Creation of fermions in a two-dimensional de Sitter space via a quantum gravity approach

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 <?CDATA $(1+1)$?> ( 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.