Are we close to measuring the neutrino hierarchy? - PowerPoint Presentation

Are we close to measuring the neutrino hierarchy? Filipe B. Abdalla ν Loureiro , Moraes , Abdalla et al. arXiv:1809.07204 Loureiro , Cuceu , Abdalla et al. arXiv:1811.02578

OutlineCosmology backgroundNeutrino effects on the observables Measuring LSS with BOSS and spherical harmonics The parameter constraints Future bounds

Standard model of cosmology:Dark energy & dark matter exists, No budget for neutrino mass: Observational data Type Ia Supernovae Galaxy Clusters Cosmic Microwave Background Large Scale StructureGravitational Lensing Physical effects: Geometry Growth of Structure

Physics Motivation: Neutrino Physics – Mass hierarchies Neutrinos Oscillate2 possible hierarchies given neutrino data: normal and inverted 2 possible scenarios: Quasi-degenerate or non-degenerate spectrum Unknowns: Which hierarchy - mass effects, 3 rd mixing angleAbsolute mass scale - beta decay / 0xnu 2xbeta

Neutrino oscillations indicate they have mass! But not on the absolute scale of mass… Beta-decay kinematics Neutrinoless double beta-decay Cosmology! KATRIN nemo Loureiro , Cuceu , Abdalla et al (2019 ) For example… Not just interesting physics but, an integral part of the cosmological model… Age of precision Cosmology Neutrino mass/hierarchy…a test of LCDM

OutlineCosmology backgroundNeutrino effects on the observables Measuring LSS with BOSS and spherical harmonics The parameter constraints Future bounds

T < eV T ~ MeV Formation of Large Scale Structures LSS Cosmic Microwave Background CMB Primordial Nucleosynthesis BBN No flavour sensitivity N eff & N mass & m ν ν e vs ν μ,τ N eff Relic neutrinos influence several cosmological epochs

Neutrino Physics - CMB CMB is affected by neutrino physics However degeneracies are large CMB insensitive to neutrino masses smaller than 1eV as they become non-relativistic after the CMB is set up. Does not consider the deflection spectrum

Neutrinos as Dark Matter Neutrinos are natural DM candidates They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter First structures to be formed when Universe became matter -dominated Ruled out by structure formation CDM Neutrino Free Streaming F b, cdm n

Colombi, Dodelson, & Widrow 1995 Three observable:overall damping of the power spectrum at small scales Scale where this damping occurGrowth of structure Neutrino Physics LSS k > k nr = 0.026 (m  /1 eV)1/2 m1/2 h/Mpc Can we distinguish between cases with N neutrinos with mass M and N/2 neutrinos with mass 2M? (0 eV,3) (0 eV,7) (2.25 eV,7)

OutlineCosmology backgroundNeutrino effects on the observables Measuring LSS with BOSS and spherical harmonics The parameter constraints Future bounds

MegaZ DR7Sloan Digital Sky Survey (BOSS) Loureiro , Moraes, Abdalla et al. arXiv:1809.07204 Luminous Red Galaxies (LRGs) 1.1M LRGs ~8000 square degrees Volume: 3.3 (Gpc /h)^3 0.45 < z < 0.65 Leading Spectroscopic Survey today, analysis in shells to combine with Photometry.

(3) + Partial Sky Convolution (2) + Redshift Space Distortions (1) Exact Equation BOSS Angular Power Spectra: Theory Project mass distribution once again Window Function Weight Theoretical Profiles (Exact equation) Dimensionless Power Spectrum

Mixing matrix profile Therefore small correlation between multipole bands introduced by partial sky after binning BOSS Angular Power Spectra: Theory Redshift Space Distortions Partial Sky Convolution Redshift distance = real distance + peculiar velocity Taylor expand + continuity equation and a little algebra… Get effectively: E.g. Fisher et al. 1994 Padmananhan et al. 2007

MegaZ DR7Angular Power Spectra: Measurement E.g. Peebles… Spherical harmonic analysis Four redshift bins: 0.45 < z < 0.50 Project galaxies in a bin onto the plane in the sky Partial sky - correction to coefficients

BOSS Angular Power Spectra: Results

OutlineCosmology backgroundNeutrino effects on the observables Measuring LSS with Boss and spherical harmonics The parameter constraints Future bounds

Bin 0-12: OmegaM Omegab plane. BOSS Angular Power Spectra: Consistency checks

Mainstream results, comparison with standard BOSS analysis

Cosmological bounds on neutrino mass(es)A unique cosmological bound on mν DOES NOT exist ! Different analyses have found upper bounds on neutrino masses, but they depend on The assumed cosmological model: number of parameters (problem of parameter degeneracies) The combination of cosmological data used Skordis et al. 06

Neutrino Modelling

Cosmology and NeutrinosKomatsu et al. [arXiv:0803.0547] < 1.3 eV (CMB) < 0.67 eV (CMB+SN+BAO)Tereno et al. [arXiv:0810.0555] < 0.54 eV (CMB+SN+BAO+WL)Ichiki , Takada & Takahashi [arXiv:0810.4921] < 0.54 eV (CMB+SN+BAO+WL)De Bernardis et al. 08 < 0.28 eV (+ bias DEEP2 /LBG) Seljak et al. [arXiv:0604335] < 0.17 eV (+ Lyman Alpha…) Thomas, Abdalla & Lahav [0911.5291] PRL < 0.28eV (CMB + LSS + SNe) Systematics limited? Using all the aforementioned probes for complementary data constraint R ecent BAO data and production of newest galaxy clustering angular power spectrum CMB+SDSS+SN+BAO+HST With luminous Red Galaxies (LRGs) sampling a large cosmic volume Cosmology is starting to predict that experiments such as KATRIN (mentioned earlier) will not detect anything GOAL : 0.05eV

Summary Presented an alternative BOSS LSS analysis Much more natural to include cross correlations with photometric data. Results on Standard LCDM comparable with state of the art analysis by the BOSS team Combined with other experiments, we find that approximations of how the neutrino mass spectrum is modeled are starting to affect constraints. A full hierarchy modelling yields a constraint on the smallest mass (<0.08eV 95%) Systematics and limitations still exist though… improvement on mass constraints was minimal over the last decade (0.17 -> 0.12 eV) The Future is promising but with work to be done… inclusion of photometric data to cross correlate. Results here don’t inlcude the latest Planck results. GOAL: 0.05eV + Hierarchy Background Impact on neutrino physics? Problems and prospects