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

Fine tuning?

What’s the problem with large/small numbers in a theory?

Huge

Measured parameters

Why the vacuum energy scale should be large

Integrate out the scalar, match to UV theory

UV theory: scalar with mass M

Technical naturalnessSuppose 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 Solution

Effective scalar potential

Higher interactions go like(As EFT it is valid up to the Planck scale)

(Carroll, Duvvuri, Trodden, Turner, 2004)

UV “completion” of CDTTR2 model

There are now two different vacuum solutions

High curvature Low curvature

Assuming

Integrate out the scalar

(Batra, Hinterbichler, Hui, Kabat, 2007)

Gauss-Bonnet model

Vacuum equations of motion Large curvature solution

Small curvature solutions

(Batra, Hinterbichler, Hui, Kabat, 2007)

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 smallnessof 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 mP 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?