Dark Energy and the MSSM

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

2. 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

3. 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

4. Supergravity Framework Observable Hidden Gravitational Interaction Gravitational Interaction Interaction Gravitational Interaction Dark Energy

5. Three Sectors Hidden sector Kahler potential Superpotential Observable Sector Kahler potential Superpotential Dark Energy sector Kahler potential Superpotential Fields Quintessence field

6. Spontaneous Susy Breaking • Susy broken in the Hidden sector • Parameterised by the vev’s • Susy broken by the F-term vev’s • The gravitino mass

7. 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

8. The Soft Breaking Terms • Susy , spontaneously broken, leads to soft terms • Soft terms depend on the dark energy sector

9. 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

10. 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 vev’s depend on quintessence too • The angle depends on quintessence

11. Boson and Fermion Masses • The Higgs scale becomes (large regime) • The gauge boson masses depend on quintessence • The matter Fermion masses depend on quintessence

12. 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

13. Fifth Force • Gravity tests are only relevant for nearly massless quintessence, Newton’s law becoming • Cassini experiments constraint • The gravitational coupling constant • At the microscopic level,

14. 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

15. Macroscopic Violation of WEP • The mass of elements dominated by QCD • The WEP violation as a function of

16. 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.

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

18. 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

19. Stabilised Hidden sector • Coupling to hidden sector with • Compatible with • Explicit example: leads to

20. 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.

21. 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

22. 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

23. 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

25. Gravity Tests • Fifth force: • Weak Equivalence Principle • Proton to Electron mass ratio • Incompatible with attractor mechanism

26. 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….