G. Mangano 1 Relic Neutrino Distribution Gianpiero Mangano INFN, Sezione di Napoli Italy.
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Transcript of G. Mangano 1 Relic Neutrino Distribution Gianpiero Mangano INFN, Sezione di Napoli Italy.
G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia 11
Relic Neutrino DistributionRelic Neutrino Distribution
Gianpiero ManganoGianpiero ManganoINFN, Sezione di NapoliINFN, Sezione di Napoli
ItalyItaly
22G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
33G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Pseudo-thermal distribution: T = 1.95 K
Number density ( v + v ): 112 cm-3 /flavor
Mean kinetic energy: 10-7(eV/m) eV
Direct searches:
GF2me Ev 10-50 (Ev/eV) cm2 hopeless ?
Standard picture
Indirect searches: cosmological observables
neutrino influence weak + gravity (T> 1 MeV)
gravity (T< 1 MeV)
44G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
How strong are present (and future) bounds
on exotic features in v distribution?
General parametrization
nnanxa xPa
exxf )(
1)(
2
Pn orthogonal polynomials with respect to Fermi-Dirac distribution
an in one to one correspondence with moments of distribution Qn
dxxxfQ nn 2)(41
3
2
3002
411
7120
411058.0
TQN
TQeVmh
eff
v
55G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
),())(/exp(
),,,,(),( )( tktTmktmBP
etkf tt
122
unstable v’s: tot, LSS, CMB, e+ flux
v chemical potential: BBN, LSS
v mass: tot, LSS,UHECR
v oscillations and magnetic moments: BBN
non-thermal effects: CMB, LSS,…
66G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Neutrinos and BBNNew species couples to gravity and speed up expansion
3 H2 = 8 G
Neff: increasing the relativistic energy density speeds up the expansion and increases the 4He mass fraction Yp
is the only free parameter (standard scenario)
Baryons are now well constrained by CMB
bh2 = 0.023(2)
CMB + Deuterium
BBN
Cuoco et al 2004
)1/(4
1178 3/4
ReffN
77G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
1) chemical potentials contribute to Neff
2) a positive electron neutrino chemical potential (more neutrinos than antineutrinos) favour n p processes with respect to p n processes.
....7
157
303 4
4
2
2
i
iieffN
Dolgov et al 2002
Cuoco et al 2004
88G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Neutrinos and CMBNeff affects the radiation-matter equality point
ISW: Integrated Sachs-Wolfe Effect on acoustic peaks
The large number of cosmological parameters does not allow for a stringent limit
99G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Neutrinos and Large Scale Structuresneutrinos suppress inhomogeneities which grow for gravitational instability until they become nonrelativistic
mv=1.2 eVmv=2.3 eV
mv=4.6 eV
mv=6.9 eV
Key parameters:
MpchmeVl
eVmh
vv
nr
v
15.38
1.94
122/1
02
1010G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
1111G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Decoupling and distortion
Residual v interactions at e+-e- annihilation stage produce non-thermal features
Kinetic eq. x=m a
)(11
1)(
)3(
)(1
34
xPae
xf
Pxxdxd
fCxH
fdxd
iixa
aa
Pi orthogonal polynomial for measure 1/exp(x)+1
f/ftherm
ka
1212G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
No mixing: z=T a e x Neff
1.4 0.94% 0.43% 3.04
Effects of v oscillations
Description in terms of density matrix
Mangano et al 2002
Dolgov et al 2002
Mangano et al 2005 )(,282
2
CEmG
pMHpi
W
Fpt
E electron/positron energy density
Three regimes:
At high temperatures (x<0.3) oscillations suppressed by medium effects
When electron density (adiabatically) decreases:MSW regime
Vacuum oscillations driven by M2/p
1313G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
1414G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
No mixing: z=T a e x Neff
1.4 0.73% 0.52% 3.05
Result for s122=0.3, s23
2=0.5, s13=0, m2solar=8 10-5 eV2, m2
atm=2.2 10-3 eV2,
Very tiny effect
))019.04.21.24(101(1
1)(
))047.01.42.21(101(1
1)(
324
324
xxxe
xf
xxxe
xf
x
xe
Small effect on 4He mass fraction: Y=2 10-4
1515G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
A model Cuoco, Lesgourgues, Mangano and Pastor 2005
Extra neutrinos from out of equilibrium decay of scalars after neutrino decoupling
In the instantaneous decay limit at TD )( DTH
22 2/*)(
2
22
211)(
xx
xa eAe
yxf
Non thermal features in neutrino distributions
Effects seen in CMB and LSS
1616G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
*2
202
712099.0104.3
)3(3299.01
2.93
AyN
AeV
mh
eff
v
Bounds from BBN
particles (decoupled) should not contribute too much to the expansion rate H
A < 0.1 at 95% C.L.
1717G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Present constraints from CMB (WMAP+ACBAR+VSA+CBI) and LSS (2dFGRS+SDSS) + SNIa data (Riess et al.)
Model: standard CDM + nonthermal v’s
Cl and P(k) computed using CAMB code (Lewis and Challinor 2002)
Likelihoods (using COSMOMC Lewis and Bridle 2002))
1818G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Degeneracies:
DM, Neff and m0
Neff >4 not forbidden
by BBN !
Future perspectives:
can we remove the
degeneracy?
1919G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Forecast:
“conservative”: Planck+ SDSS
“ambitious”: CMBPOL+ 40 h-3 Gpc survey with kmax=0.1 h Mpc-1
m0 and vh2 (q) large degeneracy
2020G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
If we add extra relativistic particles the situation gets even more involved
For each non thermal model there is a “twin” model with extra thermal relativistic particles, sharing the same value of Neff, vh2 but a different value of the neutrino mass scale.
Way to solve the degeneracy:
independent information on the absolute neutrino mass scale (beta decay experiments)
*2
202
712099.0104.3
)3(3299.01
2.93
AyN
AeV
mh
eff
v
NNeV
mh
eff
v
04.3 2.93'02
MpchmeVl vv
nr 15.3812
2/1
2121G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia
Summary
Too many neutrinos around:
Likely: purely thermal distribution which can be very hardly (or not at all) measured in the future
Unlikely but possible: exotic features in v distributions opening new perspectives for new physics
After all:
Neutrinos enjoy to falsify theoretical physicist expectations