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Kinematics and dynamics in theories with Lifshitz scaling

渡邉, 陽太 東京大学 DOI:10.15083/0002004255

2022.06.22

概要

Hořava-Lifshitz 重力理論は局所的な重力場の理論の枠組みにおける量子重力理論の候補であり、少なくとも次数勘定的にはくりこみ可能である。このくりこみ可能性は、Lorentz不変性を犠牲にする代わりに空間に関する高階微分を用いることで得られる。この理論は時間と空間に関して非対称なスケーリングである Lifshitz スケーリングを持つ。理論は時間の葉層を保つ微分同相写像の下で不変であり、この理論には重力子のスカラーモードが存在する。プロジェクタブルと呼ばれる理論の最小の枠組みではスカラー重力子の性質により摂動展開が破綻してしまい、状況によっては解析が困難になる。そこで、スカラー重力子を除くために追加の U(1)対称性が導入された。しかし、U(1)対称性があるプロジェクタブル理論は、太陽系内観測による制限と連星中性子星合体による重力波の伝播速度に対する制限が矛盾することが本博士論文で示されている。一方、プロジェクタブルではない理論に U(1)対称性を導入した場合、スカラー重力子が存在するかどうかは Minkowski 時空まわりの線形摂動でしか調べられていなかった。そこで本博士論文では、この理論における物理的自由度の数を完全な非線形レベルで任意の時空上で調べられている。その結果、スカラー重力子が存在するためのパラメータの条件が同定されており、観測的制限を満たすパラメータに対してはスカラー重力子が存在することが示されている。そのため、将来の観測により重力のスカラー偏光に対する制限が強くなれば理論を棄却できる可能性を示唆した。

さらに、分布関数が従う Boltzmann 方程式に対応する古典運動学的方程式が Hořava- Lifshitz 理論の物質セクターに対して本博士論文で導出されている。ただし、実スカラー場に着目し、Lifshitz スケーリングがz=2 の場合には任意の曲がった時空上で、z=3 の場合には空間的に平坦な時空上で導出され、U(1)対称性は導入されていない。また、技術的な理由によりプロジェクタブル条件を仮定したが、導出された方程式はノンプロジェクタブル理論における一様等方時空上の試験粒子に対しても適用可能である。さらに U(1)対称性を導入したとしても、U(1)ゲージ場とスカラー場の結合を小さな相互作用とみなせば、主要項は導出された無衝突項で表される。導出された運動学的方程式の中で、非自明な分散関係の情報は群速度の表式に含まれている。このことから、特に無衝突粒子の自由運動や拡散減衰は群速度によって生じることが示唆される。

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