see-saw models of vacuum energy kurt hinterbichler dark energy 2008, oct. 9, 2008 arxiv:0801.4526...
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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
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Fine tuning?
What’s the problem with large/small numbers in a theory?
Huge
Measured parameters
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Why the vacuum energy scale should be large
Integrate out the scalar, match to UV theory
UV theory: scalar with mass M
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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.
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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)
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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)
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Gauss-Bonnet model
Vacuum equations of motion Large curvature solution
Small curvature solutions
(Batra, Hinterbichler, Hui, Kabat, 2007)
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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).
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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
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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.
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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?
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