Transcript Weighing neutrinos with Cosmology

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”
“Theoretical” neutrinos
• 3 neutrinos, corresponding to 3 families of
leptons
• Electron, muon, and tau neutrinos
• They are massless because we see only lefthanded neutrinos.
• If not they are not necessarily mass
eigenstates (Pontecorvo): one species can
“oscillate” into another
 e
iHt
e  0
Only if masses are non-zero
Two Obvious Sources of neutrinos
1) Sun
2) Cosmic Rays
hitting the
atmosphere
SuperKamiokande
SNO
Neutrino oscillation experiments
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Are sensitive to two independent squared mass
difference, m2 and m2 defined as follows:
(m12,m22,m32) =2+(-m2/2, +m2/2, ±m2)
where :
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 fixes the absolute neutrino mass scale
the sign ± stands for the normal or inverted
neutrino mass hierarchies respectively.
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They indicate that:
m2=8•10-5 eV2
m2=2.4•10-3 eV2
STATUS OF 1-2 MIXING
STATUS OF 2-3 MIXING
(ATMOSPHERIC + K2K)
Maltoni et al. hep-ph/0405172
(SOLAR + KAMLAND)
Araki et al. hep-ex/0406035
ATMO.

K2K
SOLAR 
KAMLAND
Normal hierarchy
m3  m2  m1
Inverted hierarchy
m2  m1  m3
Moreover neutrino masses can also be
degenerate
m1 , m2 , m3  matmospheric
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:
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Tritium decay:
m<1.8 eV (2) (Maintz-Troisk)
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Neutrinoless 2 decay:
0.17 eV < m<2.0 eV (3)
(Heidelberg-Moscow)
Cosmological Neutrinos
Neutrinos are in equilibrium with the primeval plasma through weak
interaction reactions. They decouple from the plasma at a temperature
Tdec  1MeV
We then have today a Cosmological Neutrino Background at a temperature:
1/ 3
4
T    T  1.945K  kT  1.68 104 eV
 11
With a density of:
3  (3)
3
3
3
nf 
g
T

n

0
.
1827

T

112
cm
f f
 k , k

2
4 
That, for a massive neutrino translates in:
k 
n k , k mk
c
m
k
mk
1
 2
  h 2  k
93.2eV
h 93.2eV
Neutrinos in cosmology
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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.
m 0 eV
m 7 eV
m 1 eV
m 4 eV
Ma ’96
A classical result of the perturbation theory
is that:
 a
p
where:
p
1

24

1

4
= fraction of the total energy density
which can cluster
In radiation dominated era:
=0 so p=0 and the perturbation growth is
suppressed
In matter dominated era:
if all the matter contributing to the energy density
is able to cluster:
1 so p=1 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:
They contribute to the total energy density with a
fraction f 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-f for which: p<1
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
The lenght scale below which
Neutrino clustering is
suppressed
is called the neutrino freestreaming
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.
Shape of the angular and the matter power
spectrum with varying ffrom Tegmark)
Neutrino mass from Cosmology
Data
Authors
 mi
WMAP+2dF
Hannestad 03
< 1.0 eV
SDSS+WMAP
Tegmark et al. 04
< 1.7 eV
WMAP+2dF+SDSS
Crotty et al. 04
< 1.0 eV
WMAP+SDSS Lya
Seljak et al. 04
< 0.43 eV
B03+WMAP+LSS
McTavish al. 05
< 1.2 eV
All upper limits 95% CL, but different assumed priors !
Our Analysis
We constrain the lowering P/P≈-8/m
from large scale structure data (SDSS+2df+Ly-)
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We constrain the parameter mh2 from the CMB
We constrain the parameter h from the HST
Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk
hep-ph 0408045, PRD 71, 123521, (2005)
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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
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We restricted the analysis to three-flavour
neutrino mixing
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We assume a flat -cold dark matter model with
primordial adiabatic and scalar invariant
inflationary perturbations
Results
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 m ≤1.4 eV (2) (WMAP 1 year data
+SDSS+ 2dFGRS)
 m ≤0.45 eV (2) (WMAP 1 year
data+SDSS+2dFGRS+Ly )
What changes with new WMAP data ?
Doing a new, PRELIMINAR, analysis of the 3 years
WMAP data, with SDSS and HST data , we obtain:
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 m ≤ 0.8 eV (2)
Conclusions
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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 data+Ly then 
m ≤0.5 eV and there is a tension with 02
results
There is a partial, preliminar, tension also
betwenn WMAP 3 years+SDSS results with 02
results
Results are model dependent
Just an example...