On the covariant gauge $\alpha$ of the linearized gravity in de Sitter spacetime

In previous work [1,2], we studied the linearized gravity with covariant gauge $\beta=2/3$ and $\alpha=5/3$. It was found that the sum of the source and initial contributions reproduces the correct field configuration over the whole de Sitter spacetime. In this paper, we extend this work to generalizing the linearized gravitational field in an arbitrary value of the gauge parameter $\alpha$ but the gauge parameter $\beta$ remains the same.