Cosmological neutrinos - PDF Free Download

Cosmological neutrinos Yvonne Y. Y. Wong CERN & RWTH Aachen APCTP Focus Program, June 15-25, 2009

2. Neutrinos and structure formation: the linear regime

Relic neutrino background: Temperature: 4 T,0 = 11 Origin of density perturbations? 1 /3 T CMB, 0=1.95 K Number density per flavour: n,0= 6 3 3 3 T, 0= 112 cm 2 4 Nucleosynthesis Last scattering surface (CMB) Structure formation Energy density per flavour: If m > 1 mev Neutrino dark matter h2= m 93 ev

Neutrino dark matter... Evidence for neutrino masses from neutrino oscillations experiments : 2 3 2 m ~2 10 ev atm m2sun ~8 10 5 ev 2 Large mixing between flavours: [ ][ e 0.82 0.54 = 0.31 0.47 0.47 0.71 ][ ] 0.21 1 0.69 2 0.69 3

Oscillation data allow for two mass hierarchies: m2atm ~2 10 3 ev2 2 msun ~8 10 5 ev 2 Normal hierarchy min m ~0.05 ev Mininum amount of neutrino dark matter Inverted hierarchy min m ~0.05 ev min ~0.1 %

Upper limit on neutrino masses from tritium -decay: Large mixing means 2 U ei ~O 0.1 1 me U m 2 i ei 2 i 1/2 2.2 ev Electron energy (kev) max m ~7 ev max ~12 % Light neutrinos cannot be the only dark matter component

Neutrino dark matter is hot... Large velocity dispersion: v thermal 81 1 z ev m km s 1 A dwarf galaxy has a velocity dispersion of 10 km s-1 or less, a galaxy about 100 km s-1. Sub-eV neutrinos have too much thermal energy to be packed into galaxy-size self-gravitating systems. Neutrinos cannot be the dominant Galactic dark matter.

Why study neutrinos and cosmic structures... Hot dark matter leaves a distinctive imprint on the large-scale structure distribution. We can learn about neutrino properties from cosmology. Cosmological probes are getting ever more precise: Even a small neutrino mass can bias the inference of other cosmological parameters.

The concordance framework... We work within the CDM framework extended with a subdominant component of massive neutrino dark matter. Flat geometry. Initial conditions from standard single-field slow-roll inflation. Baryons

Plan... Describing massive neutrinos in cosmology: formalism Signatures of massive neutrinos and non-standard interactions Present constraints Future sensitivities

Useful references... J. Lesgourgues and S. Pastor, Massive neutrinos and cosmology, Phys. Rep. 429 (2006) 307 [astro-ph/0603494]. C.-P. Ma and E. Bertschinger, Cosmological perturbation theory in the synchronous and conformal Newtonian gauges, Astrophys. J. 455 (1995) 7 [astro-ph/9506072]. E. Bertschinger, Cosmological dynamics, astro-ph/9503125.

2.1 Describing massive neutrinos in cosmology: formalism...

Phase space density... Any fluid can be specified by its phase space distribution function f(x,p, ). Number of particles in phase space volume d3x d3p dn = 1 3 3 f x, p, d x d p 3 2 In a homogeneous and isotropic universe : All relativistic fluids and decoupled fluids after e+e- annihilation. f x, p, = f 0 p, = f 0 a p Define a comoving momentum: q a p f x, p, f x, q, f 0 a p f 0 q

Boltzmann equation... Starting point of all calculations: Collisions Phase space density f x, q, D f f dx f dq f =C [ f ] D d x d q Velocity Force Collisions = particle scattering. If C[f]=0, Boltzmann equation describes the motion of phase space elements in a conservative force field.

Linear perturbation theory... Perturbative expansion: f x, q, = f 0 q f 1 x, q,... nth-order Boltzmann equations (ignoring collisions): 0th order 1st order f0 dq/d =0 f1 q f1 dq f0 =0 x d q... is a perturbation Comoving energy 2 q 2 a 2 m2 =a 2 p 2 m2

In Fourier space... It is more convenient to compute in Fourier space. f1 q f1 dq f0 =0 x d q Fourier transform of dq/d Boltzmann eqn in k-space Formal solution [ ] f 1 q dq f0 i k q f 1 F =0 d q [ ] dq f 0 f 1 k, q, = f 1 k, q, 0 d ' exp i ' d ' ' k q/ F d q 0

What is the force dq/d... Newtonian gravity (nonrelativistic particle, subhorizon scales): dq = a m q d [ ] dq F = i a m k q d Gravitational potential

What is the force dq/d... Newtonian gravity (nonrelativistic particle, subhorizon scales): dq = a m q d [ ] dq F = i a m k q d Gravitational potential General relativity: Conformal Newtonian gauge: From the geodesic eqn ds 2=a 2 [ 1 2 d 2 1 2 dx i dxi ] dq = q 2 a 2 m2 q q d 1st order in and

Cold dark matter... We are interested in bulk quantities such as Density perturbation 1 d3q c= f1 3 n 2 Divergence of the bulk velocity field i d3q q c = f 1 k q 3 n 2 Construct equations of motion for these quantities by integrating the Boltzmann equation over momentum q: [ ] f 1 q dq f0 i k q f 1 F =0 d q

c c 3 =0 Conformal Newtonian gauge 3 d q Integrating over 2 3 EoM for density perturbations: Continuity equation Ignore all terms of order (q/ )2 and higher, i.e., ignore thermal motion of CDM d3q q Integrating over i k q 3 2 3 2 a 1 d q q 2 2 c c k k q f 1=0 3 a n 2 =0 a c c k 2 =0 a EoM for velocity divergence: Euler equation

Stress-energy tensor for CDM: Velocity perturbations i v k Unperturbed part [ T = 0 0 0 0 0 0 0 0 0 0 0 ][ v v v 0 0 0 v 0 0 0 0 0 v 0 0 0 0 v 0 Perturbed part ]

Neutrinos... Massive neutrinos are more difficult: Evolve from a relativistic to a nonrelativistic species. Must solve Boltzmann equation for each individual f 1 k, q,. Common approach: Expand f 1 k, q, in a Legendre series: n f 1 k,, q, = i 2 n 1 n k, q, P n n=0 1 1 n k, q, = d f 1 k,, q, P n n 1 2 i The nth moment Legendre polynomials q k

Each multipole moment can be related to a bulk quantity: 0th moment: d3q =a 0 3 2 4 3 2 1 4 d q q P = a 0 3 3 2 1st moment: 3 d q q 4 P =k a 1 3 2 Perturbations in the neutrino energy density and pressure 2nd moment: 2 3 2 d q q 4 P = a 2 3 3 2 Divergence in the neutrino bulk velocity field Neutrino anisotropic stress

Stress-energy tensor for neutrinos: [ T = 0 0 0 Perturbed part [ 0 P 0 0 0 0 P 0 0 0 0 P ] Unperturbed part Velocity perturbations i v k v v P v P P v P P P P v P P P P v P P P P Anisotropic stress ]

Equations of motion for the multipole moments (derived from the Boltzmann equation): Gravitational source terms for the 0th and 1st moments d f0 qk 0= 1 d ln q d f0 k qk 1= 0 2 2 3 3 q d ln q qk n 2= [n n 1 n 1 n 1 ] 2 n 1 No source terms for n 2 nth moment couples to the (n-1)th and (n+1)th moments

2 5 10 15 Lesgourgues and Pastor 2006

How the potentials relate to the perturbations... Apply the Einstein equation: G =8 G T [ 3 a i i k =4 G a i i 2 i P k a i 2 2 k =12 Ga i P i i 2 2 ] i cf. Poisson equation for Newtonian gravity: k 2 =4 G a 2 i i matter

2.2 Signatures...

2.2.1 Neutrino masses...

Neutrino masses... Neutrino masses have two effects on cosmological observables On the background: Shift in time of matter radiation equality. On the perturbations: Suppression of growth.

Background... Sub-eV neutrinos become nonrelativistic at z<1000: Radiation at early times. Matter at late times. Comoving matter density today Comoving matter density before recombination Shift in matter-radiation equality relative to model with zero neutrino mass. m = 1 ev m = 0 ev

Neutrino masses... Neutrino masses have two effects on cosmological observables On the background: Shift in time of matter radiation equality. On the perturbations: Suppression of growth.

Perturbations... At low redshifts, neutrinos become nonrelativistic:. ev But still have large thermal speed: c 81 1 z m hinder clustering on small scales. c km s 1 c Gravitational potential wells Free-streaming length scale & wavenumber: 8 2 c 2 1 z ev FS 4.2 m,0 m 3 m H 2 2 k FS FS h 1 Mpc FS Clustering k k FS FS Non-clustering k k FS

In turn, free-streaming (non-clustering) neutrinos slow down the growth of gravitational potential wells on scales << FS or wavenumbers k >> kfs. Clustering potential wells become deeper c c Some time later... Both CDM and neutrinos cluster c c c c c Only CDM clusters

Clustering regime Massive neutrinos, m =1 ev k =10 2 h Mpc 1 k FS kfs >> ~a cdm b, Lesgourgues and Pastor 2006

Non-clustering regime Massive neutrinos, m =1 ev 1 k =1 h Mpc k FS kfs << a cdm b a1-3/5f (f = / ) m, Lesgourgues and Pastor 2006

δcdm Initial time... δcdm Some time later... CDM-only CHDM k k kfs The presence of HDM slows down the growth of CDM perturbations at large wavenumbers k. The density perturbation spectrum acquires a step-like feature.

Large scale matter power spectrum, P(k) CMB Galaxy clustering surveys Lyman-α f = Neutrino fraction P 8 f 8 m P h = 2 m 93 ev

Large scale matter power spectrum, P(k) CMB Galaxy clustering surveys Linear k 3 P k 1 2 2 Lyman-α f = Neutrino fraction P 8 f 8 m P h = 2 m 93 ev

Present status... WMAP5 only Dunkley et al. 2008 95% C.L. upper limit + Galaxy clustering Tegmark et al. 2006 + SN + BAO Goobar et al. 2006 Break degenercies + Weak lensing Tereno et al. 2008 Ichiki et al. 2008 or + Lyman-α Seljak et al. 2006 WMAP3... and many more.

2.2.2 Non-standard interactions...

Non-standard neutrino interactions... A distinguishing feature of free-streaming neutrinos is their anisotropic stress. P = 3 2 2 4 d q q ka 2 3 3 2 k =0.1 h Mpc 1 Lesgourgues & Pastor 2006

Neutrino anisotropic stress changes the gravitational potentials: From Einstein eqn [ 3 a i i k =4 G a i i 2 i P k a i 2 2 k =12 Ga i P i i 2 2 ] i Serves as a damping term for the acoustic oscillations of the photonbaryon fluid before recombination. Strong effect on the CMB primary anisotropies.

CMB TT spectrum No neutrino anisotropic stress Models with no neutrino anisotropic stress before recombination are disfavoured at >95% C.L. Hannestad 2005 Trotta & Melchiorri 2005 Standard

Non-standard interactions in the neutrino sector can suppress the anisotropic stress. Consider, e.g., the interaction + + : Hannestad & Scherrer 2000 EoM for the neutrino moments d f0 qk 0= 1 CMB data favour the The fact that d ln q presence of neutrino anisotropic stress = Interaction rate d f implies: k qk 0 before and at recombination 1= 0 2 2 3 3 q d ln q rate at q k int H rec Hubble recombination n 2= [n n 1 n 1 n 1 ] int n 2 n 1 int If interactions are strong: int H n 2 0

Constraints on a specific model... Hannestad & Raffelt 2005 Consider neutrinos coupled to a low mass pseudoscalar (m >> m ): L= i g jk j 5 k Possible binary processes: Interaction rate: 4 ~ g T Assuming relativistic neutrinos

log Weak interaction, ~T5 Hubble rate, ~T2 New interaction, ~T T ~ 1 MeV log T

int H rec g 10 7 log Weak interaction, ~T5 Hubble rate, ~T2 New interaction, ~T T < Trec ~ 0.2 ev T ~ 1 MeV log T

Neutrino lifetime g 10 int H rec 11 50 mev/m 2 10 10 m /50 mev 3 s Age of universe ~ 1017 s log Weak interaction, ~T5 Hubble rate, ~T2 Decay and inverse decay New interaction, ~T ' 2 ~ g m m 16 E 3 T < Trec ~ 0.2 ev T ~ 1 MeV log T Hannestad & Raffelt 2005, Basbøll et al. 2008

2.3. Future sensitivities...

WFMOS Planck High-z spectroscopic galaxy surveys, z>2 Photometric galaxy surveys with lensing capacity, zmax~3 Radio arrays, 5 < z < 15 MW A SNAP

Possible new techniques... Weak lensing of galaxies of the CMB Song & Knox 2004 Hannestad, Tu & Y3W 2006 Kitching et al. 2008 Lesgourgues et al. 2006 Perotto, Lesgourgues, Hannestad, Tu & Y3W, 2006 21 cm emission Mao et al. 2008 Pritchard & Pierpaoli 2008 Metcalf 2009 ISW effect Ichikawa & Takahashi 2005 Lesgourgues, Valkenburg & Gaztañaga 2007 Cluster abundance Wang et al. 2005

Weak lensing of galaxies/cosmic shear... Distortion (magnification or stretching) of distant galaxy images by foreground matter. Unlensed Distortions probe both luminous and dark matter (no galaxy bias problem!) Lensed

Unlensed Galaxies are randomly oriented, i.e., no preferred direction. Average galaxy shapes over cell Lensed Lensing leads to a preferred direction.

Shear map Weak lensing theory predicts: Cluster Void

Shear map Convergence map (projected mass) Weak lensing theory predicts: Cluster Void

Convergence power spectrum C l d a 0 2 [ ] 2 D ' d ' ngal ' D ' P k =l /D

Tomography = bin galaxy images by redshift z Tomography probes spectrum evolution and the growth function.

Convergence power spectra for 2 tomography bins Bin 2 autocorrelation 1 & 2 crosscorrelation Bin 2: 1.5 < z < 3 Bin 1 autocorrelation Bin 1: 0 < z < 1.5 Hannestad, Tu & Y3W 2006

Past: Present: Cosmic shear first detected in 2000. There are some ongoing surveys (e.g., CFHTLS). Future: Dedicated lensing surveys with capacity for tomography.

Future surveys with lensing capacity 2008 Space-based 2010 2015 Ground-based 201X Time SNAP

Projected sensitivities... Currently disfavoured at 95% C.L. Planck (1 year) Lesgourgues et al. 2006 Perotto, Lesgouruges, Hannestad, Tu & Y3W 2006 + Weak lensing with LSST (tomography) 95% sensitivities Hannestad, Tu & Y3W. 2006 Kitching et al. 2008 ~ 2015-2020 + BAO Ivezic et al. 2008 www.lsst.org

Projected sensitivities... Currently disfavoured at 95% C.L. Planck (1 year) WARNING! Lesgourgues et al. 2006 Perotto, Lesgouruges, Hannestad, Tu & Y3W 2006 These sensitvities can be achieved only if theoretical predictions of the matter power spectrum are accurate+ to ~ 1%. Weak lensing with LSST Huterer & Takada 2005 (tomography) 95% sensitivities ~ 2015-2020 Next talk Hannestad, Tu & Y3W. 2006 Kitching et al. 2008 + BAO Ivezic et al. 2008 www.lsst.org

Summary... The cosmic microwave background anisotropies and the large-scale structure distribution can be used to probe neutrino physics. Existing data already place strong constraints on Neutrino masses Non-standard neutrino interactions Future probes such as the Planck satellite and weak gravitational lensing will do even better.