04/21/23

Cosmological aspects of neutrinos (III)

Sergio Pastor (IFIC Valencia)JIGSAW 2007

TIFR Mumbai, February 2007

ν

Cosmological aspects of neutrinos

3rd lecture

Bounds on mν from CMB, LSS and other data

Bounds on the radiation content (Neff)

Future sensitivities on mν from cosmology

keV sterile neutrinos as Dark Matter

Neutrino oscillations in the Early Universe

Neutrino oscillations are effective when medium effects get small enough

Compare oscillation term with effective potentials

Strumia & Vissani, hep-ph/0606054

Oscillation term prop. to Δm2/2E

First order matter effects prop. toGF[n(e-)-n(e+)]

Second order matter effects prop. toGF(E/MZ

2 )[ρ(e-)

+ρ(e+)]

Coupled neutrinos

keV sterile neutrinos mixed with active species

Consider 2ν active-sterile mixing with m2

of order keV2 and very small mixing angleProbability of

conversion in the primordial plasma (active neutrinos still interacting)

λosc=oscillation length λs=scattering length

Mixing angle suppressedby medium effectsuntil T falls belowT≈130 MeV(m2/keV2)1/6

The heavy state decaysradiatively (with lifetimelarger than the age of theUniverse): search for X-rayphoton line

Abazajian et al 2001, Dolgov & Hansen 2002

Kusenko, Neutrino 2006

keV states created in partial equilibrium with the right DM density

Would behave as WarmDark Matter: lower limits from Structure Formation

See e.g. Viel et al 2006

Dodelson & Widrow 1994 Shi & Fuller 1999

Abazajian et al 2001Dolgov & Hansen 2002

Bounds on mν from CMB, LSS and other data

Effect of massive neutrinos on the CMB and Matter Power

Spectra

Max Tegmark

www.hep.upenn.edu/~max/

Neutrinos as Hot Dark Matter

Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data)

How to get a bound (measurement) of neutrino masses from Cosmology

DATA

Fiducial cosmological model:(Ωbh2 , Ωmh2 , h , ns , τ, Σmν )

PARAMETERESTIMATES

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), …

Cosmological Parameters: example

SDSS Coll, PRD 69 (2004) 103501

Cosmological bounds on neutrino mass(es)

A unique cosmological bound on mν DOES NOT exist !

ν

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

Cosmological bounds on neutrino masses using WMAP3

Fogli et al., hep-ph/0608060

Dependence on the data set used. An example:

Neutrino masses in 3-neutrino schemes

CMB + galaxy clustering

+ HST, SNI-a…

+ BAO and/or bias

+ including Ly-α

Lesgourgues & SP, Phys. Rep. 429 (2006) 307

Tritium decay, 02 and Cosmology

Fogli et al.,

hep-ph/0608060

02 and Cosmology

Fogli et al., hep-ph/0608060

At T<me, the radiation content of the Universe is

Effective number of relativistic neutrino speciesTraditional parametrization of the energy densitystored in relativistic particles

Relativistic particles in the Universe

• Extra radiation can be:

scalars, pseudoscalars, sterile neutrinos (totally or partially thermalized, bulk), neutrinos in very low-energy reheating scenarios, relativistic decay products of heavy particles…

• Particular case: relic neutrino asymmetries

Constraints on Neff from BBN and from CMB+LSS

Extra relativistic particles

Effect of Neff at later epochs

• Neff modifies the radiation content:

• Changes the epoch of matter-radiation equivalence

CMB+LSS: allowed ranges for Neff

• Set of parameters: ( Ωbh2 , Ωcdmh2 , h , ns , A , b , Neff )

• DATA: WMAP + other CMB + LSS + HST (+ SN-Ia)

• Flat Models

Non-flat Models

• Recent result

Pierpaoli, MNRAS 342 (2003)

2.01.9eff 4.1N

95% CL

Crotty, Lesgourgues & SP, PRD 67 (2003)

3.32.1eff 3.5N

95% CL

Hannestad, JCAP 0305 (2003)

3.02.1eff 4.0N

Hannestad & Raffelt, astro-ph/06071014.6N2.7 eff

95% CL

Allowed ranges for Neff

Mangano et al, astro-ph/0612150

Using cosmological data (95% CL)

)-Ly and BAO( 6.2N 3.1

data) LSS(CMB 7.9N 3.0

eff

eff

2B10

B10 h274Ω

10

/nnη

γ

Future bounds on Neff

• Next CMB data from WMAP and PLANCK (other CMB experiments on large l’s) temperature and polarization spectra

• Forecast analysis in ΩΛ=0 modelsLopez et al, PRL 82 (1999) 3952

WMAP

PLANCK

Future bounds on Neff

Updated analysis:Larger errors

Bowen et al 2002

ΔNeff ~ 3 (WMAP)

ΔNeff ~ 0.2 (Planck)

Bashinsky & Seljak 2003

The bound on Σmν depends on the number of neutrinos

• Example: in the 3+1 scenario, there are 4 neutrinos (including thermalized sterile)

• Calculate the bounds with Nν > 3

Abazajian 2002, di Bari 2002

Hannestad JCAP 0305 (2003) 004

(also Elgarøy & Lahav, JCAP 0304 (2003) 004)

3 ν4 ν

5 ν

Hannestad

95% CL

WMAP + Other CMB + 2dF + HST + SN-Ia

Σmν and Neff degeneracy

(0 eV,3)

(0 eV,7)

(2.25 eV,7)

(0 eV,3)

(0 eV,7)

(2.25 eV,7)

Analysis with Σmν and Neff free

Hannestad & Raffelt, JCAP 0404 (2004) 008

Crotty, Lesgourgues & SP, PRD 69 (2004) 123007

2σ upper bound on Σmν (eV)

WMAP + ACBAR + SDSS + 2dF Previous + priors (HST + SN-Ia)

BBN allowed region

Analysis with Σmν and Neff free

Crotty, Lesgourgues & SP, PRD 69 (2004) 123007

WMAP + ACBAR + SDSS + 2dF

Hannestad & Raffelt, JCAP 0611 (2006) 016

BBN allowed region

BBN allowed region

Parameter degeneracy: Neutrino mass and w

In cosmological models with more parameters the neutrino mass bounds can be relaxed.

Ex: quintessence-like dark energy with ρDE=w pDE

WMAP Coll, astro-ph/0603449

Λ

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)

Non-thermal relic neutrinos

The spectrum could be distorted after neutrino decoupling

Example: decay of a light scalar after BBN

Cuoco, Lesgourgues, Mangano & SP, PRD 71 (2005) 123501

Thermal FD spectrum

Distortion from Φ decay

* CMB + LSS data still compatible with large deviations from a thermal neutrino spectrum (degeneracy NT distortion – Neff)

* Better expectations for future CMB + LSS data, but model degeneracy NT- Neff remains

/T p

Future sensitivities to Σmν

CMB (Temperature & Polarization anis.)

Galaxy redshift surveys

Galaxy cluster surveys

Weak lensing surveys

CMB lensing

Future cosmological data will be available from

WMAP, SPT, ACT, BICEP, QUaD, BRAIN, ClOVER, PLANCK, SAMPAN, Inflation Probe, SDSS, SDSS-II, ALHAMBRA, KAOS, DES, CFHTLS, SNAP, LSST, Pan-STARRS, DUO…

PLANCK+SDSS

Lesgourgues, SP & Perotto, PRD 70 (2004) 045016

Σm detectable at 2σ if larger than

0.21 eV (PLANCK+SDSS)

0.13 eV (CMBpol+SDSS)

Fiducial cosmological model:(Ωbh2 , Ωmh2 , h , ns , τ, Σmν ) =

(0.0245 , 0.148 , 0.70 , 0.98 , 0.12, Σmν )

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

Future sensitivities to Σmν: new ideas

weak gravitational and CMB lensing

lensing

No bias uncertaintySmall scales much closer

to linear regimeTomography:

3D reconstruction

Makes CMB sensitive to smaller neutrino masses

Future sensitivities to Σmν: new ideas

sensitivity of future weak lensing survey(4000º)2 to mν

σ(mν) ~ 0.1 eV

Abazajian & DodelsonPRL 91 (2003) 041301

sensitivity of CMB(primary + lensing) to mν

σ(mν) = 0.15 eV (Planck)

σ(mν) = 0.044 eV (CMBpol)

Kaplinghat, Knox & SongPRL 91 (2003) 241301

weak gravitational and CMB lensing

lensing

CMB lensing: recent analysis

σ(Mν) in eV for future CMB experiments alone : Lesgourgues et al, PRD 73 (2006) 045021

Summary of future sensitivities

Lesgourgues & SP, Phys. Rep. 429 (2006) 307

Future cosmic shear surveys

End of 3rd lecture