威尔逊宇宙学：德西特（非）稳定性
Wilsonian Cosmology: de Sitter (in)Stability
AI总结：
该研究开发了威尔逊型函数重整化群的标量宇宙学框架，推导了势的非微扰流方程与耦合弗里德曼方程，分析了德西特真空的两种情况，发现质量项可稳定系统，为暗能量和暴胀研究提供新吸引子。
AI中文摘要：
我们开发了一种用于标量宇宙学的（威尔逊型）函数重整化群框架，其中标量场的量子涨落在宇宙学类空超曲面上被粗粒化。通过积分掉波长小于哈勃半径$H(t)^{-1}$的量子涨落，我们得到了随时间演化的有效标量势$U(\boldsymbol{\phi}(t),H(t))$。我们推导了该势的非微扰流方程，以及一组耦合的（修正）弗里德曼方程。随后，我们将该形式体系应用于标量场静止时德西特真空的最简情形，考虑两种恰好满足流方程的情况：(i) 平坦势，我们发现唯一的纯德西特解是不稳定的，对应鞍点；(ii) 曲率$m^2>0$的二次势，我们发现质量项的存在可使系统稳定。后一种情况会在质量大于初始时刻哈勃尺度时，在哈勃尺度处产生德西特吸引子；若质量更小，则会引入一个位于$H=m$处的新吸引子，这可能对暗能量和暴胀理论的唯象研究尤为重要。
英文摘要：
We develop a (Wilsonian) functional-renormalisation-group framework for scalar cosmology in which quantum fluctuations of a scalar field are coarse-grained on cosmological spacelike hypersurfaces. Integrating out quantum fluctuations with wavelengths smaller than the Hubble radius $H(t)^{-1}$, we obtain an effective scalar potential $U(ϕ(t),H(t))$ that evolves in time. We derive a non-perturbative flow equation for this potential, together with the coupled set of (modified) Friedmann equations. We then apply this formalism to the simplest possible case of a de Sitter vacuum when the scalar field is at rest, in two situations which satisfy exactly our flow equation: $(i)$ A flat potential, for which we find that the only pure de Sitter solution is unstable and corresponds to a saddle point. $(ii)$ A quadratic potential with curvature $m^2>0$, for which we find that the presence of the mass term stabilises the system. The latter case leads to a de Sitter attractor either at the Hubble scale when the mass is larger than the Hubble scale at initial time, or by introducing a new attractor located at $H=m$ in the case the mass is smaller, which may be particularly relevant to the phenomenological study of dark energy and inflation theories.
