发表机构
Aix Marseille Université, Université de Toulon, CNRS, CPT（艾克斯马赛大学，土伦大学，法国国家科学研究中心，CPT）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究采用正则 ADM 框架探究德西特时空中暴胀的引力 backreaction，发现单圈阶 backreaction 可重整化宇宙学常数与哈勃参数的关系，且不同 backreaction 表示在物理上等价。
AI 中文摘要
我们发展了一种用于暴胀期间引力 backreaction 的正则 ADM 框架。该方法将原本用于计算宇宙学关联函数的形式体系扩展应用于量子背景的演化，我们将该量子背景与度规单点函数对应起来，目的是评估引力 backreaction 下暴胀几何的量子稳定性。在该框架内，backreaction 由哈密顿约束的期望值和空间度规的运动方程决定。在精确的德西特极限下，我们将该框架应用于无质量极小耦合的旁观标量场和物理引力子极化。在单圈阶，它们的 backreaction 会重整化宇宙学常数与哈勃参数之间的关系，且不会导致德西特演化出现任何长期偏离，这与之前的结果一致。我们采用硬动量截断进行计算，结果显示，固定物理截断可让均匀背景方程用与时间和背景无关的系数进行重整化，这与固定共动截断的情况形成对比。最后，我们证明 backreaction 的显式表示取决于施加在度规涨落上的规范条件以及背景-涨落拆分方式，不过这些不同的表示可通过规范变换关联起来，因此在物理上是等价的。
英文摘要
We develop a canonical ADM framework for gravitational backreaction during inflation. Our approach extends the formalism used to compute cosmological correlators by applying it to the evolution of the quantum background, which we identify with the metric one-point function. The aim is to assess the quantum stability of inflationary geometries under gravitational backreaction. Within this framework, the backreaction is determined by the expectation values of the Hamiltonian constraint and the equations of motion for the spatial metric. Working in the exact de Sitter limit, we apply the framework to a massless minimally coupled spectator scalar field and the physical graviton polarizations. At one loop, their backreaction renormalizes the relation between the cosmological constant and the Hubble parameter without inducing any secular departure from de Sitter evolution, in agreement with previous results. We perform the calculation using a hard momentum cutoff and show that a fixed physical cutoff allows the homogeneous background equations to be renormalized with time- and background-independent coefficients, in contrast to a fixed comoving cutoff. Finally, we demonstrate that the explicit representation of the backreaction depends on the gauge condition imposed on the metric fluctuations, as well as on the background-fluctuation split. Nevertheless, these different representations are related by a gauge transformation and are therefore physically equivalent.
Comments23 pages + appendix
