インフレーションモデルにおける赤外・紫外発散の問題

• Project Area: The Physical Origin of the Universe viewed through the Cosmic Background Radiation - from Cosmological Inflation to Dark Ages -
• Project/Area Number: 22111507
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Kyoto University
• Principal Investigator: 田中 貴浩 京都大学, 基礎物理学研究所, 教授 (40281117)
• Project Period (FY): 2010 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: インフレーション / 赤外発散 / 密度揺らぎ / 宇宙背景放射 / 重力波 / ゲージ不変性

Research Abstract

宇宙初期に起こったインフレーションの時期におけるゆらぎの生成過程において生じる赤外発散の問題について研究を進めた。前年度までの研究では、完全なゲージ固定をおこなわない場合であっても、問題となる残余のゲージ自由度に影響されないような真にゲージ不変な観測量を計算することで赤外発散は除かれるであろうという着想に立ち、そのような計算を遂行した。その結果、赤外発散が1-ループの補正に現れないための条件として、初期の量子状態の選び方に対する条件が得られ、状態が制限されることを発見した。
この初期状態に対する条件の導出に際して、非線形なハイゼンベルグ方程式を解く段階で特殊な解を選ぶということをおこなっていた点と、スローロール近似を用いていた点が不満であった。また、このような初期状態に対する制限なしに赤外発散が除かれているという主張をする論文が現れてきた状況から、我々の主張をより鮮明にさせる必要が大きくなった。そこで、スローロール近似に依存しない議論をおこなうことができるような枠組みの整備を進めた。その結果、やはり、そう簡単には赤外発散を起こさない状態を選ぶことはできず、状態に対する強い制限がつくことを再確認した。しかし、単純に赤外発散が自然に除かれるという主張と我々の主張は矛盾していないのかもしれない。赤外発散が自然に除かれるという主張は暗に断熱的真空状態という特殊な状態を選んで赤外発散がないと主張していることになっているようである。我々も、この特殊な状態(およびこの状態を元にしたゲージ不変な励起状態)を考えるという限られた状態に対してのみ赤外発散がないということを予想しているが、他の研究者による主張も議論の不完全な点が多々あり、我々も証明を与えるに至っていない。

Research Products

• [Journal Article] Cosmology with space-based gravitational-wave detectors---dark energy and primordial gravitational waves--- (2011)
  • Author(s): Atsushi Nishizawa, Kent Yagi, el al
  • Journal Title: Physical Review D Volume: 85 Issue: 4
  • DOI: 10.1103/physrevd.85.044047
  • Peer Reviewed
• [Journal Article] Cosmic censorship in overcharging a Reissner-Nordstrom black hole via charged particle absorption (2011)
  • Author(s): S. Isoyama, N. Sago and T. Tanaka
  • Journal Title: Physical Review D Volume: 84 Issue: 12
  • DOI: 10.1103/physrevd.84.124024
  • Peer Reviewed
• [Journal Article] Chiral Phase Transitions around Black Holes (2011)
  • Author(s): Antonino Flachi
  • Journal Title: Physical Review D Volume: 84 Issue: 6
  • DOI: 10.1103/physrevd.84.061503
  • Peer Reviewed
• [Journal Article] Black holes in braneworld models (2011)
  • Author(s): N. Tanahashi and T. Tanaka
  • Journal Title: Prog. Theor. Phys. Suppl Volume: 189 Pages: 227-268
  • DOI: 10.1143/ptps.189.227
  • NAID: 110008711103
  • Peer Reviewed
• [Journal Article] Open inflation in the landscape (2011)
  • Author(s): 山内大介、Andrei Linde、成子篤、佐々木節、田中貴浩
  • Journal Title: Physical Review D 84 Volume: 84 Issue: 4 Pages: 43513-43513
  • DOI: 10.1103/physrevd.84.043513
  • Peer Reviewed
• [Journal Article] Dominance of gauge artifact in the consistency relation for the primordial bispectrum (2011)
  • Author(s): T. Tanaka and Y. Urakawa
  • Journal Title: Journal of Cosmology and Astroparticle Physics Volume: 1105 Issue: 05 Pages: 014-014
  • DOI: 10.1088/1475-7516/2011/05/014
  • Peer Reviewed
• [Journal Article] A note on the role of the boundary terms for the non-Gaussianity in general k-inflation (2011)
  • Author(s): F. Arroja and T. Tanaka
  • Journal Title: Journal of Cosmology and Astroparticle Physics Volume: 1105 Issue: 05 Pages: 005-005
  • DOI: 10.1088/1475-7516/2011/05/005
  • Peer Reviewed
• [Journal Article] Stability of Schwarzschild-like solutions in f(R,G) gravity models (2011)
  • Author(s): A. De Felice, T. Suyama and T. Tanaka
  • Journal Title: Physical Review D Volume: 83 Issue: 10
  • DOI: 10.1103/physrevd.83.104035
  • Peer Reviewed
• [Journal Article] Probing the size of extra dimension with gravitational wave astronomy (2011)
  • Author(s): Kent Yagi, et al
  • Journal Title: Physical Review D Volume: 83 Issue: 8
  • DOI: 10.1103/physrevd.83.084036
  • Peer Reviewed
• [Journal Article] Natural selection of inflationary vacuum required by infra-red regularity and gauge-invariance (2011)
  • Author(s): Y. Urakawa and T. Tanaka
  • Journal Title: Prog. Theor. Phys. Volume: 125 Issue: 5 Pages: 1067-1089
  • DOI: 10.1143/ptp.125.1067
  • NAID: 110008661185
  • Peer Reviewed
• [Journal Article] Probing the size of extra dimension with gravitational wave astronomy (2011)
  • Author(s): Kento Yagi, Norihiro Tanahashi, Takahiro Tanaka
  • Journal Title: Phys.Rev.D Volume: (to be publishes 印刷中)
  • Peer Reviewed
• [Journal Article] A covariant approach to general field space metric in multi-field inflation (2011)
  • Author(s): Jinn-Ouk Gong, Takahiro Tanaka
  • Journal Title: JCAP Volume: 1103
  • Peer Reviewed
• [Journal Article] Chiral Modulations in Curved Space I : Formalism (2011)
  • Author(s): Antonino Flachi, Takahiro Tanaka
  • Journal Title: JHEP Volume: 1102
  • Peer Reviewed
• [Journal Article] Natural selection of inflationary vacuum required by infra-red regularity and gauge-invariance (2011)
  • Author(s): Yuko Urakawa, Takahiro Tanaka
  • Journal Title: Prog.Theor.Phys. Volume: (to be publishes 印刷中)
  • NAID: 210000112312
  • Peer Reviewed
• [Journal Article] IR divergence does not affect the gauge-invariant curvature perturbation (2010)
  • Author(s): Yuko Urakawa, Takahiro Tanaka
  • Journal Title: Phys.Rev.D Volume: 82
  • Peer Reviewed
• [Journal Article] Inevitable ghost and the degrees of freedom in f(R,G) gravity (2010)
  • Author(s): Antonio De Felice, Takahiro Tanaka
  • Journal Title: Prog.Theor.Phys. Volume: 124 Pages: 503-515
  • NAID: 110007730009
  • Peer Reviewed
• [Journal Article] Spin-2 Ghost In Brane Gravity (2010)
  • Author(s): Takahiro Tanaka
  • Journal Title: Mod.Phys.Lett.A Volume: 25 Pages: 936-943
  • Peer Reviewed
• [Journal Article] Use of delta N formalism-Difficulties in generating large local-type non-Gaussianity during inflation (2010)
  • Author(s): Takahiro Tanaka, Teruaki Suyama, Shuichiro Yokoyama
  • Journal Title: Class.Quant.Crav. Volume: 27
  • Peer Reviewed
• [Presentation] Hawking radiation of interacting fields (2011)
  • Author(s): T.Tanaka
  • Organizer: Black Holes : New Horizons
  • Place of Presentation: Banff, Canada(招待講演)
  • Year and Date: 2011-11-22
• [Presentation] Some issues about infrared divergences during inflation (2011)
  • Author(s): T.Tanaka
  • Organizer: Mini-Workshop on cosmology
  • Place of Presentation: APCTP, Pohan, Korea(招待講演)
  • Year and Date: 2011-10-28
• [Presentation] Some issues about infrared divergences during inflation (2011)
  • Author(s): T.Tanaka
  • Organizer: Pre-Planckian Inflation
  • Place of Presentation: Minnesota university, USA(招待講演)
  • Year and Date: 2011-10-06
• [Presentation] Constraints on modified gravity models from future gravitational wave observations (2011)
  • Author(s): T.Tanaka
  • Organizer: KIAS-YITP Joint workshop "String Theory, Holography and Beyond"
  • Place of Presentation: KIAS, Seoul, Korea(招待講演)
  • Year and Date: 2011-09-23
• [Presentation] 重力波物理の進展 (2011)
  • Author(s): T.Tanaka
  • Organizer: 日本物理学会
  • Place of Presentation: 弘前大学(招待講演)
  • Year and Date: 2011-09-17
• [Presentation] Infrared divergences and cosmological observables (2011)
  • Author(s): T.Tanaka
  • Organizer: UK Cosmo
  • Place of Presentation: Portsmouth university, UK(招待講演)
  • Year and Date: 2011-09-14
• [Presentation] IR issues during inflation-constraints on quantum state- (2011)
  • Author(s): T.Tanaka
  • Organizer: Cosmologicai Frontiers in Fundamental Physics Workshop
  • Place of Presentation: APC, Paris, France(招待講演)
  • Year and Date: 2011-06-17
• [Presentation] IR issues during inflation-constraints on quantum state- (2011)
  • Author(s): T.Tanaka
  • Organizer: Cosmological Non-Gaussianity : Observations Confront Theory Workshop
  • Place of Presentation: Michigan, USA(招待講演)
  • Year and Date: 2011-05-15
• [Presentation] Tensor perturbation constraint on inflation models with non-negligible spatial curvature in landscape scenario (2011)
  • Author(s): T.Tanaka
  • Organizer: Bubbles in the Sky
  • Place of Presentation: UC Davis, USA(招待講演)
  • Year and Date: 2011-04-01
• [Presentation] Quantum field in curved space～issues related to IR divergences>>in the inflationary universe～ (2011)
  • Author(s): Takahiro Tanaka
  • Organizer: 第四回超弦理論と宇宙
  • Place of Presentation: KKR箱根、神奈川県箱根町(招待講演)
  • Year and Date: 2011-02-18
• [Presentation] Gravitational Radiation Reaction (2011)
  • Author(s): Takahiro Tanaka
  • Organizer: 2011 Shanghai Asia-Pacific School and Workshop on Gravitation
  • Place of Presentation: 上海師範大学、中華人民共和国(招待講演)
  • Year and Date: 2011-02-10
• [Presentation] インフレーション宇宙論 (2010)
  • Author(s): 田中貴浩
  • Organizer: 第23回理論懇シンポジウム「林忠四郎先生と天文学・宇宙物理学」
  • Place of Presentation: 京都大学基礎物理学研究所、京都市(招待講演)
  • Year and Date: 2010-12-22
• [Presentation] 重力波が開く新しい物理学 (2010)
  • Author(s): 田中貴浩
  • Organizer: 一般講演会「重力波で宇宙を探る」
  • Place of Presentation: 東京大学柏キャンパス内柏図書館メディアホール、柏市(招待講演)
  • Year and Date: 2010-11-27
• [Presentation] IR issues in the inflationary universe (2010)
  • Author(s): Takahiro Tanaka
  • Organizer: Extra-Dimension Probe by Cosmophysics
  • Place of Presentation: KEK、つくば市
  • Year and Date: 2010-11-09
• [Presentation] ダークエネルギー再考 (2010)
  • Author(s): 田中貴浩
  • Organizer: 日本物理学会2010年秋季大会
  • Place of Presentation: 九州工業大学戸畑キャンパス北九州市(招待講演)
  • Year and Date: 2010-09-12
• [Presentation] ブレーン重力:何が面白くて、何がまだわかっていないのか (2010)
  • Author(s): 田中貴浩
  • Organizer: 天体天文若手夏の学校
  • Place of Presentation: ホテル日航豊橋、豊橋市(招待講演)
  • Year and Date: 2010-08-03
• [Presentation] IR divergence and initial vacuum state (2010)
  • Author(s): Takahiro Tanaka
  • Organizer: Gravity and Cosmology 2010
  • Place of Presentation: 京都大学基礎物理学研究所、京都市
  • Year and Date: 2010-07-14