Instability of Dark Energy with Mass Varying Neutrinos

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Instability of Dark Energy with Mass Varying
Neutrinos

• Niayesh Afshordi
• Institute for Theory and Computation
• Harvard-Smithsonian Center for Astrophysics

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My Collaborators
Matias Zaldarriaga
Kazunori Kohri
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Outline

• Dark Energy and Cosmic Coincidences
• Mass Varying Neutrinos (MaVaNs) and Dark Energy
• MaVaNs Phenomenology and Interactions
• Instability of non-relativistic MaVaNs
• Trans-Relativistic Phase Transition
• Stability of Adiabatic Dark Energy Perturbations
• Conclusions

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Cosmic Coincidences in ?CDM
Cold Dark Matter
baryons
Dark Energy/Cosmological Constant
photons
neutrinos
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Coupling Neutrinos and Dark Energy Mass Varying
Neutrinos (MaVaNs)

• A way to couple neutrinos with dark energy to
  explain their density coincidence
• Consider a scalar field, Acceleron, which
  modulates neutrino mass
• Minimizing V (non-relativistic neutrinos)
• Neutrino Mass becomes a function of neutrino
  density

Fardon, Nelson, and Weiner 2004
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Coupling Neutrinos and Dark Energy Mass Varying
Neutrinos (MaVaNs)

• A way to couple neutrinos with dark energy to
  explain their density coincidence
• Consider a scalar field, Acceleron, which
  modulates neutrino mass
• Minimizing V (non-relativistic neutrinos)
• Neutrino Mass becomes a function of neutrino
  density

Fardon, Nelson, and Weiner 2004
7
Coupling Neutrinos and Dark Energy Mass Varying
Neutrinos (MaVaNs)

• A way to couple neutrinos with dark energy to
  explain their density coincidence
• Consider a scalar field, Acceleron, which
  modulates neutrino mass
• Minimizing V (non-relativistic neutrinos)
• Neutrino Mass becomes a function of neutrino
  density

Fardon, Nelson, and Weiner 2004
8
Coupling Neutrinos and Dark Energy Mass Varying
Neutrinos (MaVaNs)

• A way to couple neutrinos with dark energy to
  explain their density coincidence
• Consider a scalar field, Acceleron, which
  modulates neutrino mass
• Minimizing V (non-relativistic neutrinos)
• Neutrino Mass becomes a function of neutrino
  density

Fardon, Nelson, and Weiner 2004
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Coupling Neutrinos and Dark Energy Mass Varying
Neutrinos (MaVaNs)

• Equation of state for acceleron/neutrino fluid
• So w ' -1 as long as neutrino density is small
• Logarithmic Model (Fardon et al. 2004)
• Assuming and integrating out
  ?r

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Coupling Neutrinos and Dark Energy Mass Varying
Neutrinos (MaVaNs)

• Equation of state for acceleron/neutrino fluid
• So w ' -1 as long as neutrino density is small
• Logarithmic Model (Fardon et al. 2004)
• Assuming and integrating out
  ?r

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Coupling Neutrinos and Dark Energy Mass Varying
Neutrinos (MaVaNs)

• Equation of state for acceleron/neutrino fluid
• So w ' -1 as long as neutrino density is small
• Logarithmic Model (Fardon et al. 2004)
• Assuming and integrating out
  ?r

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Logarithmic Model of MaVaNs

• w and Omega_nu
• Plot V(m_nu)

)
)
Expansion
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Why do we like MaVaNs?

• As n? ! 0, ?DE ! 0, i.e. no cosmological constant
  is needed
• The only constraint on acceleron mass is mA .
  n?1/3 10-4 eV, as opposed to Quintessence where
  mQ . 10-33 eV
• Both neutrino and dark energy densities are fixed
  by one parameter, ? (one coincidence solved.. two
  to go)

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Scalar Interaction of MaVaNs

• Yukawa Coupling
• However, the coupling can be small enough to
  avoid neutrino/acceleron thermalization in the
  early universe

Neutrinos attract each other
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The Negative Speed of Sound

• T? ltlt m? and mA gtgt H
• ? Adiabatic Perturbations

• If pressure follows density
• In the Logarithmic model

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The Negative Speed of Sound

• T? ltlt m? and mA gtgt H
• ? Adiabatic Perturbations

• If pressure follows density
• In the Logarithmic model

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Finite Temperature Corrections

• When neutrinos dominate the pressure
  perturbations
• For relativistic neutrinos, one has to solve
  Boltzmann equation

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Finite Temperature Corrections

• When neutrinos dominate the pressure
  perturbations
• For relativistic neutrinos, one has to solve
  Boltzmann equation

Force for the action
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Finite Temperature Corrections

• When neutrinos dominate the pressure
  perturbations
• For relativistic neutrinos, one has to solve
  Boltzmann equation
• Corrections to c2s for the Logarithmic model

Force for the action
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Thermal History of MaVaNs
Relativistic/Stable
m?
T? n?1/3
Non-relativistic/Unstable
?
z 10
a (1z)-1
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Outcome of the Instability Neutrino
Nuggets

• As a result of instability, neutrinos may
  condense into nuggets

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Outcome of the Instability Neutrino
Nuggets

• As a result of instability, neutrinos may
  condense into nuggets
• Assuming a relaxed nugget n?m? ?4
• Pauli Exclusion Principle n? . ?3
• ) ?max (? /T?)3 (Maximum nugget overdensity)
• Nuggets form when T? . m? . ?

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Outcome of the Instability Neutrino
Nuggets

• As a result of instability, neutrinos may
  condense into nuggets
• Assuming a relaxed nugget n?m? ?4

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Outcome of the Instability Neutrino
Nuggets

• As a result of instability, neutrinos may
  condense into nuggets
• Assuming a relaxed nugget n?m? ?4
• Pauli Exclusion Principle n? . ?3
• ) ?max (? /T?)3 (Maximum nugget overdensity)

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Outcome of the Instability Neutrino
Nuggets

• As a result of instability, neutrinos may
  condense into nuggets
• Assuming a relaxed nugget n?m? ?4
• Pauli Exclusion Principle n? . ?3
• ) ?max (? /T?)3 (Maximum nugget overdensity)
• Nuggets form when T? . m? . ?

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The Trans-Relativistic Phase Transition
c.f. Liquid-Gas Phase Transition
lt?gt 2
? 0
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The Trans-Relativistic Phase Transition
lt?gt 2
Homogeneous Expansion
? 0
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The Trans-Relativistic Phase Transition
lt?gt 2
Onset of Instability
? 0
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The Trans-Relativistic Phase Transition
Neutrinos condense into Nuggets with zero net
pressure
lt?gt 2
? 0
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Adiabatic Perturbations of Dark Energy The
General Case

• Assuming that
• cs2 gt 0 (stable perturbations)
• Dark Energy perturbations are adiabatic, i.e.
  PDEF(?DE)
• ) As t ! 1 ?DE ! const
• i.e. we need a cosmological constant

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Is there any way to stabilize MaVaNs?

• Light Acceleron (mA H) ? Quintessence
• Bi, Feng, Li, Xin-min Zhang 2004
• Brookfield, van de Bruck, Mota
  Tocchini-Valentini 2005
• Very Light Neutrinos (T? gt m?) ? ?CDM
• ? Only lightest neutrino couples to acceleron
• ? Lightest neutrino is relativistic (atmospheric
  neutrinos)
• m? lt 10-4 eV
• Fardon, Nelson, Weiner 2005
• Decoupled Neutrinos (m? const) ? ?CDM
• Takahashi Tanimoto 2005

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Conclusions

• Non-relativistic MaVaNs are in general unstable,
  unless there is a cosmological constant
• MaVaNs undergo a phase-transition as they become
  non-relativistic, and form neutrino nuggets
• Despite its rich phenomenology, the Logarithmic
  MaVaNs model is unlikely to act as Dark Energy
• Possible ways out give back ?CDM or Quintessence