Dark Energy and the MSSM

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Dark Energy and the MSSM
Ph.Brax and J. Martin Dark energy Workshop
Galileo Galilei Institute October 2006
astro-ph/0605228 astro-ph/0606306
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Dark Energy in Broken Supergravity

• General Framework
• Coupling the Observable, Hidden and Dark
  Energy sectors
• Breaking susy and soft Terms
• Electroweak symmetry breaking
• Gravity tests
• Chameleon effect

• The SUGRA quintessence model
• Sugra model coupled to susy breaking
• Cosmological consequences
• Gravity tests

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Motivation

• Quintessence and Attractors
• most quintessence models with insensitivity
  to initial conditions require an attractor
  mechanism
• Inverse power law potentials, exponential
  potentials
• Large values of
• Supergravity can handle large field values
  and connects gravity with high energy physics

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Supergravity Framework
Observable
Hidden
Gravitational Interaction
Gravitational Interaction Interaction
Gravitational Interaction
Dark Energy
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Three Sectors

• Hidden sector
• Kahler potential
• Superpotential
• Observable Sector
• Kahler potential
• Superpotential

• Dark Energy sector
• Kahler potential
• Superpotential
• Fields
• Quintessence field

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Spontaneous Susy Breaking

• Susy broken in the Hidden sector
• Parameterised by the vevs
• Susy broken by the F-term vevs
• The gravitino mass

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The Effective Theory

• After susy breaking, effective theory for
  Observable sector coupled to Dark Energy
• The Dark Energy potential
• with
• highly dependent on
  the susy breaking sector

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The Soft Breaking Terms

• Susy , spontaneously broken, leads to soft terms
• Soft terms depend on the dark energy sector

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Gaugino Masses

• Gauginos acquire a mass depending on the gauge
  coupling function
• The mass depends on the F-terms breaking
  supersymmetry
• The gauge coupling dependence on the dark energy
  sector leads to variations of constants

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Electro-weak Symmetry Breaking

• The Higgs potential depends on the dark energy
  sector via the soft terms evaluated at the
  electro-weak scale
• The two Higgs vevs depend on quintessence too
• The angle depends on quintessence

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Boson and Fermion Masses

• The Higgs scale becomes (large
  regime)
• The gauge boson masses depend on quintessence
• The matter Fermion masses depend on quintessence

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Violation of the Weak Equivalence Principle

• At the microscopic level, particles of types u or
  d do not have the same mass dependence on
  quintessence WEP violation
• Coupling to matter
• Scalar-tensor effective action
• Need to analyse the WEP violation for
  macroscopic bodies

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Fifth Force

• Gravity tests are only relevant for nearly
  massless quintessence, Newtons law becoming
• Cassini experiments constraint
  
• The gravitational coupling constant
• At the microscopic level,

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Variation of Constants

• The gauge coupling constants at the weak scale
• The fine structure constant at the weak scale
• The proton to electron mass ratio varies

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Macroscopic Violation of WEP

• The mass of elements dominated by QCD
• The WEP violation
• as a function of

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Chameleon Effect

• In the presence of matter, the quintessence
  potential is modified
• depends on the neutralino mass matrix
• Same effect for Baryon, could alleviate gravity
  tests.
• Depends on the QCD gauge function mainly.
  Possible link with variation of constants.

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The SUGRA Model

• Ignoring coupling to the Hidden and Observable
  sector
• Assuming
  , the scalar
  potential becomes
• Phenomenologically interesting as equation of
  state -0.82

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Fine-Tuning of Parameters

• For a GUT scale model , see-saw mechanism
• and
  for
• Control of Kahler expansion, need extra symmetry,
  e.g. modular invariance
  
  

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Stabilised Hidden sector

• Coupling to hidden sector with
• Compatible with
• Explicit example
• leads to

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Massive Quintessence Field

• In this context, the Dark Energy potential
  becomes
• Compensator coming from the Hidden sector
• Mass term due to the gravitino mass, evading
  gravity tests.

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Cosmological Evolution

• Quintessence field stabilised at small value
• Quintessence field convergence to minimum before
  BBN
• Cosmological evolution equivalent to a pure
  cosmological constant both at the background and
  perturbative levels
• Hidden sector modifies dynamics

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Runaway Potential

• Runaway potentials may be possible with
  non-trivial hidden sector dynamics
• Simplest assumption
• More complex cases, need a case by case analysis
• Explicit knowledge of the electroweak and gravity
  sectors

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Electroweak Breaking

• Boson masses depend on the quintessence sector in
  a calculable way
• No gauge coupling variation in this model
• The Weinberg angle is constant
• The angle varies with the quintessence
  field
• When cosmological evolution known, can back track
  the physical observables

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Gravity Tests

• Fifth force
• Weak Equivalence Principle
• Proton to Electron mass ratio
• Incompatible with attractor mechanism

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Conclusion

• General framework to couple Dark Energy, Hidden
  and Observable sectors in supergravity
• Tension between cosmology and gravity tests
• Tension between cosmology and particle physics
  requirements
• Need to build realistic models with broken susy,
  cosmological attractor and small gravitational
  couplings
• Chameleons and neutralinos?
• Prospects moduli fields.