Quasinormal modes in pure de Sitter spacetimes

We have studied scalar perturbations as well as fermion perturbations in pure de Sitter spacetimes. For scalar perturbations we have shown that well-defined quasinormal modes in $d$-dimensions can exist provided that the mass of scalar field $m>\frac{d-1}{2l}$. The quasinormal modes of fermion perturbations in three and four dimensional cases have also been investigated. We found that different from other dimensional cases, in the three dimensional pure de Sitter spacetime there is no quasinormal mode for the s-wave. This interesting difference caused by the spacial dimensions is true for both scalar and fermion perturbations.