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書き出し

Stochastic description and quantum aspects of curvature perturbations in the inflationary universe

安藤, 健太 東京大学 DOI:10.15083/0002006638

2023.03.24

概要

論文審査の結果の要旨
氏名









私たちの住む宇宙がなぜ、開闢以来 100 億年以上を経てなお豊かな物質と階層構造を
持っているのか、またなぜ数百億光年もの大スケールの一様等方性を保っているのか、は
初期宇宙のインフレーション的急膨張によって説明されると考えられている。初期宇宙
のインフレーションはスカラー場のポテンシャルエネルギーが優勢になることで起こり、
その量子的な性質によって階層構造の起源となった曲率ゆらぎが生成する、というのが
標準的な考え方である。ここで、ミクロなスケールに生成する量子ゆらぎが、指数関数的
膨張によって、宇宙マイクロ波背景放射や大規模構造によって観測される大スケールの
古典ゆらぎとなる点が重要である。
本論文は本文6章と付録4節からなる。第1章から第4章まではこの分野を網羅する
レビューにあてられている。第1章は宇宙論的摂動論のレビューであり、摂動量の定義か
ら本論文で使用する曲率ゆらぎ導出のためのδN 形式について述べられている。第2章
はインフレーション宇宙論と量子ゆらぎの生成について、またその古典化について纏め
られている。第3章はインフレーションの量子的性質を非摂動的に扱う確率過程インフ
レーションの方法とそのδN 形式への適用について紹介されている。さらに第4章は量
子論と古典論を区別するのに有用なベルの不等式について述べられている。
第5章と第6章が著者のオリジナルな研究成果の報告である。
第5章では、まず確率過程インフレーションの方法によって、宇宙の階層構造の起源を
与える曲率ゆらぎのパワースペクトルを計算する方法の導出がなされている。確率過程
インフレーション法の基礎方程式は、確率的ノイズ項を含むランジェバン方程式で与え
られるが、ここから各時刻におけるスカラー場の統計分布関数の従うフォッカープラン
ク方程式を導出できることが知られていた。本研究はこの時刻と場の値の関係を逆転さ
せ、インフレーションが終了する場の値の位置で、インフレーションの持続時間がどのよ
うにばらつくか、その分布関数を求める手法を開発した。各点でのインフレーションの持
続時間はその点における曲率ゆらぎの振幅に対応するので、これによって曲率ゆらぎの
分布関数が得られたことになる。本研究はさらにそこから観測量と最も密接に関係する
曲率ゆらぎのパワースペクトルを計算する手法を与えることに成功した。得られた結果
は、ランジェバン方程式のノイズ項が十分小さな、通常の場合はこれまで線形摂動論と自
由場の量子化によって得られていた公式と一致するものであった。一方、原始ブラックホ
ールが起こり得るような、一部のスケールに大きなゆらぎが生成されるような場合は、こ
のとき生じるスカラー場の一様部分の擾乱が無視できなくなり、より大きなスケールに
おいてもその影響が残り得ることが判明した。このことは、各波数が独立に進化する線形
摂動論では見いだし得ない結果であり、確率過程インフレーション法の優位性を示すも
のであるともいえる。
続く第6章では、量子論と隠れた変数を持つ古典統計論の相関を区別できるベルの不

等式の宇宙論への応用が考究されている。宇宙論では曲率ゆらぎの値が観測量となり、そ
の時間微分は直接観測できないので、将来の観測を念頭に、異なる時刻の相関について考
察した。曲率ゆらぎは宇宙膨張によってスクイーズド状態という量子状態を取るので、こ
の状態においてベルの不等式を計算し、それが破れるパラメタ領域があることを発見し
た。このことはゆらぎの量子的起源を如実に示すものであり、これが将来検出されれば、
インフレーション宇宙論に基づく構造形成論を直接検証できることになる。
なお、本論文の第5章と第6章の内容は、いずれも Vindcent Vennin 氏との共同研究
として刊行されているが、これらは理論計算、数値計算、論文執筆共に論文提出者が中心
となって行ったものであり、本委員会は同人の貢献を十分と認めた。
さらに、論文提出者が本専攻大学院に在学中に発表したそれ以外の学術論文の内容を
はじめ、物理学全般に亘って本学博士に相応しい学識を持っているかを口頭にて試問し
たが、その結果審査員全員一致にて合格と認定した。
したがって、博士(理学)の学位を授与できると認める。

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