  We present analytic solutions to the Teukolsky equation for massless
perturbations of any spin in the 4-dimensional de Sitter background. The
angular part of the equation fixes the separation constant to a discrete set
and its solution is given by hypergeometric polynomials. For the radial part,
we derive analytic power series solution which is regular at the poles and
determine a transcendental function whose zeros give the characteristic values
of the wave frequency. We study the existence of explicit polynomial solutions
to the radial equation and obtain two classes of singular closed-form
solutions, one with discrete wave frequencies and the other with continuous
frequency spectra.
