Weighing%20neutrinos%20with%20Cosmology

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Weighing neutrinos with Cosmology

• Fogli, Lisi, Marrone, Melchiorri, Palazzo,
  Serra, Silk hep-ph 0408045, PRD 71, 123521,
  (2005)
• Paolo Serra
• Physics Department
• University of Rome La Sapienza

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Theoretical neutrinos

• 3 neutrinos, corresponding to 3 families of
  leptons
• Electron, muon, and tau neutrinos
• They are massless because we see only left-handed
  neutrinos.
• If not they are not necessarily mass eigenstates
  (Pontecorvo) one species can oscillate into
  another

Only if masses are non-zero
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Two Obvious Sources of neutrinos
1) Sun 2) Cosmic Rays hitting the atmosphere
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SuperKamiokande
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SNO
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Neutrino oscillation experiments

• Are sensitive to two independent squared mass
• difference, ?m2 and ?m2 defined as follows
• (m12,m22,m32) ?2(-?m2/2, ?m2/2, ?m2)
  
• where
• ? fixes the absolute neutrino mass scale
• the sign stands for the normal or inverted
  neutrino mass hierarchies respectively.
• They indicate that ?m2810-5 eV2
• 
  ?m22.410-3 eV2

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STATUS OF 1-2 MIXING (SOLAR KAMLAND)
STATUS OF 2-3 MIXING (ATMOSPHERIC K2K)
Araki et al. hep-ex/0406035
Maltoni et al. hep-ph/0405172
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ATMO. n K2K
SOLAR n KAMLAND
Inverted hierarchy
Normal hierarchy
Moreover neutrino masses can also be degenerate
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Hovever-They can't determine the absolute mass
scale ?-They can't determine the hierarchy ?m2

• To measure the parameter ? we need non
  oscillatory neutrino experiments. Current bounds
  on neutrino mass come from
• Tritium ??decay
• m?lt1.8 eV (2?) (Maintz-Troisk)
• Neutrinoless 2? decay
• 0.17 eV lt m??lt2.0 eV (3?)
  (Heidelberg-Moscow)

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Cosmological Neutrinos
Neutrinos are in equilibrium with the primeval
plasma through weak interaction reactions. They
decouple from the plasma at a temperature
We then have today a Cosmological Neutrino
Background at a temperature
With a density of
That, for a massive neutrino translates in
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Neutrinos in cosmology

• Neutrinos affect the growth of cosmic clustering,
  so they can leave key imprints on the
  cosmological observables
• In particular, massive neutrinos suppress the
  matter fluctuations on scales smaller than the
  their free-streaming scale.

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m? 0 eV
m? 1 eV
Ma 96
m? 7 eV
m? 4 eV
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A classical result of the perturbation theory is
that

• where
• ?? fraction of the total energy density
  which can cluster?

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In radiation dominated era

• ??0 so p0 and the perturbation growth is
  suppressed
• In matter dominated era
• if all the matter contributing to the energy
  density is able to cluster
• ???? so p1 and the perturbation grows as the
  scale factor
• but if a fraction of matter is in form of
  neutrinos, the situation is different. In fact
  

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They contribute to the total energy density with
a fraction fn but they cluster only on scales
bigger than the free-streaming scale for smaller
scales, they can't do it, so we must have
??1-fn for which plt1

• And the perturbation grows less than the
  scale factor
• The result is a lowering of the matter power
  spectrum on scales smaller than the
  free-streaming scale. The lowering can be
  expressed by the formula
• ?P/P-8??/?m

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The lenght scale below which Neutrino clustering
is suppressed is called the neutrino
free-streaming scale and roughly corresponds to
the distance neutrinos have time to travel while
the universe expands by a factor of two.
Neutrinos will clearly not cluster in an
overdense clump so small that its escape velocity
is much smaller than typical neutrino velocity.
On scales much larger than the free streaming
scale, on the other hand, Neutrinos cluster just
as cold dark matter. This explains the effects on
the power spectrum.
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Shape of the angular and the matter power
spectrum with varying f?????from Tegmark)
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Neutrino mass from Cosmology
Data Authors ? mi
WMAP2dF Hannestad 03 lt 1.0 eV
SDSSWMAP Tegmark et al. 04 lt 1.7 eV
WMAP2dFSDSS Crotty et al. 04 lt 1.0 eV
WMAPSDSS Lya Seljak et al. 04 lt 0.43 eV
B03WMAPLSS McTavish al. 05 lt 1.2 eV

All upper limits 95 CL, but different assumed
priors !
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Our Analysis

• We constrain the lowering ?P/P-8??/?m from
  large scale structure data (SDSS2dfLy-?)
• We constrain the parameter ?mh2 from the CMB
• We constrain the parameter h from the HST

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Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra,
Silk hep-ph 0408045, PRD 71, 123521, (2005)

• We analized the CMB (WMAP 1 year data), galaxy
  clusters, Lyman-alpha (SDSS), SN-1A data in order
  to constrain the sum of neutrino mass in
  cosmology
• We restricted the analysis to three-flavour
  neutrino mixing
• We assume a flat ?-cold dark matter model with
  primordial adiabatic and scalar invariant
  inflationary perturbations

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Results

• ? mn 1.4 eV (2?) (WMAP 1 year data SDSS
  2dFGRS)
• ? mn 0.45 eV (2?) (WMAP 1 year
  dataSDSS2dFGRSLya )

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What changes with new WMAP data ?
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Doing a new, PRELIMINAR, analysis of the 3 years
WMAP data, with SDSS and HST data , we obtain

• ? mn 0.8 eV (2?)

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Conclusions

• Cosmological constraints on neutrino mass are
  rapidly improving (our analysis on 1 year WMAP
  data indicated that ? m? 1.4 eV, with the 3
  years WMAP data the upper bound is ? m? 0.8 eV)
• If one consider WMAP 1 year dataLya then ? m?
  0.5 eV and there is a tension with 0?2? results
• There is a partial, preliminar, tension also
  betwenn WMAP 3 yearsSDSS results with 0?2?
  results
• Results are model dependent

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Just an example...