1. and Dark Energy from Mass Varying Neutrinos
Neutrino Oscillation Experiments
Neutrino Factory 2004, based on
Rob Fardon, A.E.N., Neal Weiner; astro-ph/
David B. Kaplan, A.E.N., Neal Weiner; hep-ph/
Kathryn Zurek, hep-ph/
Kiyoshi Shiraishi, unpublished 1

2. 1998, First Convincing evidence for Physics Beyond the Standard Model from
SuperK, evidence for atmospheric neutrino oscillations
But, the“Breakthrough of the Year” is the supernovae evidence for the acceleration of the universe
Einstein was wrong about having blundered? (Cosmological Constant?)
“Why Now” and finetuning are evidence for the Anthropic Principle?

3. Our Universe is mostly mysterious dark stuff
Strong Evidence for two kinds:
23% Dark Matter -> some garden variety pressureless clumpy fluid
73% “Dark Energy” -> exotic negative pressure smooth substance
usually attributed to the energy of the vacuum⎯energy density which does not dilute with expansion and is therefore equivalent to Einstein’s cosmological constant. I will assume this is zero.
sometimes assumed to be some weird dynamical “quintessence” substance with equation of state parameter w near -1 which nevertheless does not clump (not your typical nonrelativistic stuff)

4. “Smooth, Dark, Tension” Sean Carroll
Dark Energy
“Smooth, Dark, Tension” Sean Carroll
Negative Pressure=Tension
Smooth Tension= Oxymoron?
“Normal” Stuff under tension prefers to Clump
Weird particle physics counterexamples:
1vacuum energy
la slowly rolling scalar field (m~H-1~ eV)
dfrustrated network of strings/domain walls
4relativistic, freely streaming particles

5. After Six Years of Surprises, Do we Almost Completely Understand Neutrinos Now?
q13
Flavor
Composition
of n Mass
Eigenstates
q13
Absolute mass scale? CP? Majorana or Dirac? LSND outlier?

6. Why recent Concordance in the neutrino oscillation Industry?
Neutrinos are Special! Expect exotic physics to be discovered there! Window on the Dark Sector!
Can mix with ‘dark’ fermions (aka sterile neutrinos)
Can thus experience ‘dark forces’ much more strongly than other particles
Oscillations are sensitive to tiny GUT suppressed operators (standard seesaw)
Environment dependence of oscillations is sensitive to new millimeter range forces which are subgravitational strength for other particles

7. Beyond the n Standard Model
Subject still in experimental youth
Neutrino oscillations offer incredible
sensitivity to new forces, high scales,
ultraweak interactions, new states
Conventional Wisdom about neutrinos,
neutrino expts. has always been wrong!

8. Coincidences? Density of “Dark Energy” ~ (2 10-3 )4 eV 4
Solar Neutrino Mass2 splitting ~ ( )2eV 2
Atmospheric Neutrino Mass2 splitting ~ ( ) 2eV 2
Convincing evidence for Dark Energy found in 1998
Convincing evidence for Neutrino Oscillations found in 1998
Low Scale SUSY gravitino mass ~ 10-3 eV

9. More Coincidences-
Why so complicated?
Composition of universe

10. Can dark energy be related to something we know?
Dark Matter? We know scaling behavior of dark
matter from large scale structure. Dark energy
currently scales very differently.
Scaling behavior of dark energy must have recently
changed (Why Now?)
Neutrinos? Could neutrino energy density
scale like dark energy?
Requires neutrino ‘mass’ to increase with scale factor
Isn’t varying neutrino mass crazy?
No !

11. Varying ‘Mass’ is Everywhere!
Index of refraction
KS regeneration
Quasi particles in condensed matter
MSW effect
All Standard Model fermion mass terms depend on value of Higgs scalar which can vary (slightly)
All known masses depend on environment
The issue is not ‘whether’, but
‘how much’ neutrino mass should vary !

12. A simple MassVaryingNeutrino Model
Assume “Dark Sector” (= unknown particles with no standard Model charges) contains
1 A scalar field A
1 A fermion field n
1 A Yukawa coupling A n n
1 A scalar potential V ( A )
Assume “Our sector” contains
1 Active Neutrinos n
1 Higgs Field H
Allow tiny (y =O (10-12) ) coupling y H n n
æ Neutrino mass matrix ( )
y H
y H A .

14. Neutrino Masses vary as A-1
Neutrino mass matrix ( ) n
y H
y H A n
For large <A> light neutrino mass is ( y H) 2/ A
Assume V ( A ) slowly increasing function of A.
V is then slowly decreasing function of the light neutrino mass
V(A (mn) ) ~ mn(1+w)/ w

15. Neutrino mass increases adiabatically as neutrino density dilutes
Combined neutrino + scalar potential energy decreases slowly

16. What is the Scale? We have 2 pieces of evidence suggesting
a milli-eV scale for new physics.
This is also the inverse cosmic neutrino
spacing.
A milli-eV scale for the A potential (and
mass) leads to Dark Energy
Contrast with ‘cosmon’ type quintessence
model, which requires a mass scale of
10-33 eV.

17. Smoothness of MaVaN Dark Energy
When n’s go nonrelativistic, they gravitationally clump at large scales
MaVaN’s go nonrelativistic very late (z= a few)
MaVaN’s get lighter and more relativistic inside clumps => ‘anti-clumping mechanism’
Dark energy much smoother than neutrinos V ~ (nn) (1+w)

19. Sterile Neutrinos? Sterile neutrino mass increasing function of
neutrino density
Mixing with sterile neutrino decreasing function of neutrino density
Simple to reconcile sterile neutrino with BBN F mass always much heavier than temperature
May similarly evade Supernovae bounds

20. Can we test MaVaN Dark Energy?
Cosmological tests of neutrino mass from large scale structure: MaVaN mass was much lighter at high redshift.
Model independent relation: mn= (1+w) V/nn
(V= dark energy density)
No terrestrial sources of high scalar neutrino density (neutrino density weighted by (m/E)), relative to cosmological, other than nuclear fireball.
Main interesting astrophysical source of high scalar neutrino density is supernova.
Generic tests difficult, not impossible.

21. Other effects of environment?
A should have coupling to matter
Loop suppressed and/or
Planck/String scale suppressed
Possible very interesting terms:

23. Do Neutrinos ever oscillate in air?
Recent unofficial, preliminary analysis of SuperK atmospheric neutrinos by Kiyoshi Shiraishi assuming no oscillations in air fits all data well
Very weak (consistent with LSND?) upper bound on mass squared difference in rock from contained, partially contained events, K2K
reanalysis of upward through going and upward stopping muons underway, probably yields best upper bound on Dm2 in rock

24. The Outlier:
LSND
Conventional Wisdom: need > 3 neutrinos to get 3 independent masses squared, and oscillations involving extra dark states constrained by Bugey, CDHS, Cosmology, and Supernova, so LSND must be wrong
Constraints on Standard
Neutrinos
Constraints from
oscillations in High
Density Material
only

25. To Do: Theorists Model building exploration
MaVaN consequences for Supernova
How much room for non standard environment dependence in Solar/atmospheric/terrestial neutrino oscillations?
Consequences for flavor dependence/energy spectrum of astrophysical neutrino sources
Early Universe cosmology of acceleron
More general constraints on sterile neutrinos from supernovae, cosmology

26. To Do: Experimentalists
Document and consider environment of neutrino path in neutrino oscillation experiments
Consider q13 measurements in reactor experiments with pathlength in air and in rock
Consider environment of neutrinos in direct mass search and 0nbb measurements
Short baseline experiments to search for heavier sterile neutrinos with small mixing angles; consider varying density of material in neutrino path

27. Smoking Guns for MaVaNs
Effects of environment in neutrino oscillations?
0nbb decay depends on density of source?
Tritium endpoint searches for absolute n mass depends on density of source?
Cosmologically “impossible” sterile neutrinos?
Cosmologically “inconsistent” neutrino masses?
A MiniBooNE signal for nm disappearance or ne appearance