标题： 用皮埃尔·奥古尔和望远镜阵列数据建模宇宙射线通量在 $\boldsymbol{f(R)}$ 和 $\boldsymbol{f(Q)}$ 引力理论中 显示英文标题

标题： Modelling Cosmic Rays Flux with Pierre Auger and Telescope Array Data in $\boldsymbol{f(R)}$ and $\boldsymbol{f(Q)}$ Theories of Gravity

摘要： 我们研究了磁场和红移对星系际宇宙射线（CRs）传播的影响，分别在修正引力理论（MTG）和替代引力理论（ATG）框架下进行探讨。为此，我们考虑了$f(R)$引力理论和$f(Q)$引力理论。利用这两种MTG和ATG计算CRs的密度增强因子作为磁场和红移的函数。对于这项工作，我们将磁场强度从$1-100$nG 取值，而红移取$0-2.5$。针对这些参数中的每一个，在计算时我们取它们所考虑范围内的$100$个区间。此外，本工作中还考虑了重核混合成分（直至Fe）的增强参数。 Further, we compute the $E^3$ magnified diffusive flux for $150$ sources separated by a distance $d_\text{s}$ for the different cosmological models. For the fitting with observational data from the Pierre Auger Observatory (PAO) and Telescope Array (TA), we parameterized some set that consists of the redshift $z$, the separation distances $d_\text{s}$ between the $150$ sources, and the maximum cutoff energy $E_{\text{max}}$. 对于每种情况，还添加了残差图和$\chi^2$值以检查拟合优度。 在每种情况下都对所考虑的模型进行了比较分析，并且与 CDM 模型一起进行了$\Lambda$的比较。 所考虑的 MTG 和 ATG 模型产生了显著且有趣的结果，其中$f(Q)$模型在拟合 PAO 和 TA 的超高能宇宙射线流量数据时表现出最高的 CR 密度增强和最低的归一化卡方值。 本研究为高能物理、天体物理学和宇宙学之间的联系提供了新的视角。 显示英文摘要

摘要： We investigate the effects of the magnetic field and the redshift on the propagation of galactic and extragalactic cosmic rays (CRs) in a modified theory of gravity (MTG) and an alternative theory of gravity (ATG) framework. For this purpose, we consider the $f(R)$ gravity and the $f(Q)$ gravity theories. We utilise these two MTG and ATG to compute the density enhancement factor of CRs as a function of the magnetic field and the redshift. For this work, we take the magnetic field strength from $1-100$ nG, while $0-2.5$ for the redshift. For each of these parameters, we take $100$ bins within their considered range for the computation. The enhancement parameter for the mixed composition of heavy nuclei up to Fe is also taken into account for this work. Further, we compute the $E^3$ magnified diffusive flux for $150$ sources separated by a distance $d_\text{s}$ for the different cosmological models. For the fitting with observational data from the Pierre Auger Observatory (PAO) and Telescope Array (TA), we parameterized some set that consists of the redshift $z$, the separation distances $d_\text{s}$ between the $150$ sources, and the maximum cutoff energy $E_{\text{max}}$. For each case, a residue plot and $\chi^2$ value are also added to check the goodness of fitting. A comparative analysis of considered models has been performed in each of the cases along with the $\Lambda$CDM model. The considered MTG and ATG models produce notable and fascinating outcomes, with the $f(Q)$ model showing the highest CR density enhancement and the lowest reduced chi-squared value when fitted to PAO and TA data of UHECRs flux. This research provides new perspectives on the connections between high-energy physics, astrophysics, and cosmology.