发表机构
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México; Department of Physics, Istanbul Technical University; IKERBASQUE, Basque Foundation for Science; Department of Physics, University of the Basque Country UPV/EHU; EHU Quantum Center, University of the Basque Country UPV/EHU; Department of Electrical-Electronics Engineering, Doğuş University（墨西哥国立自治大学物理科学研究所; 伊斯坦布尔理工大学物理系; 巴斯克科学基金会; 巴斯克大学物理系; 巴斯克大学量子中心; 多古斯大学电气电子工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文重建三种符号切换暗能量模型的标量场实现，评估势正则性与动力学可行性，发现ECDM闭合性良好而SSCDM结构性失败。
AI 中文摘要
现象学上相似的符号切换暗能量历史未必具有可比的标量场实现。我们为三种规定历史重建具有固定动力学符号的最小耦合标量：误差函数模型（ECDM）、紧凑光滑阶跃模型（SSCDM）和阶梯状模型（L$\Lambda$CDM）。连续的负到正能量密度穿越选择幻影分支。ECDM在每个有限红移处产生光滑的在壳势；其在密度零点处的状态方程极点仅为比值奇点。精确的SSCDM具有正则轨迹，但端点势为$C^1$、非$C^2$，满足$V-V_e\propto|\phi-\phi_e|^{4/3}$。其非Lipschitz力允许从冻结平台延迟离开，因此重建的势和平台数据不能唯一生成规定历史。精确的阶梯模型需要分布性动力学应力，在所采用的单场作用量中没有普通经典实现。在条件合成比较中，sigmoid-Gaussian族对ECDM排名最高，广义类轴子族对SSCDM排名最高，尽管拟合的轴子指数$n<1/2$意味着发散的端点力。代表性正则向前解表现出负到正标量密度穿越，且势零点先于密度零点。在闭合性测试中，排名最高的ECDM模板的未重调演化近似跟踪目标，$\max|\Delta\widetilde\Omega_\phi|\simeq0.16$。闭合性对紧凑SSCDM结构性失败：没有具有局部Lipschitz力的势能精确重现其从精确冻结初始数据出发的有限持续时间冻结平台。在将现象学历史解释为标量动力学之前，必须评估场映射的存在性、可逆性和端点正则性。幻影作用量仅用作均匀有效代理。
英文摘要
Phenomenologically similar sign-switching dark-energy histories need not have comparable scalar-field realizations. We reconstruct minimally coupled scalars with fixed kinetic sign for three prescribed histories: the error-function model (ECDM), the compact smooth-step model (SSCDM), and the ladder-like model (L$Λ$CDM). Continuous negative-to-positive density crossings select the phantom branch. ECDM yields a smooth on-shell potential at every finite redshift; its equation-of-state pole at the density zero is only a ratio singularity. Exact SSCDM has a regular trajectory but a $C^1$, non-$C^2$ endpoint potential, $V-V_e\propto|ϕ-ϕ_e|^{4/3}$. Its non-Lipschitz force permits delayed departures from frozen plateaus, so the reconstructed potential and plateau data do not uniquely generate the prescribed history. The exact Ladder requires distributional kinetic stress and has no ordinary classical realization in the adopted one-field action. In conditional synthetic comparisons, the sigmoid--Gaussian family ranks highest for ECDM and the generalized axion-like family for SSCDM, although the fitted axion exponents $n<1/2$ imply a divergent endpoint force. Representative regular forward solutions exhibit negative-to-positive scalar-density crossings, with the potential zero preceding the density zero. In a closure test, unretuned evolution of the top-ranked ECDM template tracks the target approximately, $\max|Δ\widetildeΩ_ϕ|\simeq0.16$. Closure fails structurally for compact SSCDM: no potential with a locally Lipschitz force can reproduce its exact finite-duration frozen plateaus from exactly frozen initial data. Field-map existence, invertibility, and endpoint regularity must be assessed before interpreting a phenomenological history as scalar dynamics. The phantom action is used only as a homogeneous effective proxy.
Comments42 pages, 18 figures and 5 tables
