  New spherical scalar modes on the expanding part of Sitter spacetime,
eigenfunctions of a conserved Hamiltonian-like operator are found by solving
the Klein-Gordon equation in the appropriate coordinate chart, with the help of
a time evolution picture technique specially developed for spatially flat FLRW
charts. Transition coefficients are computed between these modes and the rest
of the scalar spherical and plane wave modes, either momentum or energy
eigenfunctions on the spatially flat FLRW chart.
