See-Saw models of Vacuum Energy

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See-Saw models of Vacuum Energy

• Kurt Hinterbichler

Dark Energy 2008, Oct. 9, 2008
arXiv0801.4526 hep-th with Puneet Batra, Lam
Hui and Dan Kabat
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Fine tuning?
Measured parameters
Huge
Whats the problem with large/small numbers in a
theory?
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Why the vacuum energy scale should be large
UV theory scalar with mass M
Integrate out the scalar, match to UV theory
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Technical naturalness
Suppose symmetry ensures ?vac0. 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 wont ruin
it.
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Getting a small ? from modified gravity
CDTT model
Solution
(Carroll, Duvvuri, Trodden, Turner, 2004)
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UV completion of CDTT
R?2 model
(Batra, Hinterbichler, Hui, Kabat, 2007)
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Gauss-Bonnet model
(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 ?ltO(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 dont ruin
the smallness of the curvature in the vacuum
solution

• The VEV lt?gt 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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