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Quantum infrared effects in de Sitter space
https://ir.soken.ac.jp/records/3124
https://ir.soken.ac.jp/records/3124989cd906c6684c2fb69b61ab920a7f79
名前 / ファイル  ライセンス  アクション 

要旨・審査要旨 (262.4 kB)


本文 (938.2 kB)

Item type  学位論文 / Thesis or Dissertation(1)  

公開日  20120912  
タイトル  
タイトル  Quantum infrared effects in de Sitter space  
タイトル  
タイトル  Quantum infrared effects in de Sitter space  
言語  en  
言語  
言語  eng  
資源タイプ  
資源タイプ識別子  http://purl.org/coar/resource_type/c_46ec  
資源タイプ  thesis  
著者名 
北本, 浩之
× 北本, 浩之 

フリガナ 
キタモト, ヒロユキ
× キタモト, ヒロユキ 

著者 
KITAMOTO, Hiroyuki
× KITAMOTO, Hiroyuki 

学位授与機関  
学位授与機関名  総合研究大学院大学  
学位名  
学位名  博士（理学）  
学位記番号  
内容記述タイプ  Other  
内容記述  総研大甲第1497号  
研究科  
値  高エネルギー加速器科学研究科  
専攻  
値  14 素粒子原子核専攻  
学位授与年月日  
学位授与年月日  20120323  
学位授与年度  
値  2011  
要旨  
内容記述タイプ  Other  
内容記述  In cosmic inflation at the early universe and dark energy at the present universe, our universe is exponentially expanding with the respective cosmological constants. To investigate the quantum effects on these universes, we need to understand the quantum field theory in de Sitter (dS) space. Exploring the quantum infrared (IR) effects specific to dS space, we may better understand inflation and dark energy. In order to investigate the interacting field theories in a time dependent background like dS space, we need to employ the SchwingerKeldysh formalism. Nonequilibrium physic may play an important role in this regard. In investigating the quantum effects in dS space, we divide the momentum scale into the two regions, inside the cosmological horizon and outside the cosmological horizon. Well inside the cosmological horizon, we have derived a Boltzmann equation in dS space from a SchwingerDyson equation, which is a standard tool in nonequilibrium physics. The local physics probed by the Boltzmann equation respects the dS symmetry since the degrees of freedom inside the cosmological horizon are time independent. On the other hand, the degrees of freedom outside the cosmological horizon increase with cosmic expansion. This increase gives rise a growing time dependence to the propagator for a massless and minimally coupled scalar field and gravitational field. It is a direct consequence of their scale invariant fluctuation spectrum. In some field theoretic models on dS space, the dS symmetry is dynamically broken and physical quantities acquire time dependences through such a quantum IR effect. In particular, this IR effect may be relevant to resolve the cosmological constant problem. In the SchwingerKeldysh perturbation theory, the IR effects at each loop level manifest as a polynomial in the logarithm of the scale factor of the universe. At late times, the leading IR effect comes from the leading logarithm at each loop level. Their growing time dependences mean that the perturbation theory eventually breaks down after a large enough cosmic expansion. In order to understand such a situation, we have to investigate the IR effect nonperturbatively. Remarkably in the models with interaction potentials, the leading IR effects can be evaluated nonperturbatively by the stochastic approach. Furthermore it has been found that the equilibrium solution in the stochastic approach can be rederived in an Euclidean field theory on a 4dimensional sphere. However in a general model with derivative interactions, we still don't know how to evaluate the nonperturbative IR effects. Especially such a tool is required to understand the quantum IR effects of gravity. It is because the gravitational field contains massless and minimally coupled modes with derivative interactions. As a simple model with derivative interactions, we have investigated the nonlinear sigma model. The global symmetry guarantees that it contains massless minimally coupled scalar fields. In addition, we can perform some nonperturbative investigations as it is exactly solvable in the large N limit on an Nsphere. Another point is that there is some similarity to the Einstein action as it consists of the derivative interactions of the metric tensor field. Here we have investigated the contribution to the cosmological constant by evaluating the expectation value of the energymomentum tensor. From the perturbative investigation, we have found that the coupling constant of the nonlinear sigma model becomes time dependent at the one loop level in agreement with power counting of the IR logarithms. In contrast, the leading IR effects to the cosmological constant cancel out each other at the two loop level beyond the power counting. Furthermore, we have shown that the cancellation of the leading IR effects works to all orders on an arbitrary target space. In fact even if we consider the full IR effects, the effective cosmological constant is time independent in the large N limit on an Nsphere. Although the subleading IR effects could arise at the three loop level in a generic nonlinear sigma model, we have shown that there is a renormalization scheme to cancel it. In this thesis, I summarize the quantum IR effects due to the degrees of freedom at the two regions, inside the cosmological horizon and outside the cosmological horizon. 

所蔵  
値  有  
フォーマット  
内容記述タイプ  Other  
内容記述  application/pdf 