AI 中文总结
研究分数引力模型，其中哈勃参数和引力常数因分数重整化群效应动态演化。通过数值框架与多观测数据比较，经贝叶斯分析，\(\mu = 0\)模型可行，能再现晚期加速，为解决\(H_0\)和\(S_8\)张力提供新途径。
AI 中文摘要
我们研究了一个分数引力模型，其中哈勃参数和引力常数由于分数重整化群效应而动态演化。该模型包含一个与随时间变化的\(G\)耦合的标量场，产生分数作用宇宙学的非局部修正。解析和数值解揭示了振荡状态、循环阶段以及对大爆炸核合成和早期宇宙演化有影响的快速变化。开发了一个强大的数值框架来整合正则化系统，并将由此产生的\(H(z)\)演化与来自哈勃参数、重子声学振荡、Ia型超新星、引力透镜和黑洞阴影的观测数据进行比较，从而实现宇宙学量的一致重建。贝叶斯分析表明，\(\mu = 0\)的分数模型是唯一在统计上可行的变体。推断出的哈勃参数在各模型中稳定（\(h\simeq 0.72\)），而分数参数在\(\mu = 0\)的情况下受到更好的约束（\(\alpha = 1.20^{+0.25}_{-0.14}\)，\(\zeta = 0.43^{+0.39}_{-0.29}\)）。动力学部分得出\(m = 30.8^{+28.0}_{-20.9}\)和\(\Gamma = 108.3\pm1.1\)，导致正判别式和确定的弛豫时间尺度\(\tau_{\rm rel}\simeq 9\) Gyr，证实了过阻尼状态。尽管\(\mu = 0\)模型的\(\chi^2_{\min}\)略低于\(\Lambda\)CDM，但由于其参数空间较小，贝叶斯信息准则强烈支持\(\Lambda\)CDM。总体而言，该模型再现了晚期加速并模仿了\(\Lambda\)CDM，同时引入了独特的宇宙学特征。动力学系统分析阐明了稳定性结构和参数依赖性，表明分数非局部修正可能为解决\(H_0\)和\(S_8\)张力提供新途径。
英文摘要
We investigate a fractional gravity model in which both the Hubble parameter and the gravitational constant evolve dynamically due to fractional renormalization-group effects. The model incorporates a scalar field coupled to a time-varying $G$, generating nonlocal corrections characteristic of fractional--action cosmology. Analytical and numerical solutions reveal oscillatory regimes, cyclic phases, and rapid variations with implications for BBN and early-universe evolution. A robust numerical framework is developed to integrate the regularized system and compare the resulting $H(z)$ evolution with observational data from the Hubble parameter, baryon acoustic oscillations, type Ia supernovae, gravitational lensing, and black hole shadows, thereby enabling a consistent reconstruction of cosmographic quantities. A Bayesian analysis shows that the Fractional model with $μ=0$ is the only statistically viable variant. The inferred Hubble parameter is stable across models ($h\simeq 0.72$), while the fractional parameters are significantly better constrained in the $μ=0$ case ($α=1.20^{+0.25}_{-0.14}$, $ζ=0.43^{+0.39}_{-0.29}$). The dynamical sector yields $m=30.8^{+28.0}_{-20.9}$ and $Γ=108.3\pm1.1$, leading to a positive discriminant and a well-determined relaxation timescale $τ_{\rm rel}\simeq 9$ Gyr, confirming an overdamped regime. Although the $μ=0$ model attains a slightly lower $χ^2_{\min}$ than $Λ$CDM, the BIC strongly favors $Λ$CDM due to its smaller parameter space. Overall, the model reproduces late-time acceleration and mimics $Λ$CDM while introducing distinctive cosmographic signatures. The dynamical systems analysis clarifies the stability structure and parameter dependence, indicating that fractional nonlocal corrections may offer new pathways toward addressing the $H_0$ and $S_8$ tensions.
Comments84 pages, 14 compound figures
