The trouble with asymptotically Safe Inflation
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Transcript of The trouble with asymptotically Safe Inflation
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The trouble withasymptotically Safe Inflation
Qing-Guo Huang
Based on arXiv: 1210.7596 done with C. Fang
USTC-ICTSState Key Laboratory of Theoretical Physics
Institute of Theoretical Physics, CAS
03/14/2013
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Outline
• Why inflation?• What is the asymptotically safe inflation?• Curvature perturbation in asymptotically safe
inflation• Discussion
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Why inflation?
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Hubble, 1929
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BIG BANG
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1978, Arno A. Penzias and Robert W. Wilson
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2006, G. Smoot and J. Mather
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WMAP(世界地图)
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Matter-dominant era:
Radiation-dominant era:
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Inflation
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Old inflation:
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Dynamics of slow-roll inflation:
Reheating
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2011.06.01
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What is the nature of inflaton?
Is there an inflation model without inflaton?
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What is the asymptotically safe inflation?
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It is well-known that Einstein gravity involves a dimensionful coupling constant and is not renormalizable. Decades ago Weinberg suggested that the effective quantum theory of gravitation might be asymptotically safe, and hence UV complete. That is, the renormalization group flows might have a fixed point, with a finite-dimensional UV critical surface of trajectories attracted to the fixed point at short distance.
S. Weinberg, 1977
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Asymptotically safe gravity can be naturally applied to explore the physics in the early universe.
The beauty of asymptotically safe inflation is that it does not need any inflaton field.
S. Weinberg, 2010
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If ω=0, we obtain a pure de Sitter solution.
Inflation must end in our universe. We hope that the term with R2 might introduce an instability around dS solution.
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instability Re(ξ)>0
ξ+>0 if ω<0. For –κ/ω<<1,
Requiring Nt >60 implies κ<-ω/10.
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Requiring |δH/H|<<1 implies ε/ξ<<1.
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s is asymptotically free.
ω has a stable fixed point at ω*=-0.0228.
Niedermaier, Reuter, 2006
RG flow
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Niedermaier, 2009
At the fixed point with s=0, ω=ω*
RG flow
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In the IR limit, the Einstein Hilbert term in the action becomes
In the UV limit (μ>>μ0),
Tye, Xu, 2010
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Inflation is assumed to be away from the UV fixed point.
Tye, Xu, 2010
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Curvature perturbation
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Gravitational Waves Perturbation
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R R2 C2
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Higher derivative with respect to time implies one more degree of freedom.
Lagrange multiplier
Conjugate momenta: E.O.M:
ghostghost
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The canonical quantization conditions:
In the sub-horizon limit,
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Amplitude of gravitational waves perturbation:
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Scalar Curvature Perturbation
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Discussion
• The instability can come from the term of R2 as long as ω<0.
• The asymptotically safe inflation can achieve a large number of e-folds if -κ/ω<0.1.
• In this case the asymptotically safe inflation suffers from ghost problem.
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48
Thank You!