夏陽 悉尼大学悉尼天文研究所 2015 年 9 月 14 日 中国科学院卡弗里理论物理研究所 宇宙中微子

Jan Hamann Sydney Institute for Astronomy 14 th September 2015, KITPC Beijing Neutrinos in Cosmology

Prelude Neutrinos in particle physics

What do we know about neutrinos? Z-decay measurements at LEP: three flavours*: ν e, ν μ, ν τ *there could be more, but they would either have to be heavy, or not take part in the weak interaction (sterile neutrinos)

What do we know about neutrinos? flavour eigenstates mass eigenstates unitary (PKMS) mixing matrix (3 angles, 1 phase) They have different mass and flavour eigenstates: if m i ≠ m j, neutrino flavours oscillate

What do we know about neutrinos? Neutrino oscillations have been observed in many experiments Mixing angles measured m 1 ≠ m 2 ≠ m 3 : solar neutrinos atmospheric neutrinos

What do we not know about neutrinos? What is their absolute mass scale? In the near future: KATRIN experiment with sensitivity of about 0.6 eV oscillations β-decay experiments

What do we not know about neutrinos? What is their mass hierarchy? mass normal m3m3 m2m2 m1m1 mass inverted m1m1 m2m2 m3m3

Are there additional (light) sterile neutrinos? Anomalies observed by Accelerator experiments Reactor experiments Gallium experiments Hints for additional state with Δm 2 ≈ eV 2 ? What do we not know about neutrinos? [Aguilar-Arevalo+ 2013] [Mention+ 2010] [Giunti&Laveder 2011] [Giunti+ 2014]

Part I Neutrinos in cosmology: theory

neutrinos decouple e + e - - annihilation

The Cosmic Neutrino Background (CνB) Neutrino decoupling around T = 1 MeV, shortly before goes out of equilibrium Annihilation heats CMB relative to CνB Neutrino mixing equilibrates momentum distributions If T reheating > 10 MeV, all three flavours populated Direct detection extremely difficult, but may not be entirely impossible? Capture of relic neutrinos by Tritium nuclei (PTOLEMY) [Weinberg 1962; Betts+ 2013]

The role of neutrinos in cosmology Geometry Energy content Cosmological principle (slightly perturbed) SM particles and interactions Dark matter (cold) Dark energy (Cosmological constant) Neutrinos

Particle content of the Universe (after BBN) interactingnon-interacting relativistic (radiation) photonsneutrinos non-relativistic (matter) baryonscold dark matter

Impact of cosmological neutrinos Structure formation Evolution of perturbations Background evolution Neutrinos Big Bang Nucleosynthesis Background evolution Nuclear reactions

Neutrino parameters How much energy density do neutrinos contribute… … at early times? Fermi-Dirac vs. Bose-Einstein photon energy density lower neutrino temperature radiation energy density Effective number of neutrino species ΛCDM: N eff = (small deviation from Fermi-Dirac)

Neutrino parameters How much energy density do neutrinos contribute… … at early times? … at late times? Fermi-Dirac vs. Bose-Einstein photon energy density lower neutrino temperature radiation energy density Effective number of neutrino species neutrino energy density Sum of neutrino masses ΛCDM: N eff = 3.046ΛCDM: Σm ν = 0.06 eV (assumes lightest mass state is massless) (small deviation from Fermi-Dirac)

Part II Planck constraints on neutrinos

CMB angular power spectrum Mostly sensitive to neutrinos’ impact on background evolution Other cosmological parameters can to some extent mimic effect of changing neutrino mass or number of neutrino species (geometrical degeneracy) In extended models, combining with external data sets can help break degeneracies [Planck collaboration 2015]

Planck constraints on the sum of neutrino masses [Planck collaboration 2015] No sign of non-zero neutrino masses…

Planck constraints on the sum of neutrino masses CMB + lensing CMB + BAO + lensing Profile likelihood [Planck collaboration 2013] Constraints from Bayesian and frequentist methods are compatible

Planck constraints on the effective number of relativistic species [Planck collaboration 2015] Data confirm standard model expectation (CνB only, no more hints of additional light particles)

Planck results vs. BBN Deuterium abundance from Damped Ly-α system 4 He abundance from H II-regions [Planck collaboration 2015] Excellent match with BBN expectation + astrophysical element abundance measurements

Planck constraints on eV-mass sterile neutrinos [Planck collaboration 2015] Planck data not compatible with a fully thermalised eV-mass neutrino Want to save the scenario? Need to suppress production of steriles (e.g., lepton asymmetry, new interactions, etc.)

Part III Neutrinos and large scale structure

Free streaming gravitational potential x initial time gravitational potential x later time Velocity dispersion small wrt size of potential well Particles remain confined to potential well Cold dark matter neutrino

Free streaming gravitational potential x initial time gravitational potential x later time Velocity dispersion large wrt size of potential well Neutrinos escape from potential well, density perturbations get washed out Cold dark matter neutrino

Structure formation with massive neutrinos Σ m ν = 0 eV Σ m ν = 7 eV [simulation and movie by T. Haugbølle]

Matter power spectrum with massive neutrinos [Abazajian+ 2013] wavenumber

Matter power spectrum with massive neutrinos [Abazajian+ 2013] wavenumber Linear regime Non-linear regime

Nonlinear structure formation with massive neutrinos linear theory [Brandbyge+ 2008,2009,2010; Viel+ 2010, Ali-Haimoud+ 2012] Simulations with CDM and neutrino particles 0.15 eV 0.3 eV 0.45 eV 0.6 eV Theoretical prediction of matter power spectrum with massive neutrinos in the non-linear regime is a numerical challenge N-body simulations with neutrino particles, grid-based, hybrid approach…

Probes of the matter power spectrum Cluster counts Galaxy clustering Cosmic shear CMB lensing Lyman-α forest

Results in flux power spectrum which requires hydrodynamical simulations to be related to matter power spectrum

SDSS III Lyman-α forest data [Palanque-Delabrouille+ 2015] 1d flux power spectra

In the next 10 years… Improvements to CMB lensing data (polarisation!) from ground- and balloon- based CMB observations (e.g., POLARBEAR, SPTPol, BICEP3, etc.), possibly also space- based (LiteBird) Next-generation large scale structure surveys (DESI, Euclid, LSST) will map a good part of the local Universe out to redshift z ≈ 2

Future Large Scale Structure surveys Cluster countsGalaxy clustering Type Ia supernovae BAO scaleCosmic shear Geometric observables Perturbation-based observables

Parameter forecast (for a EUCLID-like experiment) [Hamann+ 2012] CMB Shear Galaxies (pessimistic) Galaxies (optimistic) Beautiful complementarity between different observables: combination breaks parameter degeneracies of individual probes

Parameter forecast (for a EUCLID-like experiment) Parameter sensitivities Sensitivity up to 10 meV for sum of neutrino masses, and up to 0.02 for effective number of neutrino species when observables are combined Can cleanly distinguish between effects of dark energy and neutrinos [Basse+ 2013]

Direct sensitivity to mass hierarchy? Assume minimal mass in inverted hierarchy Probably not… [Hamann+ 2012]

Conclusions The Universe continues to be boring: no evidence for anything unexpected in the cosmological neutrino sector With the next generation of large-volume galaxy surveys and CMB lensing measurements, a detection of the sum of neutrino masses is extremely likely, but still a lot of work to be done for theorists (non- linearities!)