Secret Neutrino Interactions (a pseudoscalar model)

Transcription

1 Secret Neutrino Interactions (a pseudoscalar model) MARIA ARCHIDIACONO AARHUS UNIVERSITY Updated constraints on non-standard neutrino interactions from Planck, Steen Hannestad JCAP 407 (204) 046, arxiv: Cosmology with self-interacting sterile neutrinos and dark matter - A pseudoscalar model, Steen Hannestad, Rasmus Sloth Hansen, Thomas Tram Phys.Rev. D9 (205) 6, 06502, arxiv: Sterile neutrinos with pseudoscalar self-interactions and cosmology, Steen Hannestad, Rasmus Sloth Hansen, Thomas Tram arxiv: TAUP, September Torino - Italy

2 Oscillations vs cosmology N eff Light sterile neutrinos Global fit 3+ Planck Collaboration: Cosmological sterile parameters meff ρν a+ ρextra rel ρsm νa sterile sterile = (Ts / Ta )3 mthermal = 7 (ΔN eff )4/3 m thermal 0 ote the significantly tighter constraint with the inclusion of Planck Collaboration anck high-` polarization, with Ne < at over 4 from 0.87 anck alone. This constraint is not very stable between like4.2 hoods, with the CamSpec likelihood giving a roughly wer value of Ne. However, the strong limit from polarization also consistent with the joint Planck TT+lowP+BAO result, conclusion that Ne < at over Eq. (60b) leads to the robust The addition of Planck lensing + has very little e ect on this 0 nstraint For Ne > 3, the Planck data favour higher values of the 0.72 ubble parameter than the Planck base CDM value, which as scussed in Sect. 5.4 may be in better agreement with some 0.69 ν DIS ν DIS 3.3 rect measurements of H0. This is because Planck accurately 5.0 easures the acoustic scale r /DA ; increasing Ne means (via 0.66 e Friedmann0equation) that the early Universe expands faster, 0 the sound horizon andhence at recombination, r, is smaller eff combination has to be closer (larger si n 2ϑeµH0 and hence smaller si n 2ϑ N effsi n<2ϑ3.7 µµ ee m, sterile [ev] A ) for it to subtend the same angular size observed by Planck. Gariazzo, Giunti, Lavader, Li, Zavanin (205) 2 2 owever, models with Ne Figure > 3 and higher Hubble 4. aallowed regions inconstant the sin2 2#eµ sterile m24, < sin #ee m 4 and sin 2#µµ m ev 32. Samples TT+lowP in the Ne me eff 2 so have higher values of themfluctuation amplitudein the shown Fig., sterile 3+-PrGLO globalfrom fit ofplanck short-baseline 8, aspragmatic 4 planes obtained ( lensing ) ( )with (95% c.l., Planck BAO) plane, colour-coded by, in models one massive sterile the coloured samples inneutrino Fig. 3.oscillation Thus, these models increase data compared with the 3 allowed regions obtained8 from µ! ee m, and the three ac( mass ) e tensions between the CMB measurements and astrophysical neutrino family, with e ective appearance data (APP) and the 3 constraints obtained from e short-,8sterile short-baseline TAUP, September Torino - Italy tive neutrinos as in the base CDM model. The physical mass easurements of 8 discussed in Sect It therefore seems ( ) [ev2] 2 m 4 [ev2] 2 m 4 Neff e σ νe DIS νµ DIS DIS APP % CL 90.00% CL 95.45% CL 99.00% CL 99.73% CL 68.27% CL 90.00% CL 95.45% CL 99.00% CL 99.73% CL PrGLO 3+ PrGLO µ baseline disappearance data ( e DIS), µ short-baseline disappearance data ( µ DIS) thermal

3 Pseudoscalar model The sterile neutrino is coupled to a new light pseudoscalar (m φ << ev) L ~ g s φν s γ 5 ν s Limits: No fifth force limits SN bounds: ν e ν e φ g e Farzan (2003) 0νββ decay Bernatowicz et al. (992) g s g e / sin 2 θ s = sin 2 2θ s = 0.05 Kopp et al. (203) Giunti et al. (203) Model dependent TAUP, September Torino - Italy

4 Thermal history u T > TeV φ particles are thermally produced u T ~ GeV (g s ~0-5 ) ν s and φ in thermal equilibrium ν s ν s φφ σ v = g 4 s 8πT s 2 one single tightly-coupled fluid u T > 200MeV the dark sector decouples! g T φ = * (T γ ) $ # & " g * (TeV )% /3 T SM SM ν = 0.465T ν in the relativistic limit u T ~ 0MeV neutrino oscillations become important TAUP, September Torino - Italy

5 Early Universe: Flavour evolution Density matrix ρ = " 2 f $ 0 $ # P a P x + ip y P x ip y P s % ' ' & QKEs: Potentials:!P a = V x P y + Γ a [ 2 P a ], #!P s = V x P y + Γ s 2 f 0,s(T s,µ s ) & % P s (, $ f 0 '!P x = V z P y DP x,!p y = V z P x 2 V x (P a P s ) DP y Damping: D = 2 Γ a + Γ s Repopulation Collisions: V x = Δm 2 s 2 p sin2θ s, Vacuum Background ν V z = Δm 2 s 2 p cos2θ 4π 2 s 45 2 p G F M T 4 n 2 a +V s Z V s (p s ) = g 2 s pdp( f 8π 2 φ + f s ) ~ 0 g 2 s T s p s ( ) Γ a = CG 2 F pt 4 Γ s = g 4 s 4πT s 2 n s TAUP, September Torino - Italy

6 Sterile neutrino production production Resonant production Standard neutrino decoupling &~ n/p freeze-out V/H 0 2 g 0 0 s = 2x V 0 V z V s Γ a Γ s T [MeV] To prevent sterile neutrino thermalization, we need to suppress the mixing angle in matter, i.e. V s >~ Δm 2 s 2 p prior to standard neutrino decoupling TAUP, September Torino - Italy

7 Solving the tension on N eff at BBN BBN bounds: ΔN eff (95% c.l.) When sterile neutrinos are produced, they will create non-thermal distortions in the sterile neutrino distribution, and the sterile neutrino spectrum end up being somewhat non-thermal. δ N eff LASAGNA code MA, Hannestad, Hansen, Tram (204) sin 2 2θ s = 0.05 m s = ev g s The transition between full thermalization and no thermalization occurs for coupling 0-6 < g s < 0-5 TAUP, September Torino - Italy

8 Late time phenomenology: ν s φ interactions 0 2 g s = 2x0-6 Γ s > H Γ a = CG F 2 pt 4 Γ s = g 4 s 4πT n 2 s s Γ/H Γ a Γ s The ν s φ fluid becomes strongly interacting before neutrinos go non-relativistic around recombination T [MeV] Low energy / late time process Recombination TAUP, September Torino - Italy

9 Neutrino perturbations Expansion in Legendre polynomials of the collisionless Boltzmann equation in Fourier space!ψ 0 = k q ε Ψ + 6!h d ln f 0 d lnq!ψ = k q 3ε (Ψ 0 2Ψ 2 )!Ψ 2 = k q 5ε (2Ψ # 3Ψ 3 ) % $ 5!Ψ l = k!h + 2 5! & η( d ln f 0 ' d lnq q (2l +)ε (lψ l (l +)Ψ l+ ), l 3 [ ] f (! x, q, ˆn,τ ) = f 0 (q) + Ψ(! x, q, ˆn,τ ) TAUP, September Torino - Italy

10 Neutrino perturbations collisional Expansion in Legendre polynomials of the collisionless Boltzmann equation in Fourier space!ψ 0 = k q ε Ψ + 6!Ψ = k q 3ε (Ψ 0 2Ψ 2 )!h d ln f 0 d lnq Energy-momentum conservation!ψ 2 = k q 5ε (2Ψ # 3Ψ 3 ) % $ 5!Ψ l = k!h + 2 5! & η( d ln f 0 ' d lnq Ψ 2 τ q (2l +)ε (lψ l (l +)Ψ l+ ) Ψ l τ, l 3 [ ] f (! x, q, ˆn,τ ) = f 0 (q) + Ψ(! x, q, ˆn,τ ) Scattering processes τ = (n σ v ) Relaxation time approximation Hannestad (2005) Hannestad & Scherrer (2000) TAUP, September Torino - Italy

11 Neutrino perturbations collisional Expansion in Legendre polynomials of the collisionless Boltzmann equation in Fourier space!ψ 0 = k q ε Ψ + 6!Ψ = k q 3ε (Ψ 0 2Ψ 2 )!h d ln f 0 d lnq Energy-momentum conservation!ψ 2 = k q 5ε (2Ψ # 3Ψ 3 ) % $ 5!Ψ l = k!h + 2 5! & η( d ln f 0 ' d lnq Ψ 2 τ q (2l +)ε (lψ l (l +)Ψ l+ ) Ψ l τ, l 3 [ ] f (! x, q, ˆn,τ ) = f 0 (q) + Ψ(! x, q, ˆn,τ ) Scattering processes τ = (n σ v ) Relaxation time approximation No free streaming No anisotropic stress Hannestad (2005) Hannestad & Scherrer (2000) TAUP, September Torino - Italy

12 SM neutrino free streaming Active neutrinos must be free streaming after z~5000 l 3 (l+)c l /(2π) [0 3 mk 2 ] vector boson Λ CDM Λ MDM case A, z i = case A, z i = 5000 l(l+)c l /(2π) [µk 2 ] pseudoscalar Photon monopole enhancement Λ CDM Λ MDM case B, z i = 500 case B, z i = 3000 MA, Hannestad (203) see also Cyr-Racine, Sigurdson (203) and Forastieri, Lattanzi, Natoli (205) l l The interaction is confined to the the sterile sector The pseudoscalar coupling is diagonal in mass basis TAUP, September Torino - Italy

13 m ν,s H 0 [km/s/mpc] Solving the tension on N eff at CMB N eff Pseudoscalar Fully thermalized Planck+lowP +HST +BAO 65 Each value of g s corresponds to one value of N eff. N eff ~ 3 è g s 0-5 N eff ~ 4 è g s 0-6 P/P MAX m ν,s [ev] 0.5 ΛCDM Pseudoscalar Planck + lowp 0 HST 65 H 0 MA, Hannestad, Hansen, Tram (205) 0.2 Δχ 2 0 riangle compatible plot in thewith parameter the standard space ΛCDM (N e,m,s,h 0 60 ) showing 70 the D 80 marginalized pos H model best-fit 0 [km/s/mpc] btained with various data set combinations in the pseudoscalar scenario. The partial neutrinos in the early Universe can make one sterile neutrino TAUP, September consistent with Torino a- Italy value gion), depending on g ;whilethe CDM model FIG. has 5: One todimensional be consistent posterior with for H 0 one in thefully CDMt

14 ν s φ annihilations As soon as sterile neutrinos go non-relativistic, they start annihilating into pseudoscalars ν s ν s φφ Annihilations Freez-out Γ s /H Non relativistic transition g s =0-6 g s = T [ev] TAUP, September Torino - Italy

15 ν s φ annihilations As soon as sterile neutrinos go non-relativistic, they start annihilating into pseudoscalars ν s ν s φφ ρ/ρ m ν,s =0. ev m ν,s =ev m ν,s = 0 ev w Sterile neutrino annihilations will heat up the scalars m ν,s =0. ev m ν,s =ev m ν,s = 0 ev a 0.27 p=wρ a TAUP, September Torino - Italy

16 Solving the tension on m s P(k) [(Mpc/h) 3 ] ΛCDM + ν s 00 best-fit Planck 205 m ν,s =0. ev m ν,s =ev m ν,s =3eV k [h/mpc] P(k) [(Mpc/h) 3 ] Mass constraints do not apply Pseudoscalar 00 best-fit Planck 205 m ν,s =0. ev m ν,s =ev m ν,s =3eV k [h/mpc] Drawback of the MeV-scale vector boson Mirizzi et al. 204 TAUP, September Torino - Italy

17 Solving the tension on m s 0.8 Λ +ν s + m ν,s Pseudoscalar Planck + lowp P/P MAX Oscillation data best-fit m ν,s [ev] MA, Hannestad, Hansen, Tram (205) TAUP, September Torino - Italy

18 Coupling to dark matter $ m g d χ & % MeV MA, Hannestad, Hansen, Tram (204) ' ) ( /4 $ m g d χ & % MeV ' ) ( 9/4 WDM limit m χ >~ 3.3 kev Viel (203) TAUP, September Torino - Italy

19 Solving the small scale problems of CDM (Baryon physics) Dwarf Milky Way Cluster 0. <s v>ê<s v>max v MAX = 2π 2 2 g d v rel 0-5 Loeb & Weiner (200) DM DM: s - D ü too big to fail ü cusp vs core Chu & Dasgupta (204) Dasgupta & Kopp (204) missing satellites TAUP, September Torino - Italy

20 Conclusions ü Secret sterile neutrino self-interactions mediated by a light pseudoscalar can accommodate one additional massive sterile state in cosmology without spoiling CMB measurements and, at the same time, evading mass constraints ü Secret interactions might also solve the small scale problems of the cold dark matter paradigm TAUP, September Torino - Italy

21 Backup slides

22 Coupling to dark matter χχ φφ decoupled annihilations recoupling Non-rel. DM Γ d /H 0-20 Γ d (T ) = σ v n g d 4 T Γ d (T MAX ) < H(T MAX ) $ m g d χ & % MeV ' ) ( /4 g d >2x0-5 (m χ /MeV) / T MAX ~m χ /3 g d <2x0-5 (m χ /MeV) /4 No Dark Acoustic Oscillations at CMB i.e. no χφ χφ if m χ >> m e and α d << α TAUP, September Torino - Italy

23 Galactic dynamics τ scat τ dyn = 2R2 3N χ σ τ dyn = 2π R v τ scat = n σ v N χ = M gal m χ Hard scattering The condition for having observable consequences on galactic dynamics is that the scattering time scale of DM self interactions is less than the age of the Universe. Milky Way: σ ~ 4πb 2 2 m χv 2 = α d m χ b 3 $ m g d χ & % MeV ' ) ( 9/4 α d = g 2 d 4π It is just a lower bound It requires further investigation TAUP, September Torino - Italy

24 Sommerfield enhancement The effect of Sommerfeld enhancement can be safely neglected for all reasonable values of g d MA, Hannestad, Hansen, Tram (204)