标题： 分数阶爱因斯坦-高斯-邦特标量场宇宙学 显示英文标题

标题： Fractional Einstein-Gauss-Bonnet scalar field cosmology

摘要： 本文介绍了一种新的理论框架，称为分数阶爱因斯坦-高斯-博内标量场宇宙学，它具有重要的物理意义。通过使用分数阶微积分修改引力作用量积分，我们推导出了修正的弗里德曼方程和修正的克莱因-戈登方程。我们的研究表明了与指数势、高斯-博内项的指数耦合以及对数标量场相关的非平凡解，这些解依赖于两个宇宙学参数$m$和$\alpha_{0}=t_{0}H_{0}$以及分数导数阶数$\mu$。通过采用线性稳定性理论，我们揭示了相空间结构并分析了高斯-博内耦合的动力学效应。在某些平衡点处的尺度行为表明，与高斯-博内标量的几何修正可以模仿修正引力中暗物质部门的行为。 利用宇宙时钟、Ia型超新星、超大质量黑洞阴影以及强引力透镜的数据，我们估算了$m$和$\alpha_{0}$的值，表明该解与晚期加速膨胀一致，其值为$\alpha_0=1.38\pm 0.05$、$m=1.44\pm 0.05$和$\mu=1.48 \pm 0.17$（与$\Omega_{m,0}=0.311\pm 0.016$和$h=0.712\pm 0.007$一致），从而得出宇宙年龄为$t_{0}=19.0\pm 0.7$[Gyr]（在1$\sigma$置信水平下）。 最终，我们获得了由最近的宇宙学数据支持的晚期加速幂律解，并提出了宇宙加速起源的一种替代解释，而非基于 $\Lambda$冷暗物质模型。 我们的研究结果扩展并显著改进了文献中的先前成果，突显了分数微积分在宇宙学中的实际意义。 显示英文摘要

摘要： Our paper introduces a new theoretical framework called the Fractional Einstein--Gauss--Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein--Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss--Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, $m$ and $\alpha_{0}=t_{0}H_{0}$ and the fractional derivative order $\mu$. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss--Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss--Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of $m$ and $\alpha_{0}$, indicating that the solution is consistent with an accelerated expansion at late times with the values $\alpha_0=1.38\pm 0.05$, $m=1.44\pm 0.05$, and $\mu=1.48 \pm 0.17$ (consistent with $\Omega_{m,0}=0.311\pm 0.016$ and $h=0.712\pm 0.007$), resulting in an age of the Universe $t_{0}=19.0\pm 0.7$ [Gyr] at 1$\sigma$ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than $\Lambda$CDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology.