Neutrinos and Reionization

Maria ArchidiaconoUniversity of Rome “La Sapienza”

IntroductionThe connection between cosmological observations and neutrino physics is one of the most interesting and hot topics in astroparticle physics.

Precision observations of the cosmic microwave background and large scale structure of galaxies can be used to probe neutrino mass with greater precision than current laboratory experiments. But the cosmological results are model dependent. So it’s important to investigate the changes on neutrino mass bounds if we use different theoretichal assumptions.

In this case we look at the influence of the reionization model on neutrino mass bounds. Until now these cosmological data have been analyzed in the framework of a standard reionization scenario. But how could these constraints change if we analyze these cosmological data using a different parametrization for the reionization process?

Neutrinos

231.18.0

213

250.18.0

212

102.2

109.7

eVm

eVm

Subdury Neutrino Observatory: solar neutrinos: e→

SuperKamiokande: atmospheric neutrinos:→

Oscillation experiments

Only mass squared differences

m ≠0

Beta decayEssentially a search for a distortion in the shape of the b-spectrum in the endpoint energy region

Normal hierarchy

Neutrinos in cosmology

p + e‾ ↔ n + e

neutrinos decoupling kT=1MeV

free streaming FS~vth /H where vth ≈ 150 (1+z) (1eV/M) Km/s

Matter power spectrum suppression Pm(k)/Pm(k) ~ -8 Ω/Ωm= -8 f,where Ωh²=NM/92.5eV

non-relativistic transition knr ≈ 0.018 (√ Ωm) (M/1eV)^½ hMpc ^-1

Neutrinos effects on CMBAt the state of art of the nuclear physics experiments, we know that at the energy of plasma when neutrinos decoupled they were higly relativistic and so they were a radiation component and the equivalence was delayed

EarlyISW

eVm 3.1

Conservative limit

But is this result stable if we change the reionization process?...

arXiv:1001.4635v2Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived ParametersD. Larson, J. Dunkley, G. Hinshaw, E. Komatsu, M. R. Nolta et al.

eV

mNh

5.922

Reionization

Ionization history

Quasar

Reionization20>z>6

Gunn-Petersoneffect

Ionized Universe

Neutral Universe Dark Age

Reionized Universe

The Gunn-Peterson effect

due to the presence of neutral hydrogen in the intergalactic medium. The trough is characterized by suppression of electromagnetic emission from the quasar at wavelengths less than that of Lyman alpha line at the redshift of the emitted light.

"Evidence For Reionization at z ~ 6: Detection of a Gunn-Peterson Trough In A z=6.28 Quasar“Becker, R. H.; et al. (2001).

Gunn-Peterson trough

The effect has been observed only in the spectra of the quasars at z>6

The Gunn-Peterson trough is a feature of the spectra of the quasars

CMB and ReionizationDurig reionization the rescattering of photons suppresses the anisotropies on angular scales below the horizon at the rescattering epoch by a damping factor exp(-reion) where

reion = c T ∫ dt ne (1+z)³

The uniform reduction of power at small scales has the same effect as a change in the overall normalization. Moreover at l<30 the observations are limited by “cosmic variance”. So you cannot see reionization effects in temperature spectrum.

CMB and ReionizationInstead you can clearly recognize reionization effects in the polarization spectrum at l<30.Infacts, CMB photons cannot spread themselves on such large scales before the recombination has ended. The polarization signal is expected to be zero at low l. So the peak at low l is due to the rescattering of CMB photons during reionization.

arXiv:astro-ph/9706147v1A CMB Polarization PrimerWayne Hu and Martin White

Reionization Models

WMAP-3

=0.105

=0.090

NB: there is no direct correspondence between z and lMoreover we don’t know the behaviour of xe between z=20 and z=6

Mortonson & Hu (2008) ApJ, 672, 737, arXiv:0705.1132

Sudden reionizationDouble peak reionization

The sudden reionization model produces only one single peak at l < 10. Instead the models with a partial reionization at higher redshift produce a less high peak, but also a bump at 10 < l < 30.

Principal Components

Nz + 1 = (zMAX – zmin)/z

zmin = 6 (QSO)z = 0.25 (z→0 results indipendent of the bin)zMAX = 30

Nz = 95

)()(2 )(

ln

)(

ln

2

1j

fidei

fide

MAX

zxje

EEl

zxie

EEl

l

lij zx

C

zx

ClF

lMAX = 100 (beyond the effects are negligible), xe,fid = 0.15 (not important)

PCs: Fisher matrix eigenfunctions

zN

jizij zSzSNF1

22 )()(1

2 PC variance

21

2

The higher the modes, the higher the oscillation frequency in redshift

Principal Components

)()()( zSmzxzx fidee

Any reionization process can be decomposed in PCs

The mode amplitudes are

)()(1

minmin

zxzdzSzz

m e

z

zMAX

MAX

Any reionization process between zMAX and zmin is fully described by a set of mode amplitudes.

Principal ComponentsThe PCs satisfy the orthogonality and completeness relations

ijz

N

ji

z

z MAX

NzSzS

zzzSzdzS

z

MAX

1)()(

)()(

1

minmin

UtilityThe first 3-5 modes provide all the informations about reionization that are relevant in the E mode polarization spectrum at larger scales. The higher mode oscillations in redshift at higher frequency can be mediate to zero.NB: This is not true for the whole reionization process.

The default case is with 10 PCs

Caveat: the physical consistence

fm2

The constraints on the fraction of ionized hydrogen 0≤xe≤1 are not built in to the method.A necessary but not sufficient condition is:

where

221,max fid

efide xxf

It’s important to notice that the higher modes have a great effect on xe(z), while they are irrelevant for the polarization spectrum.

CMB neutrino mass bounds and reionization

How do the constraints on the cosmological parameters (in particular on the neutrinos mass) change, if, instead of using a sudden reionization model, we analyze the process of reionization through the Principal Components, making it indipendent from the model?

10.1103/PhysRevD.82.087302

Results

Parameters WMAP7(Sudden reionization)

WMAP7(model indipendent

reionization)

bh^2 0.0221±0.0012 0.0226±0.0015

ch^2 0.117±0.013 0.115±0.017

0.674±0.134 0.675±0.148

n 0.955±0.033 0.975±0.045

H0 65.7±8.2 66.0±10.2

m <1.15eV(95%) <1.66eV(95%)

CosmoMC modifiyed to account for a model independent reionization with the first 5 PCs.

Results

Sudden reionizationModel indipendent reionization

Positive correlation:Massive neutrinos

Sudden reionizationModel indipendent reionization

Results

Negative correlation:Free streaming

Sudden reionizationModel indipendent reionization

The model indipendent reionization agrees with the Harrison Zel’dovich primordial spectrum within 1

Sudden reionizationModel indipendent reionization

Conclusions

We investigated the influence of the theoretical assumptions about reionization on the cosmological neutrino mass bounds. We saw that the cosmological constraints on the neutrino masses are weakened if we parametrize the reionization process trough the Principal Components, making it independent from the model.

THANKS

Number of effective neutrino species and Reionization

EarlyISW

22Ha

kk

The current best measurement of the number of neutrino types comes from observing the decay of the Z boson.

044.0

3

N

NN

N

eff

effrel

Results

Parameters WMAP7(Sudden reionization)

WMAP7(model indipendent

reionization)

bh^2 0.02234±0.00056 0.02226±0.0007

ch^2 0.147±0.037 0.151±0.035

0.738±0.029 0.727±0.032

n 0.986±0.022 0.987±0.023

eff >0.45(95%) >1.13(95%)

CosmoMC modifiyed to account for a model independent reionization with the first 5 PCs.

Results

Work in progress …

Sudden reionizationModel indipendent reionization