Neutrino physics imprinted in the Cosmic Microwave Background Manoj Kaplinghat University of California Irvine
Massive Neutrinos and Cosmology: Overview Masses, number, BSM ν scattering, large asymmetry … Early phase Lensed CMB BBN structure formation Cosmic shear Primary CMB Galaxies Ly- α forest 21 cm
Future of Laboratory Constraints Tritium endpoint Aim: m ν e < 0.2 eV at 95% CL (KATRIN) 0 ν ββ : Test if neutrinos are Majorana particles Next gen ~ 100 meV and lower in double beta decay mass
Mass schemes from measurement of neutrino oscillation solar atmospheric atmospheric Sum of neutrino solar masses greater than about 100 meV Sum of neutrino masses greater than about 60 meV Both double beta decay experiments and cosmology should be able to probe this regime.
Massive Neutrino and Primary CMB 1 x 0.8 eV neutrino (dashed) 3.5 ¥ 10 - 10 � Expansion rate increases 3. ¥ 10 - 10 � Temperature l H l + 1 L C l êH 2 p L Changes: gravitational potential, 2.5 ¥ 10 - 10 damping and angle subtended 2. ¥ 10 - 10 by sound horizon 1.5 ¥ 10 - 10 For a precision probe, we need the physics 1. ¥ 10 - 10 after last scattering. 5. ¥ 10 - 11 0 600 800 1000 1200 1400 1600 1800 2000 Multipole
Jeans Instability for Neutrinos Neutrino perturbations on length scales larger than the Jeans length become unstable and collapse into dark matter potential wells. k J (z) -1 Bond and Szalay, ApJ 274, 443 (1983) Hu and Eisenstein, ApJ 498, 497 (1998) Hu, Eisenstein and Tegmark, PRL 80, 5255 (1998)
Effect of non-zero neutrino mass on the density perturbations 1.00 0.99 Δ P/P ~ 4 Ω nu / Ω M 0.98 PS H S m n = 0.12 eV in 3 n L ~ 4( Σ m/94 eV)/( Ω M h 2 ) PS H S m n = 0 L 0.97 z=100 10 0.96 2 0.95 0 0.94 k J (now) H 0 0.93 0.001 0.005 0.010 0.050 0.100 0.500 1.000 k H h ê Mpc L
Effect of Lensing on the CMB Deflection ~ arcmin z
Coherence of (CMB) Lensing Deflection Peak sensitivity ~ z=2 Estimate d from CMB maps Hu and Okamoto, 2002 Coherence ~ 10 deg
Effect of Lensing on galaxy shapes: Cosmic Shear
Effect of massive neutrino on CMB lensing 0.02 EE Unlensed TT, EE - 1 not the way for C l H S m n = 0.12 eV in 3 n L TT precision Σ m ν . 0.00 C l H S m n = 0 L Best CMB dd - 0.02 constraints from lensing The dominant effect is due deflection to the change in the angle - 0.04 measure (dd) subtended by the sound horizon 5 10 50 100 500 1000 Multipole
Effect of massive neutrino on CMB lensing 0.04 0.02 0.02 EE Unlensed TT, EE - 1 - 1 not the way for C l H S m n = 0.12 eV in 3 n L C l H S m n = 0.12 eV in 1 n L TT precision Σ m ν . 0.00 0.00 C l H S m n = 0 L C l H S m n = 0 L Best CMB dd - 0.02 - 0.02 constraints from lensing The dominant effect is due deflection - 0.04 to the change in the angle - 0.04 measure (dd) subtended by the sound horizon - 0.06 5 5 10 10 50 50 100 100 500 500 1000 1000 Multipole Multipole
Effect of dynamical dark energy on the density perturbations 1.01 1.00 0.99 0.98 PS H w0 = - 0.9 L PS H w0 = - 1 L Depends on w(a) 0.97 and matter density 0.96 0.95 0.94 ~m φ H 0 0.93 0.001 0.005 0.010 0.050 0.100 0.500 1.000 k H h ê Mpc L
Neutrino mass and dark energy: can we infer them separately? The answer is yes! ** � � ** if DE is only important at late times Both ν mass and DE are unknown late-time effects. Kaplinghat, Knox and Song, PRL (2003)
Prospects: CMB Lensing CMB lensing (by itself) can measure the effect of finite neutrino mass allowing for DE EOS and running at the level of ~ 40 meV (1 σ ). Kaplinghat, Knox and Song, PRL 2003 Lesgourgues, Perroto, Pastor, Piat PRD 2006
Extra radiation parameterized as N eff Not a late time 0.6 effect, but since CMB lensing is an integrated effect, EE 0.4 this is important. C l H Neff = 3.04 L - 1 C l H Neff = 4.04 L 0.2 TT 0.0 dd - 0.2 - 0.4 5 10 50 100 500 1000 Multipole
Phase shift: a way to measure N e fg precisely Information in phase shift: Bashinsky and Seljak 2004 (separate from damping!) Follin, Knox, Millea and Pan 2015 Future: σ (N ν ) ~ 0.3 (Planck polarization), 0.1 (CMB-S4) Baumann, Green, Meyers and Wallisch 2015 (very nice description of the physics)
Key caveat Cosmological probes are sensitive to the energy density of neutrinos. While the Jeans length does depend on the mass, it does not seem that we will be able to exploit this scale dependence to measure the mass hierarchy directly.
Current limits: assuming base Λ CDM model X m ν < 0 . 72 eV Planck TT + lowP ; X m ν < 0 . 21 eV Planck TT + lowP + BAO ; X m ν < 0 . 49 eV Planck TT , TE , EE + lowP ; X m ν < 0 . 17 eV Planck TT , TE , EE + lowP + BAO . 95% C.L. assuming Λ CDM (Planck 2015 results XIII) WMAP+HST+CMASS (conservative): ∑ m v <0.36 eV ( 95% C.L. De Putter et al 2012 )
Current limits: effect of dark energy EOS DE with constant EOS+CDM+flatness (wCDM) WMAP7+H 0 +BAO (SDSS): ∑ m v <1.3 eV WMAP7+SNe (constitution)+BAO (SDSS): ∑ m v <0.9 eV WMAP7+LRGs (SDSS)+H 0 : ∑ m v <0.8 eV Previous+SNe (constitution): ∑ m v <0.5 eV ( 95% C.L. WMAP collaboration ) � Planck (including lensing)+WMAPpol+SDSS DR9: ∑ m v <0.48 eV ( 95% C.L. Guisarma et al 2013 )
Current limits: complementarity of data sets — the case of Ly- α forest + CMB data 1.1 (massless) Lyman-alpha 1 0.9 Level from CMB k (massive) / P 0.8 Σ m = 0.5 eV, z=4 0.7 ν m = 0.5 eV, z=2 π Σ ν P(k)*k/ 0.6 m = 0.5 eV, z=0 Σ ν k 0.5 m = 1.0 eV, z=4 Σ P ν m = 1.0 eV, z=2 Σ ν 0.4 m = 1.0 eV, z=0 Σ -1 10 ν 0.3 -3 -4 -2 -1 10 10 10 10 1 -1 k (h Mpc ) z=3.4 z=2.2 z=2.4 z=3.6 z=2.6 z=3.8 -2 z=2.8 z=4.0 10 z=3.0 z=4.2 z=3.2 z=4.4 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 -1 k (km/s) Palanque-Delabrouille et al 2015 (BOSS + Planck 2015)
Current limits: complementarity of data sets — the case of Ly- α forest + CMB data Planck (TT+lowP) 1 ν ν Ly- + H α m m s n Planck (TT+lowP) 0 Planck (TT+lowP) 1.2 1.2 Ly- + Planck (TT+lowP) α 0.99 Σ Σ Ly- + H α Ly- α + H 0 0 Ly- α + Planck (TT+lowP) Ly- α + Planck (TT+lowP) 0.98 1 1 0.97 0.8 0.8 0.96 0.6 0.6 0.95 0.94 0.4 0.4 0.93 0.2 0.2 0.92 0.91 0 0 0.65 0.7 0.75 0.8 0.85 0.9 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.65 0.7 0.75 0.8 0.85 0.9 σ σ Ω 8 8 m Σ m ν < 0 . 19 eV (95%CL) Planck (TT , TE , EE + lowP) + Ly α P P Σ m ν < 0 . 12 eV (95%CL) Planck (TT , TE , EE + lowP) + BAO + Ly α m 0 12 eV (95%CL) Palanque-Delabrouille et al 2015 Planck (TT+lowP) 0.8 ν m Planck (TT+lowP) + Ly- α Planck (TT,TE,EE+lowP) + Ly- Σ α 0.7 Planck (TT,TE,EE+lowP) + Ly- + BAO α 0.6 0.5 ~ 3 σ preference for negative running 0.4 ~ 2 σ with older Ly- α data ( Minor and Kaplinghat 2014 ). 0.3 0.2 0.1 0 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 dn /dlnk s
Near Term CMB Lensing Experiments South Pole Telescope Atacama Cosmology Polarization Telescope (SPTPol → SPT-3G) Polarization (ACTPol) Near: ACTPol and SPTPol : σ ( Σ m ν ) ~ 100 meV; σ ( N eff ) ~ 0.12 Mid: SPT-3G forecast to σ ( Σ m ν ) ~ 74 meV; σ ( N eff ) ~ 0.076 (Benson et al arXiv:1407.2973; CMB 2015 at U Minnesotta)
Key degeneracies for the future: spatial curvature of the universe Degeneracy between neutrino mass and curvature in lensing measurements. Smith, Hu and Kaplinghat, PRD 2004; PRD 2006. If neutrino mass measurement is known to 0.1 eV accuracy, then it helps in the determination of curvature (0.3%) and dark energy equation of state from next generation ground based CMB experiments, Planck and SNAP. Smith, Hu and Huterer, ApJL 2007
Key degeneracies for the future: unknown expansion history of the universe Parameterizing our ignorance of H(z) in terms of early DE, we find this to be a significant source of degeneracy. ( De Putter, Zahn, Linder PRD 2009, Joudaki and Kaplinghat, PRD 2012) This degeneracy can be tamed if other data sets are used. Specifically the cosmic shear and CMB lensing degeneracies are not aligned and the addition of these two data sets can extend the reach to the 40 meV level.
Complementarity of data sets: the future 0.3 (Planck) 0.22 0.15 (Planck) 0.1 rted 0.08 0.06 ormal lensing, 0.04 0.001 0.005 0.01 0.02 0.05 0.1 Joudaki and Kaplinghat PRD 2012
Neutrino mass forecasts 0.3 CMB lensing (Planck) Sum of neutrino masses H eV L 0.2 0.16 CMB lensing (Planck) fixing Curvature and 0.1 Early Dark Energy Inverted 0.08 0.06 Normal CMB lensing, Weak lensing, Galaxy power spectrum, SNe 0.04 0.001 0.005 0.01 0.02 0.05 0.1 Lightest Neutrino Mass H eV L Joudaki and Kaplinghat PRD 2012 0.500 CMB CMB lensing CMB lensing, lensing (Planck) fixing Weak lensing, Abazajian et al 2013 (Snowmass) Double beta decay mass H eV L (Planck) Curvature and Galaxy power Early Dark spectrum, SNe 0.100 Wu et al 2014 Energy 0.050 0.010 0.005 0.001 0.05 0.10 0.20 0.50 Sum of neutrino masses H eV L
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