  The scalar mode functions on the spatially flat FLRW chart of the de Sitter
spacetime are redefined in order to obtain a natural frequencies separation in
the special local charts where the momentum vanishes, called here (natural)
rest frames. This can be done since in such frames the mode functions are
eigenfunctions of the energy operator. Moreover, the most general criteria for
choosing the suitable phase factors of the mode functions able to
simultaneously determine the correct rest and flat limits are established.
These results are compared to the different original choices from the
literature.
  Pacs: 04.62.+v
