We discuss the production process of Dirac particles in a two-dimensional de Sitter geometry via the framework of rainbow gravity from the general relativity and the teleparallel theory perspectives. On this purpose, we find out the exact analytical solutions for the selected space-time model and then conclude that the general relativity and the teleparallel theory versions of the covariant Dirac equation in the (1+1) -dimensional deformed de Sitter space-time have the same exact solutions. In the subsequent step, making use of the explicit form of the Dirac spinor components and the Bogoliubov coefficients, we turn our attention to investigating the density of produced half-spin particles. Finally, we obtain two mathematical solutions for the fermionic energy spectrum.

中文翻译：

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通过量子引力方法在二维德西特空间中创建费米子

我们从广义相对论和远程平行理论的角度，通过彩虹引力的框架，讨论了二维德西特几何中狄拉克粒子的产生过程。为此，我们找出所选时空模型的精确解析解，然后得出结论：广义相对论和远程平行理论版本的协变狄拉克方程 （1+1） 维变形德西特时空具有相同的精确解。在接下来的步骤中，利用狄拉克旋量分量和 Bogoliubov 系数的显式形式，我们将注意力转向研究所产生的半自旋粒子的密度。最后，我们得到了费米子能谱的两个数学解。