AI 中文总结
本文在f(Q)引力框架下证明，f(Q)宇宙学中严格曲率中性要求f为常数，弱曲率抵消会导致违反零能量条件的不可行模型，确立了背景层面的曲率中性不可能性。
AI 中文摘要
在f(Q)引力框架下，我们研究是否能让空间曲率在宇宙学背景方程中动态不可见。我们考虑在明确指定的均匀各向同性对称-远平行联络分支上的开放空间截面（k<0）。对于k≠0，无法同时施加重合规范和标准弯曲-FLRW坐标形式。从极小超空间作用量重新推导背景方程，我们表明曲率通过x=H+δ√(-k)/a进入，并在能量和压力方程中以不等权重出现。对于f∈C³((0,∞))，我们证明了一个分支特定的不可能性定理：对每个尺度因子和每个k<0，严格的曲率独立性要求f=常数，其不含度规动能项。STEGR不具有曲率中性，因为其弗里德曼方程保留了通常的3k/a²项贡献。仅对满足δ√(-k)/a=cH的背景施加较弱抵消，必然会产生滑行膨胀，并得到f(Q)=A Q^((c+2)/2)+B，当c=-2时得到f(Q)=A ln Q+B。对于说明性选择c=-3，解变为f=α₁/√Q+β₁。在常规正耦合假设f_Q>0下，所需源违反零能量条件。此外，添加正辐射或无压物质会在足够早的时间迫使出现补偿性负能量分量。因此，弱分支既不具有不变意义上的曲率中性，也不是可行的宇宙学模型。主要结果是背景层面的阻碍本身。微扰稳定性和引力波传播需要单独分析，包括对非平凡仿射联络的微扰，且本工作未确立这些。
英文摘要
In the framework of $f(Q)$ gravity, we investigate whether spatial curvature can be made dynamically invisible in the cosmological background equations. We consider open spatial sections, $k<0$, on an explicitly specified homogeneous and isotropic symmetric-teleparallel connection branch. For $k\neq0$, the coincident gauge cannot be imposed simultaneously with the standard curved-FLRW coordinate form. Re-deriving the background equations from the minisuperspace action, we show that curvature enters through $x=H+δ\sqrt{-k}/a$ and appears with inequivalent weights in the energy and pressure equations. For $f\in C^3((0,\infty))$, we prove a branch-specific no-go theorem: strict curvature independence for every scale factor and every $k<0$ requires $f=\mathrm{const}$, which contains no metric kinetic term. STEGR is not curvature-neutral, since its Friedmann equation retains the usual $3k/a^2$ contribution. A weaker cancellation, imposed only on backgrounds satisfying $δ\sqrt{-k}/a=cH$, necessarily produces a coasting expansion and yields $f(Q)=A Q^{(c+2)/2}+B$, or $f(Q)=A\ln Q+B$ when $c=-2$. For the illustrative choice $c=-3$, the solution becomes $f=α_1/\sqrt Q+β_1$. Under the conventional positive-coupling assumption $f_Q>0$, the required source violates the null energy condition. Moreover, adding positive radiation or pressureless matter forces a compensating negative-energy component at sufficiently early times. The weak branch is therefore neither curvature-neutral in an invariant sense nor a viable cosmological model. The principal result is the background-level obstruction itself. Perturbative stability and gravitational-wave propagation require a separate analysis including perturbations of the nontrivial affine connection and are not established in this work.
Comments15 pages, 2 figures
