Dark Energy from Mass Varying Neutrinos
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Dark Energy from Mass Varying Neutrinos. and. Neutrino Oscillation Experiments. Neutrino Factory 2004, based on Rob Fardon, A.E.N., Neal Weiner; astro-ph/0309800 David B. Kaplan, A.E.N., Neal Weiner; hep-ph/0401099 Kathryn Zurek, hep-ph/0405141 Kiyoshi Shiraishi, unpublished.

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Dark Energy from Mass Varying Neutrinos


Neutrino Oscillation Experiments

Neutrino Factory 2004, based on

Rob Fardon, A.E.N., Neal Weiner; astro-ph/0309800

David B. Kaplan, A.E.N., Neal Weiner; hep-ph/0401099

Kathryn Zurek, hep-ph/0405141

Kiyoshi Shiraishi, unpublished

1998 first convincing evidence for physics beyond the standard model from
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?

Strong Evidence for two kinds:

23% Dark Matter -> some garden variety pressureless clumpy fluid

73% “Dark Energy” -> exotic negative pressure smoothsubstance

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)

Our Universe is mostly mysterious dark stuff

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~ 10-33eV)

    dfrustrated network of strings/domain walls

    4relativistic, freely streaming particles

After six years of surprises do we almost completely understand neutrinos now
After Six Years of Surprises, Do we Almost Completely Understand Neutrinos Now?




of n Mass



Absolute mass scale? CP? Majorana or Dirac? LSND outlier?

Why recent concordance in the neutrino oscillation industry
Why recent Concordance in the neutrino oscillation Industry? Understand Neutrinos Now?

  • 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

Beyond the n standard model
Beyond the Understand Neutrinos Now?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!

Coincidences? Understand Neutrinos Now?

  • Density of “Dark Energy” ~ (2 10-3 )4 eV 4

  • Solar Neutrino Mass2 splitting ~ (4 10-3 )2eV 2

  • Atmospheric Neutrino Mass2 splitting ~ (3 10-2 ) 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

More Coincidences- Understand Neutrinos Now?

Why so complicated?

Can dark energy be related to something we know
Can dark energy be related to something we know? Understand Neutrinos Now?

  • 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 !

Varying mass is everywhere
Varying ‘Mass’ is Everywhere! Understand Neutrinos Now?

  • 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 !

A simple ma ss va rying n eutrino model
A simple Ma Understand Neutrinos Now?ssVaryingNeutrino Model

Assume “Dark Sector” (= unknown particles with no standard Model charges) contains

1A scalar field A

1A fermion field n

1A Yukawa coupling A n n

1 A scalar potential V ( A )

Assume “Our sector” contains

1Active Neutrinos n

  • 1Higgs Field H

  • Allow tiny (y =O (10-12) )coupling yH n n


æNeutrino mass matrix ( )

y H

y H



Neutrino masses vary as a 1
Neutrino Masses vary as Understand Neutrinos Now?A-1



Neutrino mass matrix ( )



y H

y H



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

What is the scale
What is the Scale? dilutes

  • We have 2 pieces of evidence suggesting

    a milli-eV scale for new physics.

  • This is also the inverse cosmic neutrino


  • 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.

Smoothness of mavan dark energy
Smoothness of MaVaN Dark Energy dilutes

  • 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)

Sterile neutrinos
Sterile Neutrinos? dilutes

  • 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

Can we test mavan dark energy
Can we test MaVaN Dark Energy? dilutes

  • 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.

A dilutesshould have coupling to matter

Loop suppressed and/or

Planck/String scale suppressed

Possible very interesting terms:

Other effects of environment?

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

Do Neutrinos ever oscillate in air?

The Outlier: atmospheric neutrinos by Kiyoshi Shiraishi assuming


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 from

oscillations in High

Density Material


Constraints on Standard


To do theorists
To Do: Theorists atmospheric neutrinos by Kiyoshi Shiraishi assuming

  • 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

To do experimentalists
To Do: Experimentalists atmospheric neutrinos by Kiyoshi Shiraishi assuming

  • 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

Effects of environment in neutrino oscillations? atmospheric neutrinos by Kiyoshi Shiraishi assuming

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 nmdisappearanceor ne appearance

Smoking Guns for MaVaNs