SeeSaw models of Vacuum Energy Kurt Hinterbichler Dark

See-Saw models of Vacuum Energy Kurt Hinterbichler Dark Energy 2008, Oct. 9, 2008 ar. Xiv: 0801. 4526 [hep-th] with Puneet Batra, Lam Hui and Dan Kabat

Fine tuning? Measured parameters Huge What’s the problem with large/small numbers in a theory?

Why the vacuum energy scale should be large UV theory: scalar with mass M Integrate out the scalar, match to UV theory

Technical naturalness Suppose symmetry ensures vac=0. Quantum corrections to vac will vanish. Now add a term with a small parameter that breaks the symmetry. Quantum corrections are proportional to , since they must vanish as 0. Now we can hope to find a UV mechanism to make the bare vac small. Quantum mechanics won’t ruin it.

Getting a small from modified gravity CDTT model (Carroll, Duvvuri, Trodden, Turner, 2004) Effective scalar potential Higher interactions go like (As EFT it is valid up to the Planck scale) Solution

UV “completion” of CDTT R 2 model (Batra, Hinterbichler, Hui, Kabat, 2007) Integrate out the scalar There are now two different vacuum solutions Assuming High curvature Low curvature

Gauss-Bonnet model (Batra, Hinterbichler, Hui, Kabat, 2007) Vacuum equations of motion Large curvature solution Small curvature solutions

Total derivative structure of the non-minimal coupling ensures: Only one small parameter needed: Same tuning as a bare CC: Low curvature solution is unstable, but is stable on cosmological time scales provided <O(1).

Quantum corrections Leading corrections to the scalar mass vanish because of the total derivative structure of the GB term graviton scalar First correction comes at 2 -loops Does not spoil see-saw for

Large corrections to the vacuum energy don’t ruin the smallness of the curvature in the vacuum solution • The VEV < > shifts to maintain a small effective vacuum energy. • Gauss-Bonnet structure is crucial. Assures that the effective m. P is not shifted, and that potentially dangerous quantum corrections vanish. • Technically natural tuning of the CC.

Conclusions • Modified gravity can not really cure fine tuning problems, but it can push tuning into other parameters. • Pushing the tuning into other parameters can make it technically natural, as in the Gauss-Bonnet model. Future questions: • Realistic cosmological solutions with inflation? High curvature vacuum low curvature vacuum? • Realization in fundamental theory? • Landscape?