1. See-Saw models of Vacuum Energy Kurt Hinterbichler Dark Energy 2008, Oct. 9, 2008 arXiv:0801.4526 [hep-th] with Puneet Batra, Lam Hui and Dan Kabat

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

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

4. 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.

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

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

7. Gauss-Bonnet model Vacuum equations of motionLarge curvature solution Small curvature solutions (Batra, Hinterbichler, Hui, Kabat, 2007)

8. 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).

9. 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

10. 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.

11. 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?