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