Grant-in Aid for Scientific Research c (2)

科学研究补助金 c (2)

• 批准号: 11640270
• 负责人: NAMBU Yasusada
• 金额: $ 2.3万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640270/
• 关键词: inhomogeneous universe; back reaction; renormalization group; inflationv; アインシュタイン方程式; 重力崩壊; 非線形効果

1 ) For long wavelength expansion of Einstein's equation, we obtained the renormalization group equation that describes non-linear dynamics of the long wave fluctuation. The solution of the renormalization group equation shows that the renormalized metric describes the behavior of the gravitational collapse in the expanding universe qualitatively well.In modern cosmology, general relativity plays an essential role in explaining the origin and the evolution of our universe. However its basic equation, Einstein's equation, is non-liner partial differential equation and it is difficult to obtain its solution in general. We must use some approximation method or numeral method to investigate problems in general relativity. The purpose of this research is to construct non-linear approximation method for Einstein's equation based on the renormalization group method. The results of this research are2)We investigate the back reaction of cosmological perturbation on the evolution of the Universe using the renormalization group method. Staring from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor that includes back reaction effect due to inhomogeneities of the Universe.

1）对Einstein方程进行长波展开，得到了描述长波涨落非线性动力学的重整化群方程。重整化群方程的解表明，重整化度规能很好地描述膨胀宇宙中的引力坍缩行为，在现代宇宙学中，广义相对论在解释宇宙起源和演化中起着至关重要的作用。但它的基本方程爱因斯坦方程是非线性偏微分方程，一般情况下很难求解。研究广义相对论中的问题，必须采用某种近似方法或数值方法。本研究的目的是在重整化群方法的基础上构造爱因斯坦方程的非线性近似方法。研究结果如下：2）利用重整化群方法研究了宇宙学微扰对宇宙演化的反作用。本文从二阶微扰的爱因斯坦方程出发，重整化了宇宙的一个标度因子，导出了包含宇宙不均匀性引起的反作用效应的有效标度因子的演化方程。

项目成果

南部保貞: "Renormalization-Group Method and Inhomogeneous Universe in "Fluctuating Paths and Fields""edited by W.Janke, A.Pelster, H-J.Schmidt and M.Bachmann World Scientifc, Singapore. 11 (2001)

Yasusada Nanb​​u：““波动路径和场”中的重正化群方法和非齐次宇宙”，W.Janke、A.Pelster、H-J.Schmidt 和 M.Bachmann 编辑，新加坡世界科学 11 (2001)。

南部保貞、山口義幸: "Renormalization of the long-wavelength solution of Einstein's equation"Physical Review D. 60. 104011-1-104011-7 (1999)

Yasusada Nanb​​u、Yoshiyuki Yamaguchi：“爱因斯坦方程长波长解的重整化”物理评论 D. 60. 104011-1-104011-7 (1999)

南部保貞: "Back reaction problem in the inflationary universe"Physical Review D. 63. 044013-1-044013-9 (2001)

南部安定：“膨胀宇宙中的反反应问题”Physical Review D. 63. 044013-1-044013-9 (2001)

南部保貞: "Back reaction problem in the inflationary universe "Physical Review D. 63. 044013-1-044013-9 (2001)

南部安定：“膨胀宇宙中的反反应问题”Physical Review D. 63. 044013-1-044013-9 (2001)

南部保貞: "Renormalization group approach to cosmological back reaction problems"Physical Review D. 62. 104010-1-104010-10 (2000)

Yasusada Nanb​​u：“宇宙学反反应问题的重正化群方法”Physical Review D. 62. 104010-1-104010-10 (2000)