Neutrino masses from cosmological observables

1
Neutrino masses from cosmological observables

• Sergio Pastor (IFIC)
• Benasque Cosmology workshop
• 15 / 08 / 2006

2
Outline
Introduction the Cosmic Neutrino Background
Relic Neutrinos as DM
Neutrino masses from cosmological observables
Effect of neutrino masses on cosmological
observables
Current bounds and future sensitivities
3
This is a neutrino!
4
Neutrinos coupled by weak interactions(in
equilibrium)
Free-streaming neutrinos (decoupled) Cosmic
Neutrino Background
Neutrinos keep the energy spectrum of a
relativistic fermion with eq form
Primordial Nucleosynthesis
TMeV tsec
5
Relativistic neutrinos
At least 2 species are NR today
TeV

• Neutrino cosmology is interesting because Relic
  neutrinos are very abundant
• The CNB contributes to radiation at early times
  and to matter at late times (info on the number
  of neutrinos and their masses)
• Cosmological observables can be used to test
  non-standard neutrino properties

6
Evolution of the background densities 1 MeV ? now
Oi ?i/?crit
7
The Cosmic Neutrino Background

• Number density
• Energy density

Massless
Massive m?gtgtT
8
We know that flavour neutrino oscillations exist
From present evidences of oscillations from
experiments measuring atmospheric, solar, reactor
and accelerator neutrinos
Evidence of Particle Physics beyond the Standard
Model !
9
Mixing Parameters...
From present evidences of oscillations from
experiments measuring atmospheric, solar, reactor
and accelerator neutrinos
Mixing matrix U
Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122
10
Mixing Parameters...
From present evidences of oscillations from
experiments measuring atmospheric, solar, reactor
and accelerator neutrinos
Mixing matrix U
Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122
11
... and neutrino masses
Data on flavour oscillations do not fix the
absolute scale of neutrino masses
eV
NORMAL
INVERTED
atm
solar
What is the value of m0 ?
12
Direct laboratory bounds on m?
Searching for non-zero neutrino mass in
laboratory experiments

• Tritium beta decay measurements of endpoint
  energy
• m(?e) lt 2.2 eV (95 CL) Mainz-Troitsk
• Future experiments (KATRIN) m(?e) 0.3 eV
• Neutrinoless double beta decay if Majorana
  neutrinos
• 76Ge experiments ImeeI lt 0.4hN eV

13
Absolute mass scale searches
Tritium ? decay lt 2.2 eV
Neutrinoless double beta decay lt 0.4-1.6 eV
14
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

15
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

16
Neutrinos as Hot Dark Matter
Massive Neutrinos can still be subdominant DM
limits on m? from Structure Formation (combined
with other cosmological data)
17
Power Spectrum of density fluctuations
18
Neutrinos as Hot Dark Matter effect on P(k)
Massive Neutrinos can still be subdominant DM
limits on m? from Structure Formation (combined
with other cosmological data)

• Effect of Massive Neutrinos suppression of
  Power at small scales

f?
19
Structure formation after equality
baryon and CDM experience gravitational clustering
20
Structure formation after equality
baryon and CDM experience gravitational clustering
21
Structure formation after equality
baryon and CDM experience gravitational clustering
22
Structure formation after equality
baryon and CDM experience gravitational clustering
growth of dr/r (k,t) fixed by  gravity vs.
expansion  balance ? dr/r ? a
23
Structure formation after equality
baryon and CDM experience gravitational clustering
neutrinos experience free-streaming with v c
or ltpgt/m
24
Structure formation after equality
baryon and CDM experience gravitational clustering
baryon and CDM experience gravitational clustering
neutrinos experience free-streaming with v c
or ltpgt/m
25
Structure formation after equality
baryon and CDM experience gravitational clustering
baryon and CDM experience gravitational clustering
neutrinos experience free-streaming with v c
or ltpgt/m

• neutrinos cannot cluster below a diffusion
  length
• l ? v dt lt ? c dt

26
Structure formation after equality
baryon and CDM experience gravitational clustering
baryon and CDM experience gravitational clustering
neutrinos experience free-streaming with v c
or ltpgt/m

• neutrinos cannot cluster below a diffusion
  length
• l ? v dt lt ? c dt

27
Structure formation after equality
J.Lesgourgues SP, Phys Rep 429 (2006) 307
astro-ph/0603494
28
Structure formation after equality
a
dcdm
db
1-3/5fn
a
Massive neutrinos f?0.1
dn
dg
metric
J.Lesgourgues SP, Phys Rep 429 (2006) 307
astro-ph/0603494
29
Effect of massive neutrinos on P(k)
Observable signature of the total mass on P(k)
P(k) massive P(k) massless
various f?
Lesgourgues SP, Phys. Rep. 429 (2006)
307
30
DATA on CMB temperature /polarization anisotropies
31
Effect of massive neutrinos on the CMB spectra

• Direct effect of sub-eV massive neutrinos on the
  evolution of the baryon-photon coupling is very
  small
• Impact on CMB spectra is indirect non-zero O?
  today implies a change in the spatial curvature
  or other Oi . The background evolution is
  modified
• Ex in a flat universe,
• keep O?OcdmObO?1
• constant

32
Effect of massive neutrinos on the CMB spectra
Problem with parameter degeneracies change
in other cosmological parameters can mimic the
effect of nu masses
33
Effect of massive neutrinos on the CMB and Matter
Power Spectra
Max Tegmark www.hep.upenn.edu/max/
34
How to get a bound (measurement) of neutrino
masses from Cosmology
Fiducial cosmological model (Obh2 , Omh2 , h ,
ns , t, Sm? )
PARAMETER ESTIMATES
35
Cosmological Data

• CMB Temperature WMAP plus data from other
  experiments at large multipoles (CBI, ACBAR,
  VSA)
• CMB Polarization WMAP,
• Large Scale Structure
• Galaxy Clustering (2dF,SDSS)
• Bias (Galaxy, ) Amplitude of the Matter P(k)
  (SDSS,s8)
• Lyman-a forest independent measurement of
  power on small scales
• Baryon acoustic oscillations (SDSS)
• Bounds on parameters from other data SNIa (Om),
  HST (h),

36
Cosmological Parameters example
SDSS Coll, PRD 69 (2004) 103501
37
Cosmological bounds on neutrino mass(es)
A unique cosmological bound on m? DOES NOT exist !
38
Cosmological bounds on neutrino mass(es)
A unique cosmological bound on m? DOES NOT exist !

• Different analyses have found upper bounds on
  neutrino masses, since they depend on
• The combination of cosmological data used
• The assumed cosmological model number of
  parameters (problem of parameter degeneracies)
• The properties of relic neutrinos

39
Cosmological bounds on neutrino masses using WMAP1
Bound on Sm? (eV) 95 CL Data used
Ichikawa et al, PRD 71 (2005) 043001 Sánchez et al, MNRAS 366 (2006) 189 MacTavish et al, astro-ph/0507503 1.6 - 3.1 CMB only
Hannestad, JCAP 0305 (2003) 004 SDSS Coll., PRD 69 (2004) 103501 Barger et al, PLB 595 (2004) 55 Crotty et al, PRD 69 (2004) 123007 Rebolo et al, MNRAS 353 (2004) 747 Fogli et al. PRD 70 (2004) 113003 Seljak et al, PRD 71 (2005) 103515 Sánchez et al, MNRAS 366 (2006) 189 MacTavish et al, astro-ph/0507503 1.0 - 1.7 0.6-1.2 WMAP1, other CMB, 2dF/SDSS-gal HST,SNIa
WMAP Coll., ApJ Suppl 148 (2003) 175 Fogli et al. PRD 70 (2004) 113003 Seljak et al, PRD 71 (2005) 103515 MacTavish et al, astro-ph/0507503 Hannestad, hep-ph/0409108 0.42-0.68 WMAP1, other CMB, 2dF/SDSS-gal, 2dF/SDSS-bias and/or Ly-a
40
Cosmological bounds on neutrino masses using WMAP3
Bound on Sm? (eV) 95 CL Data used
WMAP Coll., astro-ph/0603449 Fukugita et al, astro-ph/0605362 Kristiansen et al, astro-ph/0608017 1.7 2.3 CMB only
WMAP Coll., astro-ph/0603449 Goobar et al, astro-ph/0602155 0.68 0.91 WMAP3, other CMB, 2dF/SDSS-gal, SNIa
Goobar et al, astro-ph/0602155 Seljak et al, astro-ph/0604335 Kristiansen et al, astro-ph/0608017 0.17-0.48 WMAP3, other CMB, 2dF/SDSS-gal, SDSS-BAO and/or Ly-a
Fogli et al., hep-ph/0608060
41
Neutrino masses in 3-neutrino schemes
CMB galaxy clustering
Fig from Strumia Vissani, NPB726(2005)294
42
0?2? and Cosmology
Fogli et al., hep-ph/0608060
43
Future sensitivities to Sm?
When future cosmological data will be available

• CMB (TP) galaxy redshift surveys
• CMB (TP) and CMB lensing
• Weak lensing surveys
• Weak lensing surveys CMB lensing

44
PLANCKSDSS

• Fisher matrix analysis expected sensitivities
  assuming a fiducial cosmological model, for
  future experiments with known specifications

Fiducial cosmological model (Obh2 , Omh2 , h ,
ns , t, Sm? ) (0.0245 , 0.148 , 0.70 , 0.98 ,
0.12, Sm? )
45
Future sensitivities to Sm? new ideas
weak gravitational and
CMB lensing lensing
No bias uncertainty Small scales much closer to
linear regime Tomography 3D reconstruction
Makes CMB sensitive to smaller neutrino masses
46
Future sensitivities to Sm? new ideas
weak gravitational and
CMB lensing lensing
sensitivity of future weak lensing
survey (4000º)2 to m? s(m?) 0.1 eV Abazajian
Dodelson PRL 91 (2003) 041301
sensitivity of CMB (primary lensing) to
m? s(m?) 0.15 eV (Planck) s(m?) 0.044 eV
(CMBpol) Kaplinghat, Knox Song PRL 91 (2003)
241301 Lesgourgues, Perotto, SP Piat PRD 73
(2006) 045021
47
CMB lensing recent analysis
s(M?) in eV for future CMB experiments alone
Lesgourgues et al, PRD 73 (2006) 045021
48
CMB lensing recent analysis
Perotto et al, astro-ph/06062271
49
Summary of future sensitivities
Lesgourgues SP, Phys. Rep. 429 (2006) 307
Future cosmic shear surveys
50
For more details see
Physics Reports 429 (2006) 307-379
astro-ph/0603494
51
Conclusions
Cosmological observables can be used to bound
(or measure) the absolute scale of neutrino
masses. Information complementary to laboratory
results
?
Current bounds on the sum of neutrino masses
from cosmological data (best Sm?lt0.2-0.4 eV,
conservative Sm?lt1 eV)
Sub-eV sensitivity in the next future (0.1-0.2
eV and better) Test degenerate mass region
and eventually the IH case