1. Precision cosmology and neutrinosν
Sergio Pastor (IFIC)
NOW 2006
Conca Specchiulla, September 2006
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

2. Precision cosmology and neutrinosν
Sergio Pastor (IFIC)
NOW 2006
Conca Specchiulla, September 2006
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

3. Outline Precision cosmology and neutrinos Introduction: the Cosmic
Neutrino Background
Precision cosmology and neutrinos
Relic Neutrinos as DM
Effect of neutrino masses
on cosmological observables
Current bounds and
future sensitivities
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

4. This is a
neutrino!
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

5. Neutrinos coupled by weak interactions (in equilibrium)
Nucleosynthesis
Primordial
T~MeV
t~sec
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

6. Neutrinos coupled by weak interactions (in equilibrium)
Free-streaming neutrinos (decoupled)
Cosmic Neutrino Background
Neutrinos coupled by weak interactions (in equilibrium)
Neutrinos keep the energy
spectrum of a relativistic
fermion with eq form
T~MeV
t~sec
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

7. Relativistic neutrinos
T~eV
At least 2 species are NR today
Relativistic neutrinos
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
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

8. The Cosmic Neutrino Background
Neutrinos decoupled at T~MeV, keeping a
spectrum as that of a relativistic species
Number density
Energy density
At present per flavour
Contribution to the energy
density of the Universe
Massless
Massive
mν>>T
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

9. Evolution of the background densities: 1 MeV → now
photons
neutrinos
cdm
baryons Λ
Ωi= ρi/ρcrit
m3=0.05 eV
m2=0.009 eV
m1≈ 0 eV
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

10. Possible values of the neutrino masses
Data on flavour oscillations do not fix the absolute scale of neutrino masses eV m0 eV
atm
solar
NORMAL
INVERTED
atm
solar
What is the value of m0 ?
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

11. Absolute mass scale searches
Tritium  decay
< 2.2 eV
Neutrinoless double beta decay
< eV
< eV
Cosmology
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

12. 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 are very large
Ruled out by structure formation CDM
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

13. Neutrinos as Hot Dark Matter
Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data)
Talks by Ø. Elgarøy
and M. Viel
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

14. Power Spectrum of density fluctuations
Field of density
Fluctuations
Matter power spectrum is
the Fourier transform of the
two-point correlation function
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

15. Neutrinos as Hot Dark Matter: effect on P(k)
Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data)
Effect of Massive Neutrinos: suppression of Power at small scales fν
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

16. Structure formation after equality
baryon and CDM
experience
gravitational
clustering

17. Structure formation after equality
baryon and CDM
experience
gravitational
clustering

18. 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

19. Structure formation after equality
baryon and CDM
experience
gravitational
clustering
neutrinos
experience
free-streaming
with
v = c or <p>/m

20. Structure formation after equality
baryon and CDM
experience
gravitational
clustering
baryon and CDM
experience
gravitational
clustering
neutrinos
experience
free-streaming
with
v = c or <p>/m

21. Structure formation after equality
baryon and CDM
experience
gravitational
clustering
baryon and CDM
experience
gravitational
clustering
neutrinos
experience
free-streaming
with
v = c or <p>/m
neutrinos cannot cluster below a diffusion length
l = ∫ v dt < ∫ c dt

22. Structure formation after equality
baryon and CDM
experience
gravitational
clustering
baryon and CDM
experience
gravitational
clustering
neutrinos
experience
free-streaming
with
v = c or <p>/m
for (2p/k) < l ,
free-streaming supresses growth of structures during MD
 dr/r  a1-3/5 fn with fn = rn /rm ≈ (Smn)/(15 eV)
neutrinos cannot cluster below a diffusion length
l = ∫ v dt < ∫ c dt

23. Effect of massive neutrinos on P(k)
Observable signature of the total mass on P(k) :
P(k) massive
P(k) massless
various fν
Lesgourgues & SP, Phys. Rep. 429 (2006) 307

24. DATA on CMB temperature /polarization anisotropies
Map of CMBR temperature
Fluctuations
Multipole Expansion
Angular Power Spectrum
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

25. 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 Ων today implies a change in the spatial curvature or other Ωi . The background evolution is modified
Ex: in a flat universe,
keep ΩΛ+Ωcdm+Ωb+Ων=1
constant
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

26. Effect of massive neutrinos on the CMB spectra
Problem with parameter degeneracies: change in other cosmological parameters can mimic the effect of nu masses
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

27. Effect of massive neutrinos on the CMB and Matter Power Spectra
Max Tegmark
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

28. How to get a bound (measurement) of neutrino masses from Cosmology
Fiducial cosmological model:
(Ωbh2 , Ωmh2 , h , ns , τ, Σmν )
DATA
PARAMETER
ESTIMATES

29. 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,σ8)
* Lyman-α forest: independent measurement of power on small scales
* Baryon acoustic oscillations (SDSS)
Bounds on parameters from other data: SNIa (Ωm), HST (h), …
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

30. Cosmological Parameters: example
SDSS Coll, PRD 69 (2004)
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

31. Cosmological bounds on neutrino mass(es)
A unique cosmological bound on mν DOES NOT exist ! ν
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

32. Cosmological bounds on neutrino mass(es)
A unique cosmological bound on mν 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
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

33. Cosmological bounds on neutrino masses using WMAP1
Bound on Σmν (eV) [95% CL]
Data used
Ichikawa et al, PRD 71 (2005)
Sánchez et al, MNRAS 366 (2006) 189
MacTavish et al, astro-ph/
CMB only
Hannestad, JCAP 0305 (2003) 004
SDSS Coll., PRD 69 (2004)
Barger et al, PLB 595 (2004) 55
Crotty et al, PRD 69 (2004)
Rebolo et al, MNRAS 353 (2004) 747
Fogli et al. PRD 70 (2004)
Seljak et al, PRD 71 (2005)
[ ]
WMAP1, other CMB, 2dF/SDSS-gal [HST,SNIa]
WMAP Coll., ApJ Suppl 148 (2003) 175
Hannestad, hep-ph/
WMAP1, other CMB, 2dF/SDSS-gal, 2dF/SDSS-bias and/or Ly-α
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

34. Cosmological bounds on neutrino masses using WMAP3
Bound on Σmν (eV) [95% CL]
Data used
WMAP Coll., astro-ph/
Fukugita et al, astro-ph/
Kristiansen et al, astro-ph/
1.7 – 2.3
CMB only
Goobar et al, astro-ph/
SDSS Col, astro-ph/
0.68 – 0.91
WMAP3, other CMB, 2dF/SDSS-gal, SNIa
Seljak et al, astro-ph/
WMAP3, other CMB, 2dF/SDSS-gal, SDSS-BAO and/or Ly-α
Fogli et al., hep-ph/
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

35. Neutrino masses in 3-neutrino schemes
CMB + galaxy clustering
+ HST, SNI-a…
+ BAO and/or bias
+ including Ly-α
Fig from Strumia & Vissani, NPB726(2005)294
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

36. Tritium  decay, 02 and Cosmology
Fogli et al.,
hep-ph/
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

37. 02 and Cosmology Fogli et al., hep-ph/0608060
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

38. Relativistic particles in the Universe
At T<me, the radiation content of the Universe is
Effective number of relativistic neutrino species
Traditional parametrization of the energy density
stored in relativistic particles
# of flavour neutrinos:
Talks by F. Villante
and P. di Bari
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

39. Analysis with Σmν and Neff free
BBN allowed region
WMAP + ACBAR + SDSS + 2dF
Previous + priors (HST + SN-Ia)
2σ upper bound on Σmν (eV)
Hannestad & Raffelt, JCAP 0404 (2004) 008
Crotty, Lesgourgues & SP, PRD 69 (2004)
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

40. Analysis with Σmν and Neff free
BBN allowed region
WMAP + ACBAR + SDSS + 2dF
Crotty, Lesgourgues & SP, PRD 69 (2004)
Hannestad & Raffelt, astro-ph/
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

41. Non-standard relic neutrinos
The cosmological bounds on neutrino masses are modified if relic neutrinos have non-standard properties (or for non-standard models)
Two examples where the cosmological bounds do not apply
Massive neutrinos strongly coupled to a light scalar field: they could annihilate when becoming NR
Neutrinos coupled to the dark energy: the DE density is a function of the neutrino mass (mass-varying neutrinos)
Talks by G. Mangano
and P. Serra
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

42. Future sensitivities to Σmν
Future cosmological data will be available from
CMB (T+P) + galaxy redshift surveys
CMB (T+P) and CMB lensing
Weak lensing surveys
Weak lensing surveys + CMB lensing
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

43. Fiducial cosmological model:
PLANCK+SDSS
Fisher matrix analysis: expected sensitivities assuming a fiducial cosmological model, for future experiments with known specifications
Fiducial cosmological model:
(Ωbh2 , Ωmh2 , h , ns , τ, Σmν ) =
( , , 0.70 , 0.98 , 0.12, Σmν )
Lesgourgues, SP & Perotto, PRD 70 (2004)
Σm detectable at 2σ if larger than
0.21 eV (PLANCK+SDSS)
0.13 eV (CMBpol+SDSS)
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

44. Future sensitivities to Σmν: new ideas
weak gravitational and CMB lensing
lensing
Future sensitivities to Σmν: new ideas
No bias uncertainty
Small scales much closer
to linear regime
Tomography:
3D reconstruction
Makes CMB sensitive to
smaller neutrino masses
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

45. Future sensitivities to Σmν: new ideas
weak gravitational and CMB lensing
lensing
Future sensitivities to Σmν: new ideas
sensitivity of future weak lensing survey
(4000º)2 to mν
σ(mν) ~ 0.1 eV
Abazajian & Dodelson
PRL 91 (2003)
sensitivity of CMB
(primary + lensing)
to mν
σ(mν) = 0.15 eV (Planck)
σ(mν) = eV (CMBpol)
Kaplinghat, Knox & Song
PRL 91 (2003)
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

46. CMB lensing: recent analysis
σ(Mν) in eV for future CMB experiments alone :
Lesgourgues et al, PRD 73 (2006)
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

47. Summary of future sensitivities
Lesgourgues & SP, Phys. Rep. 429 (2006) 307
Future cosmic
shear surveys
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003

48. ν Conclusions Cosmological observables can be used to
bound (or measure) neutrino properties, in particular the sum of neutrino masses (info complementary to laboratory results) ν
Current bounds on the sum of neutrino
masses from cosmological data
(best Σmν< eV, conservative Σmν<1 eV)
Sub-eV sensitivity in the next future
( eV and better) Test degenerate
mass region and eventually the IH case
Sergio Pastor, Relic Neutrinos, Venice March 11-14, 2003