Determining neutrino masses from cosmology Yvonne Y. Y. Wong The University of New South Wales Sydney, Australia NuFact 2013, Beijing, August 19 24, 2013
The cosmic neutrino background... Embedding the standard model in FLRW cosmology necessarily leads to a thermal neutrino background (decoupling at T ~ 1 MeV). Fixed by weak interactions Present temperature: ( ) 4 T ν= 11 1/ 3 T γ =1.95K Number density per flavour: nν = 6 ζ (3) 3 3 T = 112 cm 4 π2 ν
The cosmic neutrino background: energy density... The present-day neutrino energy density depends on whether the neutrinos are relativistic or nonrelativistic. Relativistic (m << T): Photon energy density ( ) 7 π2 4 7 4 ρν = T ν= 8 15 8 11 4 /3 3ρν ρ γ 0.68 ργ Nonrelativistic (m >> T ~ 10-4 ev): ρ ν =mν n ν ΛCDM (since Planck) mν 2 Ων, 0 h = >0.1 % h 94 ev 2 From neutrino oscillations mν > 0.05 ev Neutrino dark matter!
Detecting neutrino masses via free-streaming... For most of the observable history of the universe neutrinos have significant speeds. ev-mass neutrinos become nonrelativistic near γ decoupling. Even when nonrelativistic, neutrinos have large thermal motion. vthermal = ( ) Tν ev 50.4(1+ z) mν mν ν Avoid gravitational capture 1 ν Gravitational potential wells c 2 2 thermal 2 m Large-scale structure km s c ν CMB anistropies ( ) 8π v 1+ z ev 2π Free-streaming λ FS 4.2 h 1 Mpc ; k FS Ωm,0 mν λ FS scale: 3Ω H c ν c Non-clustering FS k k FS
Consider a neutrino and a cold dark matter particle encountering two gravitational potential wells of different sizes in an expanding universe: ν ν c Ψ c ν c c ν λ λ FS Ψ Some time later... Both CDM and neutrinos cluster c ν c ν Potential stays the same (during matter domination) c ν λ λ FS c c ν Only CDM clusters Potential decays Cosmological neutrino mass measurement is based on observing this freestreaming induced potential decay at λ<< λfs.
Large-scale matter distribution... 2 P (k )= δ(k ) Galaxy redshift surveys Replace some CDM with neutrinos Cluster abundance Lyman-α fν = Neutrino fraction ΔP Ω 8 f ν 8 ν Ωm P Ω ν h = 2 mν 94eV
CMB anisotropies... WMAP Planck ACT, SPT mν =1 1.2 ev mν =3 0.4 ev mν =0 ev Early ISW Effect (after photon decoupling) Uplifting in the acoustic oscillation phase Fixed total matter density Free H0 (sound horizon adjusted)
Observed CMB temperature fluctuation Sachs-Wolfe effect: Gravitational potential Redshift ΔT ΔT = +Ψ T observed T intrinsic Blueshift Ψ=0 Ψ CMB photon Observer
Observed CMB temperature fluctuation Sachs-Wolfe effect: Gravitational potential Redshift ΔT ΔT = +Ψ T observed T intrinsic Blueshift Ψ=0 Ψ Potential decay before γ decoupling: CMB photon ΔT T intrinsic acoustic oscillations Observer Ψ ΔT T observed
Observed CMB temperature fluctuation Sachs-Wolfe effect: Gravitational potential Redshift ΔT ΔT = +Ψ T observed T intrinsic Blueshift Ψ=0 Ψ CMB photon ΔT T intrinsic Potential decay before γ decoupling: Observer Ψ ΔT T observed acoustic oscillations Integrated Sachs-Wolfe effect (potential decay after γ decoupling): τ0 time Temperature Δ T ( n )= d τ e κ( τ) [ Ψ (τ, n (τ τ))+ Φ (τ, n ( τ τ))] 0 0 enhancement T ISW 0
Observed CMB temperature fluctuation Sachs-Wolfe effect: Gravitational potential Redshift ΔT ΔT = +Ψ T observed T intrinsic Blueshift Ψ=0 Ψ CMB photon Potential decay happens inδstandard ΛCDM T Ψ Potential decay before γ decoupling: cosmology anyway. T intrinsic Observer ΔT T observed Replacing some CDM with massive neutrinos simply causesacoustic the potentials oscillations to decay more on scales below the freestreaming scale. Integrated Sachs-Wolfe effect (potential decay after γ decoupling): τ0 time Temperature Δ T ( n )= d τ e κ( τ) [ Ψ (τ, n (τ τ))+ Φ (τ, n ( τ τ))] 0 0 enhancement T ISW 0
CMB anisotropies... WMAP Planck ACT, SPT mν =1 1.2 ev mν =3 0.4 ev mν =0 ev Early ISW Effect (after photon decoupling) Uplifting in the acoustic oscillation phase Fixed total matter density Free H0 (sound horizon adjusted)
Present constraints...
Post-Planck... Ade et al.[planck] 2013 ΛCDM+neutrino mass (7 parameters) 95% C.L. upper limits WMAP (9 years) W9 + ACT Planck + WMAP Polarisation Planck + WP + ACT ℓ > 1000 + SPT ℓ > 2000 mν <0.66 ev Best CMB-only bound (95 % C.L.)
Post-Planck... Ade et al.[planck] 2013 ΛCDM+neutrino mass (7 parameters) 95% C.L. upper limits WMAP (9 years) W9 + ACT Planck + WMAP Polarisation Planck + WP + ACT ℓ > 1000 + SPT ℓ > 2000 mν <0.66 ev (95 % C.L.) Best CMB-only bound W7+ matter power spectrum + HST H 0 Planck + WP + (ACT ℓ > 1000 + SPT ℓ > 2000) + baryon acoustic oscillations mν <0.25 ev (95 % C.L.) Best minimal bound Formally similar to the pre-planck best minimal bound, but arguably less prone to issues of nonlinearities.
Matter power spectrum vs BAO... 3 k P(k ) Linear 2 <1 2π Nonlinear 3 k P (k ) 2 >1 2π Galaxy redshift surveys Replace some CDM with neutrinos Lyman-α fν = Neutrino fraction ΔP Ω 8 f ν 8 ν Ωm P Ω ν h = 2 mν 94eV
Matter power spectrum (normalised to smooth spectrum) Matter power spectrum = Shape Baryon acoustic oscillations = Location of oscillatory features 1-loop (nonlinear) Time RG (nonlinear) N-body (nonlinear) HaloFit (nonlinear) Linear theory Pietroni 2008
In a nutshell... Formally, the best minimal (7-parameter) upper bound on Σ mν is still hovering around 0.3 ev post-planck. The bound has however become more robust against uncertainties: Less nonlinearities in BAO than in the matter power spectrum. Does not rely on local measurement of the Hubble parameter... or on the choice of lightcurve fitters for the Supernova Ia data. Dependence on cosmological model used for inference?
Model dependence: parameter degeneracies... We do not measure the neutrino mass per se, but rather its indirect effect on the clustering statistics of the CMB/large-scale structure. It is not impossible that other cosmological parameters could give rise to similar effects (within measurement errors/cosmic variance). mν =0 ev mν =1.2 ev
Model dependence: parameter degeneracies... We do not measure the neutrino mass per se, but rather its indirect effect on the clustering statistics of the CMB/large-scale structure. It is not impossible that other cosmological parameters could give rise to similar effects (within measurement errors/cosmic variance). mν =0 ev mν =1.2 ev Tweak H0
Model dependence: parameter degeneracies... We do not measure the neutrino mass per se, but rather its indirect effect on the clustering statistics of the CMB/large-scale structure. It is not impossible that other cosmological parameters could give rise to similar effects (within measurement errors/cosmic variance). mν =0 ev mν =1.2 ev Tweak H0 and ωdm Imagine what might happen if we drop spatial flatness, or vary the dark energy EoS, etc. too...
Post-Planck... Ade et al.[planck] 2013 ΛCDM+neutrino mass (7 parameters) 95% C.L. upper limits WMAP (9 years) W9 + ACT Planck + WMAP Polarisation Planck + WP + ACT ℓ > 1000 + SPT ℓ > 2000 mν <0.66 ev (95 % C.L.) Best CMB-only bound W7+ matter power spectrum + HST H 0 Planck + WP + (ACT ℓ > 1000 + SPT ℓ > 2000) + baryon acoustic oscillations mν <0.25 ev (95 % C.L.) Best minimal bound Dropping assumption of spatial flatness: mν <0.32 ev Other extensions?? (95 % C.L.)
Discrepancies potentially resolved by neutrino physics??
Planck discrepancies with other observations... Hubble parameter H0: Planck-inferred value lower than local HST measurement. Alleviated by postulating Neff > 3? Small-scale RMS fluctuation σ8: Planck CMB prefers a higher value than galaxy cluster count and galaxy shear from CFHTLens. Planck SZ clusters 0.3 σ 8 (Ωm / 0.27) =0.782±0.01 0.46 CFHTLens galaxy shear σ 8 (Ωm /0.27) =0.774±0.04 Ade et al. [Planck collaboration] 2013 Heymans et al. 2013
A neutrino solution?? My take: These discrepancies are most likely due to poorly understood nonlinearities. Cluster counts are particularly difficult to model. But at face value a sterile neutrino solution is possible. CMB+all (ΛCDM+ΔNeff+ms 8-parameter model) Δ N eff =0.61±0.30 ms =(0.41±0.13) ev Hamann & Hasenkamp 2013 also Wyman et al. 2013
A neutrino solution?? 68% and 95% contours CMB+all Reactor anomaly LSND CMB only Hamann & Hasenkamp 2013 also Wyman et al. 2013
Future sensitivities... (Planck is not the end of the story!!)
ESA Euclid mission selected for implementation... Launch planned for 2019. 6-year lifetime 15000 deg2 (>1/3 of the sky) Galaxies and clusters out to z~2 Photo-z for 1 billion galaxies Spectro-z for 50 million galaxies Optimised for weak gravitational lensing (cosmic shear)
Expected sensitivity... A 7-parameter forecast: Hamann, Hannestad & Y3W 2012 Most optimistic c = CMB (Planck); g = Euclid galaxy clustering s = Euclid cosmic shear; x = Euclid shear-galaxy cross Σmν potentially detectable at 5σ+ with Planck+Euclid (assuming nonlinearities to be completely under control)
Expected sensitivity... A 7-parameter forecast: Hamann, Hannestad & Y3W 2012 Moderate 2σ+ detection (only shear nonlinearities under control) Very pessimistic No knowledge of nonlinearities Most optimistic c = CMB (Planck); g = Euclid galaxy clustering s = Euclid cosmic shear; x = Euclid shear-galaxy cross Σmν potentially detectable at 5σ+ with Planck+Euclid (assuming nonlinearities to be completely under control)
Summary... Precision cosmological observables can be used to measure the absolute neutrino mass scale based on the effect of neutrino free-streaming. Existing precision cosmological data already provide strong constraints on the neutrino mas sum. No significant formal improvement between the best pre-planck and postplanck upper bounds (at least not for the minimal 7-parameter model). But the post-planck bound is arguably more robust. There are outstanding discrepancies between Planck and measurements from HST, clusters, and cosmic shear. Taken at face value these discrepancies can be resolved by new neutrino physics (although not necessarily the same physics in all cases...). But personally I'd take it cum grano salis.