戈德斯通玻色子觉醒：标度不变\(R^2\)引力中的幺正暗能量
The Goldstone Awakens: Unimodular dark energy in scale-invariant $R^2$ gravity
AI总结：
该研究基于标度不变性和幺正引力构建\(R^2\)宇宙学模型，戈德斯通玻色子联系暴胀与暗能量。通过诺特定流守恒限制暴胀轨迹，幺正积分常数产生指数势，暗能量势斜率由场空间几何决定，紧密关联早晚期宇宙可观测量。
AI中文摘要：
我们基于标度不变性和幺正引力构建了一个\(R^2\)宇宙学模型，其中伸缩的戈德斯通玻色子在暴胀和暗能量之间建立了一种可预测的联系。相应诺特定流的守恒将暴胀轨迹限制在场空间的一维轨道上，冻结戈德斯通方向，使暴胀动力学有效地变为单场。暴胀后，系统稳定在闵可夫斯基真空流形上。幺正积分常数在完整理论中已存在，在暴胀期间可忽略，它提升了平坦的戈德斯通方向，为正则归一化场产生指数势。与唯象的精质模型不同，其斜率不是自由的暗能量参数，而是由暴胀吸引子继承的场空间几何决定。这种几何排除了物质时代的跟踪，并在整个暴胀可行区域使场处于与加速膨胀兼容的解冻状态。对于一个代表性的暴胀基准，现在的准戈德斯通场一直冻结到接近当前时代，在CPL参数化\(w(a)=w_0+w_a(1 - a)\)中产生暗能量状态方程参数\((w_0,w_a)\simeq(-0.992,-0.011)\)。更一般地，控制暴胀谱倾斜的相同参数也固定了暗能量势的斜率，导致早期和晚期宇宙可观测量之间的紧密关联：增加解冻信号会降低\(n_s\)，而\(n_s\)更接近1的值会使模型趋向于\(\Lambda\)CDM。
英文摘要：
We construct an $R^2$ cosmology based on scale invariance and unimodular gravity in which the Goldstone boson of dilatations establishes a predictive connection between inflation and dark energy. The conservation of the corresponding Noether current confines the inflationary trajectory to a one-dimensional orbit in field space, freezing the Goldstone direction and rendering the inflationary dynamics effectively single field. After inflation, the system settles on a Minkowski vacuum manifold. The unimodular integration constant, already present in the full theory but negligible during inflation, lifts the flat Goldstone direction, generating an exponential potential for the canonically normalised field. Unlike in phenomenological quintessence models, its slope is not a free DE parameter, but is instead fixed by the field-space geometry inherited from the inflationary attractor. This geometry excludes matter-era tracking and, throughout the inflationary viability region, places the field in the thawing regime compatible with accelerated expansion. For a representative inflationary benchmark, the now pseudo-Goldstone field remains frozen until close to the present epoch, yielding DE equation-of-state parameters $(w_0,w_a)\simeq(-0.992,-0.011)$ in the CPL parametrisation $w(a)=w_0+w_a(1-a)$. More generally, the same parameter controlling the inflationary spectral tilt also fixes the slope of the DE potential, leading to a tight correlation between early- and late-Universe observables: increasing the thawing signal lowers $n_s$, while values of $n_s$ closer to unity drive the model towards $Λ$CDM.
