Instability of Dark Energy with Mass Varying Neutrinos

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1 Instability of Dark Energy with Mass Varying Neutrinos Niayesh Afshordi Institute for Theory and Computation Harvard-Smithsonian Center for Astrophysics

2 My Collaborators Matias Zaldarriaga Kazunori Kohri

3 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

4 Cosmic Coincidences in ΛCDM Cold Dark Matter Dark Energy/Cosmological Constant photons baryons neutrinos

5 Coupling Neutrinos and Dark Energy: Mass Varying Neutrinos (MaVaNs( 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

6 Coupling Neutrinos and Dark Energy: Mass Varying Neutrinos (MaVaNs( 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( 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( 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

9 Coupling Neutrinos and Dark Energy: Mass Varying Neutrinos (MaVaNs( 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 ν r

10 Coupling Neutrinos and Dark Energy: Mass Varying Neutrinos (MaVaNs( 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 ν r

11 Coupling Neutrinos and Dark Energy: Mass Varying Neutrinos (MaVaNs( 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 ν r

12 Logarithmic Model of MaVaNs w and Omega_nu Plot V(m_nu) Expansion

13 Why do we like MaVaNs? As n ν 0, ρ DE 0, i.e. no cosmological constant is needed The only constraint on acceleron mass is m A. n ν 1/ ev, as opposed to Quintessence where m Q ev Both neutrino and dark energy densities are fixed by one parameter, Λ (one coincidence solved.. two to go)

14 Scalar Interaction of MaVaNs Yukawa Coupling: Neutrinos attract each other However, the coupling can be small enough to avoid neutrino/acceleron thermalization in the early universe

15 The Negative Speed of Sound T ν << m ν and m A >> H Adiabatic Perturbations If pressure follows density: In the Logarithmic model:

16 The Negative Speed of Sound T ν << m ν and m A >> H Adiabatic Perturbations If pressure follows density: In the Logarithmic model:

17 Finite Temperature Corrections When neutrinos dominate the pressure perturbations: For relativistic neutrinos, one has to solve Boltzmann equation:

18 Finite Temperature Corrections When neutrinos dominate the pressure perturbations: For relativistic neutrinos, one has to solve Boltzmann equation: Force for the action:

19 Finite Temperature Corrections When neutrinos dominate the pressure perturbations: For relativistic neutrinos, one has to solve Boltzmann equation: Force for the action: Corrections to c 2 s for the Logarithmic model:

20 Thermal History of MaVaNs Relativistic/Stable T ν ~ n ν 1/3 m ν Λ Non-relativistic/Unstable z ~ 10 a = (1+z) -1

21 Outcome of the Instability: Neutrino Nuggets As a result of instability, neutrinos may condense into nuggets

22 Outcome of the Instability: Neutrino Nuggets As a result of instability, neutrinos may condense into nuggets Assuming a relaxed nugget: n ν m ν Λ 4 Pauli Exclusion Principle: n ν. Λ 3 max = (Λ /T ν ) 3 (Maximum nugget overdensity) Nuggets form when T ν. m ν. Λ

23 Outcome of the Instability: Neutrino Nuggets As a result of instability, neutrinos may condense into nuggets Assuming a relaxed nugget: n ν m ν Λ 4

24 Outcome of the Instability: Neutrino Nuggets As a result of instability, neutrinos may condense into nuggets Assuming a relaxed nugget: n ν m ν Λ 4 Pauli Exclusion Principle: n ν. Λ 3 max = (Λ /T ν ) 3 (Maximum nugget overdensity)

25 Outcome of the Instability: Neutrino Nuggets As a result of instability, neutrinos may condense into nuggets Assuming a relaxed nugget: n ν m ν Λ 4 Pauli Exclusion Principle: n ν. Λ 3 max = (Λ /T ν ) 3 (Maximum nugget overdensity) Nuggets form when T ν. m ν. Λ

26 The Trans-Relativistic Phase Transition c.f. Liquid-Gas Phase Transition µ = 0 <γ> = 2

27 The Trans-Relativistic Phase Transition µ = 0 <γ> = 2 Homogeneous Expansion

28 The Trans-Relativistic Phase Transition µ = 0 <γ> = 2 Onset of Instability

29 The Trans-Relativistic Phase Transition µ = 0 <γ> = 2 Neutrinos condense into Nuggets with zero net pressure

30 Adiabatic Perturbations of Dark Energy: The General Case Assuming that 1) c s2 > 0 (stable perturbations) 2) Dark Energy perturbations are adiabatic, i.e. P DE =F(ρ DE ) As t ; ρ DE const; i.e. we need a cosmological constant

31 Is there any way to stabilize MaVaNs? Light Acceleron (m A ~ H) Quintessence Bi, Feng, Li, Xin-min & Zhang 2004 Brookfield, van de Bruck, Mota & Tocchini-Valentini 2005 Very Light Neutrinos (T ν > m ν ) ΛCDM Only lightest neutrino couples to acceleron Lightest neutrino is relativistic (atmospheric neutrinos) m ν < 10-4 ev Fardon, Nelson, & Weiner 2005 Decoupled Neutrinos (m ν ~ const) ΛCDM Takahashi & Tanimoto 2005

32 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 ΛCDM or Quintessence