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

2. Outline Cosmology background Neutrino effects on the observables
Measuring LSS with BOSS and spherical harmonics
The parameter constraints
Future bounds

3. 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 Structure
Gravitational Lensing
Physical effects:
Geometry
Growth of Structure

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

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

6. Outline Cosmology background Neutrino effects on the observables
Measuring LSS with BOSS and spherical harmonics
The parameter constraints
Future bounds

7. Relic neutrinos influence several cosmological epochs
T < eV
T ~ MeV
Formation of Large Scale Structures
LSS
Cosmic Microwave Background
CMB
Primordial
Nucleosynthesis
BBN
No flavour sensitivity Neff & Nmass & mν
νevs νμ,τ Neff

8. 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

9. 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 n F
b, cdm

10. Neutrino Physics LSS Three observable: (0 eV,3) (0 eV,7) (2.25 eV,7)
overall damping of the power spectrum at small scales
Scale where this damping occur
Growth of structure
Colombi, Dodelson, & Widrow 1995
k > knr = (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?

11. Outline Cosmology background Neutrino effects on the observables
Measuring LSS with BOSS and spherical harmonics
The parameter constraints
Future bounds

12. Luminous Red Galaxies (LRGs)
MegaZ DR7
Leading Spectroscopic Survey today, analysis in shells to combine with Photometry.
Luminous Red Galaxies (LRGs)
Sloan Digital Sky Survey (BOSS)
1.1M LRGs
~8000 square degrees
0.45 < z < 0.65
Volume: 3.3 (Gpc /h)^3
Loureiro, Moraes, Abdalla et al. arXiv:

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

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

15. MegaZ DR7 Angular Power Spectra: Measurement
Spherical harmonic analysis
E.g. Peebles…
Four redshift bins: 0.45 < z < 0.50
Project galaxies in a bin onto the plane in the sky
Partial sky - correction to coefficients

16. BOSS Angular Power Spectra: Results
Will be in paper and online will be able to get these Cls, as well as the full galaxy catalogue, cross Cls and various useful entities. Start to see anything interesting?

17. Outline Cosmology background Neutrino effects on the observables
Measuring LSS with Boss and spherical harmonics
The parameter constraints
Future bounds

18. BOSS Angular Power Spectra: Consistency checks
Bin 0-12: OmegaM Omegab plane.
About 3 1sigma error bars from profile BUT with data errors - therefore worse than that.

19. Mainstream results, comparison with standard BOSS analysis

20. 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

21. Neutrino Modelling

23. GOAL : 0.05eV Cosmology and Neutrinos
Komatsu et al. [arXiv: ] < 1.3 eV (CMB) < 0.67 eV (CMB+SN+BAO)
Tereno et al. [arXiv: ] < 0.54 eV (CMB+SN+BAO+WL)
Ichiki, Takada & Takahashi [arXiv: ] < 0.54 eV (CMB+SN+BAO+WL)
De Bernardis et al < 0.28 eV (+ bias DEEP2 /LBG)
Seljak et al. [arXiv: ] < 0.17 eV (+ Lyman Alpha…)
Thomas, Abdalla & Lahav [ ] PRL < 0.28eV (CMB + LSS + SNe)
Systematics limited?
Using all the aforementioned probes for complementary data constraint
Recent 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

24. 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