AI 中文总结
本文探讨超越爱因斯坦-嘉当的扭转伪暴胀，计算Weyssenhoff自旋流体的加速窗口，提出黎曼-嘉当宇宙学中两分支方案，轴分支的德西特解为吸引子，限定在普朗克尺度，背景层面已研究，扰动谱待研究。
AI 中文摘要
扭转在早期宇宙宇宙学中以两种方式出现：一是通过无奇点的爱因斯坦-嘉当反弹，其中费米子的量子自旋阻止收缩；二是提出该反弹后的膨胀可承担宇宙暴胀的作用。本文以建设性的精神重新探讨第二种想法。首先计算其预算：对于具有正压源的Weyssenhoff自旋流体，w∈[0,1]，反弹后的加速窗口跨度为Nₑ=ln[4/(1+3w)]/[3(1−w)]≤(1/3)ln4≈0.46个e折叠，正空间曲率只会缩小该窗口。该机制是合理的；其扭转“燃料”随a⁻⁶稀释，且该机制的有效程度比暴胀所需低两个数量级。随后研究为维持类德西特相扭转所需的条件，在具有非最小耦合的黎曼-嘉当宇宙学中给出两分支答案，其中扭转由耦合而非自旋提供。矢量分支重现了帕拉蒂尼暴胀，在观测上可行；轴分支中展示了由扭转凝聚体维持的精确德西特解：恒定轴扭转f₀、线性高斯-博内耦合，以及通过弗里德曼约束固定的势V₀=6f₀²+(5/2)v²。该解是均匀动力学的吸引子，特征值恰好为−3H。当斜率U′（固定平坦势下随滚动速度减小的函数）降至最小值5/16V₀且凝聚体自动关闭时，该阶段结束；有效理论的一致性将整个过程限定在普朗克尺度附近，约化普朗克单位下H≳0.3。本文在背景层面研究了该分支，其扰动谱仍待研究。
英文摘要
Torsion entered early-universe cosmology twice: through the nonsingular Einstein--Cartan bounce, where the quantum spin of fermions halts the contraction, and through the proposal that the expansion following that bounce could take over the duties of cosmic inflation. We revisit the second idea in a constructive spirit. First we compute its budget: for a Weyssenhoff spin fluid with barotropic source, $w\in\left[0,1\right]$, the accelerated window that follows the bounce spans $N_e=\ln\left[4/\left(1+3w\right)\right]/3\left(1-w\right)\leq\tfrac{1}{3}\ln4\simeq0.46$ e-folds, and positive spatial curvature only shrinks it. The mechanism is sound; its torsional ``fuel'' dilutes as $a^{-6}$, and the engine stops two orders of magnitude short of inflationary needs. We then ask what torsion would need in order to sustain a quasi-de Sitter phase, and give a two-branch answer in Riemann--Cartan cosmology with nonminimal couplings, where torsion is fed by the couplings rather than by spin. The vectorial branch reproduces Palatini inflation, observationally alive. On the axial branch we exhibit an exact de Sitter solution sustained by a torsion condensate: constant axial torsion $f_{0}$, a linear Gauss--Bonnet coupling, and a potential fixed to $V_{0}=6f_{0}^{2}+\tfrac{5}{2}v^{2}$ by the Friedmann constraint. The solution is an attractor of the homogeneous dynamics, with eigenvalue exactly $-3H$. The phase ends when the slope $U^{\prime}$, a decreasing function of the roll speed at fixed flat potential, drifts down to the floor $5/16V_{0}$ and the condensate switches itself off; consistency of the effective theory pins the whole episode near the Planck scale, $H\gtrsim0.3$ in reduced Planck units. We studied this branch at background level; its perturbation spectrum remains open.
Comments13 pages, 1 figure
