the trouble with asymptotically safe inflation

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!