Neutrino (Mass) in
Cosmology
Thomas J. Weiler
Vanderbilt University
Nashville TN 37235,
and
CERN, Geneva, Switzerland
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Early-Universe Timeline
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Friedmann eqns, and energy partitions Omega
with “a” being the
cosmic scale factor
So Λ behaves like a “matter” with 3p+ρ < 0 !
Can relate F1 parameters to today’s values to write
Inflation and data
Î OmegaK ~ 0
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Neutrino Decoupling
Looking back, ν’s last scattered at time t such that
TνDC H ~ 1,
i.e. TνDC ~ MeV, t ~ 1 s, z ~ 1010.
Coincidentally, TνDC ~ TBBN ~ Te+evs. zeq = a0/aeq = Omegarad/Omegam ~ 4000,
and zrecomb ~ 1000
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Neutrino stat mech
per flavor
SLAC Summer School 2004
HDM models tried (top-down)
Thomas J. Weiler, Vanderbilt University & CERN
Omega
ν=1, i.e. each mν~30eV
Neutrino density
from BB photon density
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
nν, nγ >> any other density
SN87a sun
TeV
CERN/Fermilab
Cosmic-rays
γ-wall
IR
Visible
UV
x-rays
γ-rays
CMB
Radio
~CνB
Neutrino
Incognito
hadron wall?
ν
no wall a’tall
(after Ressell & Turner ‘90)
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Neutrino time
Liberated at T=Mev, t= 1 sec
Depends on energy (Lorentz boost)
Consider a 1020 eV neutrino.
Lorentz factor = 1021 for mν = 0.1 eV.
Age of Uni is 1018 sec,
But age of ν is 1018/1021 sec = 1 millisecond !
And it doesn’t even see the stream of radiation
rushing past it – untouched !
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
CR Spectrum above a TeV
from Tom Gaisser
50 Joules
VLHC
(100 TeV)2
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
BBN limits on Nν and asymmetry
Competing effects:
1. Weak int’n rate equilibrates νe+n ÅÆ p+e- , as n/p ~ exp[-δmN/TνDC] ;
So more νe Î less neutrons Î less He/H
2. Expansion rate (monotonic with Nν) decouples weak int’n;
So more Nν Î faster movie, earlier hotter TνDC and more neutrons Æ more He/H
Kneller & Steigman
HÆ S H, S =
So one extra species is ∆S=0.08
Best fit is ∆N=0.25, L=2.5%
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Compensation and LSND
Order 5% neutrino asymmetry
-- to be contrasted with
10-9 baryon asymmetry
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Four roads to absolute neutrino mass
(SN discounted)
1. Tritium decay
2. 0vββ decay
3. WMAP Æ LSS
4. Z-bursts on the relic CνB
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Tritium decay limits on neutrino mass
Q: Why tritium?
A: It has a small Q-value, mT-(mD+mp+me)
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
The oscillation “box” from a Feynman graph
Where does the “mixing matrix” come in?
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
PMNS neutrino-mixing matrix
Weak-interaction and mass “vectors” point differently:
|nk>=Uki |ni>, or Uki = <ni | nk> = <nk | ni>*
⎛ Ue1 Ue 2 Ue 3 ⎞ ⎛ c12
⎜
⎟ ⎜
U li = ⎜ U µ1 U µ 2 U µ3 ⎟ = ⎜ − s12
⎜U
⎟ ⎜
⎝ τ1 Uτ 2 Uτ 3 ⎠ ⎝ 0
s12 0 ⎞ ⎛ 1
0 ⎞ ⎛ c13 0 s13 ⎞
0
0 ⎞ ⎛1 0
⎟ ⎜
⎟ ⎜
⎟ ⎜
⎟
1 0⎟
c12 0 ⎟ ⋅ ⎜ 0 c23 s23 ⎟ ⋅ ⎜ 0 1
0 ⎟⋅⎜ 0
0 1 ⎟⎠ ⎜⎝ 0 − s23 c23 ⎟⎠ ⎜⎝ 0 0 e − iδ ⎟⎠ ⎜⎝ − s13 0 c13 ⎟⎠
where cij = cosθ ij , and sij = sin θ ij
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
What we think we know about neutrino mass
It “probably” looks
something like this
Log m2
m3
∆m223 ~ 2.5 x 10-3 eV2
m2
∆m212 ~ 7 x 10-5 eV2
m1
νe
SLAC Summer School 2004
νµ
ντ
Thomas J. Weiler, Vanderbilt University & CERN
Or maybe
…
It looks like this
Log m2
m3
m2
m1
m2
m1
m3
νe
SLAC Summer School 2004
νµ
ντ
Thomas J. Weiler, Vanderbilt University & CERN
Naturalness may be over-rated
Do these look natural?
A rodent with a bill?
Or a bug with a
light-emitting butt?
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
0νββ decay limits on neutrino mass
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Neutrino parameters:
fundamental to physics, and
a tool for astrophysics/cosmology
As an astro tool, useful NOW
(e.g. Le = Lµ = Lτ ) ;
As a physics window, the view is unclear.
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
neutrino masses and cosmology
ρ [% of ρcr]
first task: bound ν mass
second task:
decide whether ν contribute
as Hot Dark Matter
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Cosmic structure formation
WMAP Æ 2dF/SDSS
*
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
COBE data
*The raw temperature map (top) has a large
diagonal asymmetry due to our motion with
respect to the cosmic microwave background
-a Doppler shift.
*The temperature fluctuations after
subtraction of the velocity contribution,
showing primordial fluctuations and a large
radio signal from nearby sources in our own
galaxy (the horizontal strip).
V
*The primordial fluctuations after subtraction
of the galaxy signal.
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
WMAP data
The Universe at trecombination , ~ tequality
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
2dF Galaxy Redshift Survey
Peak from horizon scale at teq
HDM contribu
to suppression
Small scales
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Tegmark cosmic cinema - CDM
http://www.hep.upenn.edu/~max/cmb/movies.html
Increasing the total density of matter (baryons + cold dark matter)
pushes the epoch of matter-radiation equality back in time and
moves the peak scale (the horizion size at that time) to the right.
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Tegmark cosmic cinema - HDM
Increasing the density of massive neutrinos suppresses all scales
smaller than a certain cutoff, which in turn shifts to the left as you
increase
the neutrino mass (and density) Thomas J. Weiler, Vanderbilt University & CERN
SLAC Summer School 2004
Tegmark cosmic cinema – more HDM
If a CMB theorist gloats that he or she can measure the neutrino density,
make sure to point out that galaxy surveys are much more sensitive.
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
A little HDM history
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Neutrino fits
Elgaroy and Lahav
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
SDSS (Seljak et al)
Increasing nu mass increases CMB spectrum,
But decreases matter power spectrum ??
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Role of priors (Elgaroy and Kahav)
Elgaroy and Lahav
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Resonant Neutrino Annihilation Mean-Free-Path
λ=(nν σν)−1 = 40 DH/h70
Fig: Fargion, Mele, Salis
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Escher’s “Angels and Devils”
The early Uni was
denser, more absorbing.
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Neutrino mass-spectroscopy: absorption and emission
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Z-bursts
TJW, 1982;
Revival – 1997
∼ 50 Mpc
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
ν-mass spectroscopy
SLAC Summer School 2004
zmax=2, 5, 20 (top to bottom), n-α=2
(bottom-up acceleration)
Eberle, Ringwald, Song, TJW, 2004
Thomas J. Weiler, Vanderbilt University & CERN
Dips & sobering realism
hidden MX=4 1014 and 1016 GeV,
to explain >GZK w/ Z-bursts;
ν mass = 0.2 (0.4) eV - dashed (solid);
Error bars – per energy decade, by 2013,
for flux saturating present limits
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
The GZK puzzle
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Z-burst spectrum
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Fitted Z-burst (Emission) Flux
Gelmini,
Varieschi,
TJW
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Nu-mass limit for Z-burst fitted to EECRs
Gelmini,
Varieschi,
TJW
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Size matters
EUSO ~ 300 x AGASA ~ 10 x Auger
EUSO (Instantaneous) ~3000 x AGASA ~ 100 x Auger
Exposure
10000
AGASA
HiRes
Auger
EUSO
100
10
1
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
20
10
20
12
20
14
Exposure
1000
Year
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
“clear moonless nights”
Blackout_14aug03.jpeg
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
See-saw (Leptogenesis to follow)
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Leptogenesis
Three Sakharov conditions for Violate baryon number (BL conserved => Baryogenesis:
1. ∆B (=∆L) nonzero
2. Violate C and CP Ù T (complex couplings)
3. Out of Thermal Equilibrium
(decouple at T > M so no Boltzmann suppression,
then decay at T < M when over-abundant)
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Extra-dimensions and neutrino mass
Right-handed “sterile” neutrinos may be
our probe of extra-dimensions
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Summary:
Neutrinos are a splendid example
of the interplay among particle physics,
astrophysics, and cosmology
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
The “Learned Plot”
Oscillation phase is
. ( L δm2 / 4 Eν )
Figure
parameterized
by δm2 / (eV)2
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Neutrino Decay -Models, Signatures, and Reach
P(survive)= e –t/τ = e –(L/E)(m/τ0)
Beacom, Bell, Hooper, Pakvasa, TJW
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
The cosmic ν flavor-mixing thm
If theta32 is maximal (it is),
And if Re(Ue3) is minimal (it is),
Then νµ and ντ equilibrate;
Further, if initial νe flux is 1/3
(as from pion-muon decay chain),
Then all three flavors equilibrate.
νe:νµ:ντ = 1 : 1 : 1
at Earth
(and deviations Î new physics)
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
AMANDA/IceCube νµ event
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Flavor ratio Æ Topology ratio Map
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Sensitivity of ν1 flavor-projection
to MNS parameters
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
pseudo-Dirac masses and cosmic neutrinos
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Z-burst schematic
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Neutrino Mass tomography
in the Local Super-galactic Cluster
(Fodor, Katz, Ringwald)
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN
Integrated Sachs-Wolfe effect
SLAC Summer School 2004
Thomas J. Weiler, Vanderbilt University & CERN