013

not enough flattening H of cuspy profiles

=109M Kersten Mcut & D OK missing satellites MeV

1 Hasenkamp @ 10 , Mcut =510 M V

m ruled out by

cored profiles Bringmann astrophysics + 0.1 1 10 m Χ @TeVD

Blue band can be moved vertically by changing sterile neutrino charge and temperature Crosses: simulations show that too big to fail solved

19 / 23 ! 4 58.4 3 ! ∆ | < Neff BBN dpl . 1 g∗,ν(Tx ) dpl BBN bounds satisﬁed for Tx & 1 GeV Correct order of magnitude for hot dark matter hint

Sterile Neutrino Abundance

T ↓ Higgs portal no longer effective dpl U(1)X sector decouples at Tx (depending on κ) SM particles becoming non-relativistic afterwards heat SM bath, not U(1)X bath TN < Tν (depending on number of d.o.f. g∗)

4 4 4 T g 3 g 3 N ∗,ν ∗,N ∆Neff(T ) = = Tν g∗,N g∗,ν dpl T Tx

20 / 23 Sterile Neutrino Abundance

4 4 4 T g 3 g 3 N ∗,ν ∗,N ∆Neff(T ) = = Tν g∗,N g∗,ν dpl T Tx ! 4 58.4 3 ! ∆ | < Neff BBN dpl . 1 g∗,ν(Tx ) dpl BBN bounds satisﬁed for Tx & 1 GeV Correct order of magnitude for hot dark matter hint

20 / 23 Hot Dark Matter Parameter Space

dpl g*,ΝJTx N 200 100

2.0 L t m 2013 H TeV TeV TeV p 1 = 0.5 0.1 dpl x Χ = = T m Χ Χ Kersten 1.5 m m &

D Ν anomalies eV @ 1.0 Hasenkamp 1 , N m

0.5 HDM signal Bringmann

not possible 0.0 with SM d.o.f. 0.2 0.4 0.6 0.8 1.0

DNeff cmb ! 4 58.4 3 ∆ | = Neff CMB dpl g∗,ν(Tx )

21 / 23 T < MeV: mixing unsuppressed Oscillations + U(1)X -mediated scatterings NN → NN N re-thermalize TN = Tν Mirizzi, Mangano, Pisanti, Saviano, arXiv:1410.1385 Cherry, Friedland, Shoemaker, arXiv:1411.1071

With full re-thermalization:

∆Neff|CMB ' const. √ √ 2 2 2 2 m = meff ' 0.4 eV < 1 eV N 3/4 s 3.63/4 Neff|CMB Cosmology still ﬁne but neutrino anomalies not explained

Sterile Neutrino Production by Oscillations

22 / 23 With full re-thermalization:

∆Neff|CMB ' const. √ √ 2 2 2 2 m = meff ' 0.4 eV < 1 eV N 3/4 s 3.63/4 Neff|CMB Cosmology still ﬁne but neutrino anomalies not explained

Sterile Neutrino Production by Oscillations

Standard scenario: mixing between active and sterile neutrinos oscillations ∆Neff ' 1 U(1)X interactions effective matter potential suppresses mixing no production by oscillations for T & MeV Hannestad, Hansen, Tram, PRL 112 (2014); Dasgupta, Kopp, PRL 112 (2014) T < MeV: mixing unsuppressed Oscillations + U(1)X -mediated scatterings NN → NN N re-thermalize TN = Tν Mirizzi, Mangano, Pisanti, Saviano, arXiv:1410.1385 Cherry, Friedland, Shoemaker, arXiv:1411.1071

22 / 23 Sterile Neutrino Production by Oscillations

With full re-thermalization:

∆Neff|CMB ' const. √ √ 2 2 2 2 m = meff ' 0.4 eV < 1 eV N 3/4 s 3.63/4 Neff|CMB Cosmology still ﬁne but neutrino anomalies not explained 22 / 23 Outlook Interaction by scalar exchange possible and favorable? Further options for model building Connection to 3.5 keV X-ray line? Re-thermalization Improved treatment of scattering in Yukawa potential

Conclusions

Particle physics solution for tensions in standard ΛCDM cosmology:

23 / 23 Conclusions

Particle physics solution for tensions in standard ΛCDM cosmology:

Sterile neutrinos N with mass . eV + self-interacting dark matter N small hot DM component New interaction mediated by gauge boson with mass ∼ MeV DM-DM scatterings cusp-core, too big to fail solved DM-N scattering missing satellites solved Outlook Interaction by scalar exchange possible and favorable? Further options for model building Connection to 3.5 keV X-ray line? Re-thermalization Improved treatment of scattering in Yukawa potential

23 / 23 Timeline t

� B B N �

C M B

T 24 / 23 Dark Radiation and Big Bang Nucleosynthesis

T ∼ 1 MeV: freeze-out of n ↔ p n/p ratio ﬁxed T ∼ 0.1 MeV: p + n → D Afterwards formation of 3He, 4He, 7Li

ρrad ↑ faster expansion more n available for D fusion 4 more He +0.8 Neff = 3.8−0.7 at 2σ CL Izotov, Thuan, arXiv:1001.4440

∆Neff ≤ 1 at 2σ CL Mangano, Serpico, arXiv:1103.1261

25 / 23 Dark Radiation Effects on the CMB

ρrad ↑ later matter-radiation equality st rd 1 /3 peak ratio no change ρm ↑ teq unchanged ρrad ↑ sound horizon rs ∝ 1/H ↓ Peak positions no change of rs angular size θs = D ∝ 1/H ↓ DA A (by ρΛ ↑) Remaining effect: increased Silk damping reduced power on small scales Hou et al., arXiv:1104.2333

26 / 23