The trouble with asymptotically Safe Inflation Qing-Guo Huang Based on arXiv: 1210.7596 done with C. Fang USTC-ICTS State Key Laboratory of Theoretical Physics Institute of Theoretical Physics, CAS 03/14/2013
Feb 23, 2016
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
Outline
• Why inflation?• What is the asymptotically safe inflation?• Curvature perturbation in asymptotically safe
inflation• Discussion
Why inflation?
Hubble, 1929
BIG BANG
1978, Arno A. Penzias and Robert W. Wilson
2006, G. Smoot and J. Mather
WMAP(世界地图)
Matter-dominant era:
Radiation-dominant era:
Inflation
Old inflation:
Dynamics of slow-roll inflation:
Reheating
2011.06.01
What is the nature of inflaton?
Is there an inflation model without inflaton?
What is the asymptotically safe inflation?
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
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
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.
instability Re(ξ)>0
ξ+>0 if ω<0. For –κ/ω<<1,
Requiring Nt >60 implies κ<-ω/10.
Requiring |δH/H|<<1 implies ε/ξ<<1.
s is asymptotically free.
ω has a stable fixed point at ω*=-0.0228.
Niedermaier, Reuter, 2006
RG flow
Niedermaier, 2009
At the fixed point with s=0, ω=ω*
RG flow
In the IR limit, the Einstein Hilbert term in the action becomes
In the UV limit (μ>>μ0),
Tye, Xu, 2010
Inflation is assumed to be away from the UV fixed point.
Tye, Xu, 2010
Curvature perturbation
Gravitational Waves Perturbation
R R2 C2
Higher derivative with respect to time implies one more degree of freedom.
Lagrange multiplier
Conjugate momenta: E.O.M:
ghostghost
The canonical quantization conditions:
In the sub-horizon limit,
Amplitude of gravitational waves perturbation:
Scalar Curvature Perturbation
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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Thank You!